diff --git a/head/settings_custom.tex b/head/settings_custom.tex index 24d0612..f8be584 100644 --- a/head/settings_custom.tex +++ b/head/settings_custom.tex @@ -1,41 +1,43 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Thesis Settings % Custom settings % % 2011 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % Use this file for your own custom packages, command-definitions, etc... % % % % % % Packages for references - cleverref must be last % \usepackage{nameref} % \usepackage{hyperref} % \usepackage{cleveref} % \usepackage[shortlabels]{enumitem} % % Reduce spacing in bibliography % \setlength{\bibsep}{0pt plus 0.3ex} % % Allow equations to break between pages % \allowdisplaybreaks % % Penalty for widow and orphan % \widowpenalty=9999 % \clubpenalty=9999 % %Penalty for relation and binary operation breaks in equations % \relpenalty=9999 % \binoppenalty=9999 \usepackage[labelfont=bf]{caption} \usepackage[linesnumbered,lined,boxed,commentsnumbered, ruled]{algorithm2e} 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The red line indicates the AUC value achieved by the true motifs. \textbf {Right} the 50 ROC curves corresponding to each partition. The red lines indicates the true motifs ROC curve. The curves under the diagonal are the cases where the 1st discovered class corresponded to the 2nd true class and vice-versa. For these cases, the AUC is actually the area over the curve.\relax }}{83}{figure.caption.34}} -\newlabel{atac_seq_emseq_auc_roc}{{6.5}{83}{\textbf {Classification performances on simulated data :} \textbf {Left} 50 different data partitions were run using EMSequence. The discovered models were then used to assign a class label to each sequence. These assigned labels were then compared to the true labels using the AUC under the ROC curve. The red line indicates the AUC value achieved by the true motifs. \textbf {Right} the 50 ROC curves corresponding to each partition. The red lines indicates the true motifs ROC curve. 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For the score correlations with matrix\_scan scores, the Spearman correlation was used. Table and legend taken and adapted from \citep {ambrosini_pwmscan:_2018}.\relax }{table.caption.29}{}} +\@writefile{lot}{\contentsline {table}{\numberline {6.1}{\ignorespaces \textbf {Motif scanning software comparison}. The performances of matrix\_scan were assessed by comparing how many of the regions listed by matrix\_scan were also returned by other programs and if the region scores were comparable. For the percentage of overlap with the match list returned by matrix\_scan, the shorter of the two lists always serves as the reference (100\%). For the score correlations with matrix\_scan scores, the Spearman correlation was used. Table and legend taken and adapted from \citep {ambrosini_pwmscan:_2018}.\relax }}{76}{table.caption.35}} +\newlabel{lab_resources_pwmscan_benchmark_table}{{6.1}{76}{\textbf {Motif scanning software comparison}. The performances of matrix\_scan were assessed by comparing how many of the regions listed by matrix\_scan were also returned by other programs and if the region scores were comparable. For the percentage of overlap with the match list returned by matrix\_scan, the shorter of the two lists always serves as the reference (100\%). For the score correlations with matrix\_scan scores, the Spearman correlation was used. Table and legend taken and adapted from \citep {ambrosini_pwmscan:_2018}.\relax }{table.caption.35}{}} \citation{ambrosini_pwmscan:_2018} -\@writefile{toc}{\contentsline {section}{\numberline {5.4}Conclusions}{69}{section.5.4}} +\@writefile{toc}{\contentsline {section}{\numberline {6.4}Conclusions}{77}{section.6.4}} \@setckpt{main/ch_pwmscan}{ -\setcounter{page}{70} +\setcounter{page}{78} \setcounter{equation}{0} \setcounter{enumi}{13} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{0} -\setcounter{chapter}{5} +\setcounter{chapter}{6} \setcounter{section}{4} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{2} \setcounter{table}{1} \setcounter{NAT@ctr}{0} \setcounter{FBcaption@count}{0} \setcounter{ContinuedFloat}{0} \setcounter{KVtest}{0} \setcounter{subfigure}{0} \setcounter{subfigure@save}{0} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{subtable@save}{0} \setcounter{lotdepth}{1} \setcounter{lips@count}{2} \setcounter{lstnumber}{1} \setcounter{Item}{13} \setcounter{Hfootnote}{0} \setcounter{bookmark@seq@number}{0} \setcounter{AM@survey}{0} \setcounter{ttlp@side}{0} \setcounter{myparts}{0} \setcounter{parentequation}{0} \setcounter{AlgoLine}{17} \setcounter{algocfline}{2} \setcounter{algocfproc}{2} \setcounter{algocf}{2} \setcounter{float@type}{8} \setcounter{nlinenum}{0} \setcounter{lstlisting}{0} \setcounter{section@level}{0} } diff --git a/main/ch_smile-seq.aux b/main/ch_smile-seq.aux index 914a5b0..87f8e13 100644 --- a/main/ch_smile-seq.aux +++ b/main/ch_smile-seq.aux @@ -1,85 +1,85 @@ \relax \providecommand\hyper@newdestlabel[2]{} \citation{isakova_smile-seq_2017} \citation{isakova_smile-seq_2017} \citation{isakova_smile-seq_2017} \citation{maerkl_systems_2007} \citation{berger_universal_2009} \citation{zhao_inferring_2009,jolma_multiplexed_2010} \citation{isakova_smile-seq_2017} -\@writefile{toc}{\contentsline {chapter}{\numberline {4}SMiLE-seq data analysis}{55}{chapter.4}} +\@writefile{toc}{\contentsline {chapter}{\numberline {5}SMiLE-seq data analysis}{63}{chapter.5}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{loa}{\addvspace {10\p@ }} -\newlabel{smile_seq}{{4}{55}{SMiLE-seq data analysis}{chapter.4}{}} -\@writefile{toc}{\contentsline {chapter}{SMiLE-seq data analysis}{55}{chapter.4}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.0.1}Introduction}{55}{subsection.4.0.1}} -\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces \textbf {SMiLE-seq pipeline :} \textbf {a} Schematic representation of the experimental setup. A snapshot of three units of the microfluidic device is shown. In vitro transcribed and translated bait TF, target dsDNA, and a nonspecific competitor poly-dIdC are mixed and pipetted in one of the wells of the microfluidic device. The mixtures are then passively pumped in the device (bottom panel). Newly formed TF\IeC {\textendash }DNA complexes are trapped under a flexible polydimethylsiloxane membrane, and unbound molecules as well as molecular complexes are washed away (upper panel). Left, schematic representation of three individual chambers. Right, corresponding snapshots of an individual chamber taken before and after mechanical trapping. \textbf {b} Data processing pipeline. The bound DNA is eluted from all the units of the device simultaneously and collected in one tube. Recovered DNA is amplified and sequenced. The sequencing reads are then demultiplexed, and a seed sequence is identified for each sample. This seed is then used to initialize a probability matrix representing the sequence specificity model for the given TF. The model parameters are then optimized using a Hidden Markov Model-based motif discovery pipeline. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}.\relax }}{56}{figure.caption.24}} -\newlabel{smile_seq_pipeline}{{4.1}{56}{\textbf {SMiLE-seq pipeline :} \textbf {a} Schematic representation of the experimental setup. A snapshot of three units of the microfluidic device is shown. In vitro transcribed and translated bait TF, target dsDNA, and a nonspecific competitor poly-dIdC are mixed and pipetted in one of the wells of the microfluidic device. The mixtures are then passively pumped in the device (bottom panel). Newly formed TF–DNA complexes are trapped under a flexible polydimethylsiloxane membrane, and unbound molecules as well as molecular complexes are washed away (upper panel). Left, schematic representation of three individual chambers. Right, corresponding snapshots of an individual chamber taken before and after mechanical trapping. \textbf {b} Data processing pipeline. The bound DNA is eluted from all the units of the device simultaneously and collected in one tube. Recovered DNA is amplified and sequenced. The sequencing reads are then demultiplexed, and a seed sequence is identified for each sample. This seed is then used to initialize a probability matrix representing the sequence specificity model for the given TF. The model parameters are then optimized using a Hidden Markov Model-based motif discovery pipeline. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}.\relax }{figure.caption.24}{}} +\newlabel{smile_seq}{{5}{63}{SMiLE-seq data analysis}{chapter.5}{}} +\@writefile{toc}{\contentsline {chapter}{SMiLE-seq data analysis}{63}{chapter.5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.0.1}Introduction}{63}{subsection.5.0.1}} +\@writefile{lof}{\contentsline {figure}{\numberline {5.1}{\ignorespaces \textbf {SMiLE-seq pipeline :} \textbf {a} Schematic representation of the experimental setup. A snapshot of three units of the microfluidic device is shown. In vitro transcribed and translated bait TF, target dsDNA, and a nonspecific competitor poly-dIdC are mixed and pipetted in one of the wells of the microfluidic device. The mixtures are then passively pumped in the device (bottom panel). Newly formed TF\IeC {\textendash }DNA complexes are trapped under a flexible polydimethylsiloxane membrane, and unbound molecules as well as molecular complexes are washed away (upper panel). Left, schematic representation of three individual chambers. Right, corresponding snapshots of an individual chamber taken before and after mechanical trapping. \textbf {b} Data processing pipeline. The bound DNA is eluted from all the units of the device simultaneously and collected in one tube. Recovered DNA is amplified and sequenced. The sequencing reads are then demultiplexed, and a seed sequence is identified for each sample. This seed is then used to initialize a probability matrix representing the sequence specificity model for the given TF. The model parameters are then optimized using a Hidden Markov Model-based motif discovery pipeline. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}.\relax }}{64}{figure.caption.30}} +\newlabel{smile_seq_pipeline}{{5.1}{64}{\textbf {SMiLE-seq pipeline :} \textbf {a} Schematic representation of the experimental setup. A snapshot of three units of the microfluidic device is shown. In vitro transcribed and translated bait TF, target dsDNA, and a nonspecific competitor poly-dIdC are mixed and pipetted in one of the wells of the microfluidic device. The mixtures are then passively pumped in the device (bottom panel). Newly formed TF–DNA complexes are trapped under a flexible polydimethylsiloxane membrane, and unbound molecules as well as molecular complexes are washed away (upper panel). Left, schematic representation of three individual chambers. Right, corresponding snapshots of an individual chamber taken before and after mechanical trapping. \textbf {b} Data processing pipeline. The bound DNA is eluted from all the units of the device simultaneously and collected in one tube. Recovered DNA is amplified and sequenced. The sequencing reads are then demultiplexed, and a seed sequence is identified for each sample. This seed is then used to initialize a probability matrix representing the sequence specificity model for the given TF. The model parameters are then optimized using a Hidden Markov Model-based motif discovery pipeline. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}.\relax }{figure.caption.30}{}} \citation{isakova_smile-seq_2017} \citation{isakova_smile-seq_2017} \citation{weirauch_evaluation_2013} -\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces \textbf {Example of a Hidden Markov model :} initial HMM representation with a seed sequence 'ATGCC'. The upper Markov chain models + strand motif containing sequences, the middle one - strand motif containing sequences and the lower zero motif occurrence sequences. The FB, FE, RB and RE positions represents positions in the sequence that occur before and after the binding site on the forward and reverse strand. For these nodes, a self transition exist to allow the binding site to occur at a variable distance from the beginning and the end of the sequence. Once transiting toward the 1st position of the binding site, the next transition is forced toward the 2nd position in the binding site, and so on until the end of the binding site. The + strand and - strand Markov chains emission parameters are paired together (they have the same values), as represented by the grey dashed lines. The transition probabilities in red are not subjected to the Baum-Welch training. Finally, a binding model represented as a probability matrix is composed of the emission probabilities at the binding site positions. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}\relax }}{57}{figure.caption.25}} -\newlabel{smile_seq_hmm}{{4.2}{57}{\textbf {Example of a Hidden Markov model :} initial HMM representation with a seed sequence 'ATGCC'. The upper Markov chain models + strand motif containing sequences, the middle one - strand motif containing sequences and the lower zero motif occurrence sequences. The FB, FE, RB and RE positions represents positions in the sequence that occur before and after the binding site on the forward and reverse strand. For these nodes, a self transition exist to allow the binding site to occur at a variable distance from the beginning and the end of the sequence. Once transiting toward the 1st position of the binding site, the next transition is forced toward the 2nd position in the binding site, and so on until the end of the binding site. The + strand and - strand Markov chains emission parameters are paired together (they have the same values), as represented by the grey dashed lines. The transition probabilities in red are not subjected to the Baum-Welch training. Finally, a binding model represented as a probability matrix is composed of the emission probabilities at the binding site positions. 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Once transiting toward the 1st position of the binding site, the next transition is forced toward the 2nd position in the binding site, and so on until the end of the binding site. The + strand and - strand Markov chains emission parameters are paired together (they have the same values), as represented by the grey dashed lines. The transition probabilities in red are not subjected to the Baum-Welch training. Finally, a binding model represented as a probability matrix is composed of the emission probabilities at the binding site positions. Figure and legend taken and adapted from \citep {isakova_smile-seq_2017}\relax }}{65}{figure.caption.31}} +\newlabel{smile_seq_hmm}{{5.2}{65}{\textbf {Example of a Hidden Markov model :} initial HMM representation with a seed sequence 'ATGCC'. The upper Markov chain models + strand motif containing sequences, the middle one - strand motif containing sequences and the lower zero motif occurrence sequences. The FB, FE, RB and RE positions represents positions in the sequence that occur before and after the binding site on the forward and reverse strand. For these nodes, a self transition exist to allow the binding site to occur at a variable distance from the beginning and the end of the sequence. Once transiting toward the 1st position of the binding site, the next transition is forced toward the 2nd position in the binding site, and so on until the end of the binding site. The + strand and - strand Markov chains emission parameters are paired together (they have the same values), as represented by the grey dashed lines. The transition probabilities in red are not subjected to the Baum-Welch training. Finally, a binding model represented as a probability matrix is composed of the emission probabilities at the binding site positions. 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For each motif, the AUC-ROC values on the 500 top peaks of the ENCODE ChIP-seq data sets for the corresponding TF was computed. The heatmap represents the AUC values computed for each method on the respective ChIP-seq data sets that were selected based on the highest mean AUC values among all five models. \textbf {B} the predictive performances of MAX and YY1 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }}{61}{figure.caption.26}} -\newlabel{smileseq_auc}{{4.3}{61}{\textbf {Predictive power of SMiLE-seq :} \textbf {A} the motifs compared to that of previously reported motifs that are retrievable from the indicated databases. For each motif, the AUC-ROC values on the 500 top peaks of the ENCODE ChIP-seq data sets for the corresponding TF was computed. The heatmap represents the AUC values computed for each method on the respective ChIP-seq data sets that were selected based on the highest mean AUC values among all five models. \textbf {B} the predictive performances of MAX and YY1 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }{figure.caption.26}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.0.5}Conclusions}{62}{subsection.4.0.5}} +\newlabel{smile_seq_algo_auc}{{2}{68}{Binding motif evaluation}{algocfline.2}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Computes the AUC-ROC\relax }}{68}{algocf.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.0.4}Results}{68}{subsection.5.0.4}} +\@writefile{lof}{\contentsline {figure}{\numberline {5.3}{\ignorespaces \textbf {Predictive power of SMiLE-seq :} \textbf {A} the motifs compared to that of previously reported motifs that are retrievable from the indicated databases. For each motif, the AUC-ROC values on the 500 top peaks of the ENCODE ChIP-seq data sets for the corresponding TF was computed. 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The heatmap represents the AUC values computed for each method on the respective ChIP-seq data sets that were selected based on the highest mean AUC values among all five models. \textbf {B} the predictive performances of MAX and YY1 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }{figure.caption.32}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.0.5}Conclusions}{70}{subsection.5.0.5}} \@setckpt{main/ch_smile-seq}{ -\setcounter{page}{63} +\setcounter{page}{71} \setcounter{equation}{1} \setcounter{enumi}{13} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{0} -\setcounter{chapter}{4} +\setcounter{chapter}{5} \setcounter{section}{0} \setcounter{subsection}{5} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{3} \setcounter{table}{0} \setcounter{NAT@ctr}{0} \setcounter{FBcaption@count}{0} \setcounter{ContinuedFloat}{0} \setcounter{KVtest}{0} \setcounter{subfigure}{0} \setcounter{subfigure@save}{0} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{subtable@save}{0} \setcounter{lotdepth}{1} \setcounter{lips@count}{2} \setcounter{lstnumber}{1} \setcounter{Item}{13} \setcounter{Hfootnote}{0} \setcounter{bookmark@seq@number}{0} \setcounter{AM@survey}{0} \setcounter{ttlp@side}{0} \setcounter{myparts}{0} \setcounter{parentequation}{0} \setcounter{AlgoLine}{17} \setcounter{algocfline}{2} \setcounter{algocfproc}{2} \setcounter{algocf}{2} \setcounter{float@type}{8} \setcounter{nlinenum}{0} \setcounter{lstlisting}{0} \setcounter{section@level}{0} } diff --git a/main/ch_spark.aux b/main/ch_spark.aux new file mode 100644 index 0000000..5a8e3e6 --- /dev/null +++ b/main/ch_spark.aux @@ -0,0 +1,89 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\citation{groux_spar-k:_2019} +\citation{kundaje_ubiquitous_2012} +\citation{nair_probabilistic_2014} +\@writefile{toc}{\contentsline {chapter}{\numberline {4}SPar-K}{55}{chapter.4}} +\@writefile{lof}{\addvspace {10\p@ }} +\@writefile{lot}{\addvspace {10\p@ }} +\@writefile{loa}{\addvspace {10\p@ }} +\newlabel{spark}{{4}{55}{SPar-K}{chapter.4}{}} +\@writefile{chapter}{\contentsline {toc}{SPar-K}{55}{chapter.4}} +\@writefile{toc}{\contentsline {section}{\numberline {4.1}Algorithm}{55}{section.4.1}} +\citation{arthur_k-means++:_2007} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}Implementation}{56}{subsection.4.1.1}} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{ambrosini_chip-seq_2016} +\citation{ambrosini_chip-seq_2016} +\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces \textbf {Clustering accuracy using random seeding :} to compare the clustering accuracies of the different methods, several simulated dataset containing 3 classes, different coverages (10, 50 and 100 reads per region indicated as "cov10", "cov50" and "cov100") and noise proportions (no noise, 10\% noise, 50\% noise and 90\% noise indicated as "0.0", "0.1", "0.5" and "0.9") were generated. Each dataset was clustered 50 times with each method. The Adjusted Rand Index (ARI) was computed for each partition. The ARI values are displayed as boxplots. SPar-K and ChIPPartitioning were run allowing flipping and shifting. The ARI was measured on each of the resulting data partitions. For SPar-K, "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. "R" stands for "random" and indicates the ARI values obtained when comparing the true cluster labels with a randomly shuffled version of it, 100 times. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }}{57}{figure.caption.25}} +\newlabel{spark_ari}{{4.2}{57}{\textbf {Clustering accuracy using random seeding :} to compare the clustering accuracies of the different methods, several simulated dataset containing 3 classes, different coverages (10, 50 and 100 reads per region indicated as "cov10", "cov50" and "cov100") and noise proportions (no noise, 10\% noise, 50\% noise and 90\% noise indicated as "0.0", "0.1", "0.5" and "0.9") were generated. Each dataset was clustered 50 times with each method. The Adjusted Rand Index (ARI) was computed for each partition. The ARI values are displayed as boxplots. SPar-K and ChIPPartitioning were run allowing flipping and shifting. The ARI was measured on each of the resulting data partitions. For SPar-K, "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. "R" stands for "random" and indicates the ARI values obtained when comparing the true cluster labels with a randomly shuffled version of it, 100 times. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }{figure.caption.25}{}} +\@writefile{toc}{\contentsline {section}{\numberline {4.2}Results}{57}{section.4.2}} +\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Synthethic datasets : \textbf {A} The class signal densities, as described in section \ref {methods_simulated_data}. \textbf {B} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 0\% noise ($p_{s}$=1, $p_{b}$=0) and \textbf {C} one of the corresponding SPar-K partition, with shifting and flipping. The color ribbons on the side indicate the cluster assignments. \textbf {D} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 90\% noise ($p_{s}$=0.1, $p_{b}$=0.9) and \textbf {E} one of the corresponding SPar-K partition, with shifting and flipping.\relax }}{57}{figure.caption.24}} +\newlabel{spark_simulated_data}{{4.1}{57}{Synthethic datasets : \textbf {A} The class signal densities, as described in section \ref {methods_simulated_data}. \textbf {B} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 0\% noise ($p_{s}$=1, $p_{b}$=0) and \textbf {C} one of the corresponding SPar-K partition, with shifting and flipping. The color ribbons on the side indicate the cluster assignments. \textbf {D} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 90\% noise ($p_{s}$=0.1, $p_{b}$=0.9) and \textbf {E} one of the corresponding SPar-K partition, with shifting and flipping.\relax }{figure.caption.24}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces \textbf {Median SSE :} for the simulated ChIP-seq dataset containing 3 classes, with coverage 100 and no noise, partitioned into 2 to 5 clusters. To judge whether the elbow method could be used to estimate the optimal number of clusters, this dataset was partitioned with SPar-K, allowing flip and shifting, into 2 to 5 clusters, 50 times for each set of parameters. For each number of clusters, the median SSE is shown, +/- 1 standard deviation (bars). \textbf {A} Seeding done at random, \textbf {B} seeding done at random and outlier smoothing \textbf {C} seeding done with the K-means++ method \textbf {D} seeding done with the K-means++ method and outlier smoothing. In all cases, the optimal number of clusters seemed to be 3 (which was the expected value). Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }}{58}{figure.caption.26}} +\newlabel{spark_sse}{{4.3}{58}{\textbf {Median SSE :} for the simulated ChIP-seq dataset containing 3 classes, with coverage 100 and no noise, partitioned into 2 to 5 clusters. To judge whether the elbow method could be used to estimate the optimal number of clusters, this dataset was partitioned with SPar-K, allowing flip and shifting, into 2 to 5 clusters, 50 times for each set of parameters. For each number of clusters, the median SSE is shown, +/- 1 standard deviation (bars). \textbf {A} Seeding done at random, \textbf {B} seeding done at random and outlier smoothing \textbf {C} seeding done with the K-means++ method \textbf {D} seeding done with the K-means++ method and outlier smoothing. In all cases, the optimal number of clusters seemed to be 3 (which was the expected value). Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }{figure.caption.26}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces \textbf {Running times :} to compare the run times of each program, the synthetic dataset with coverage 100 and no noise was partitioned 20 times with each program. The run times (wall clock) in second were measured. For all SPar-K and the regular K-means, the partitions were initialized using a random and K-means++ (indicated as "k++"). For ChIPPartitioning, only a random seeding was used. The partitions were then optimized for 30 iterations at most. For SPar-K and ChIPPartitioning, a shifting of 71 bins and flipping were allowed. For SPar-K, only one thread was used and "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }}{58}{figure.caption.27}} +\newlabel{spark_time}{{4.4}{58}{\textbf {Running times :} to compare the run times of each program, the synthetic dataset with coverage 100 and no noise was partitioned 20 times with each program. The run times (wall clock) in second were measured. For all SPar-K and the regular K-means, the partitions were initialized using a random and K-means++ (indicated as "k++"). For ChIPPartitioning, only a random seeding was used. The partitions were then optimized for 30 iterations at most. For SPar-K and ChIPPartitioning, a shifting of 71 bins and flipping were allowed. For SPar-K, only one thread was used and "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }{figure.caption.27}{}} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\citation{groux_spar-k:_2019} +\@writefile{lof}{\contentsline {figure}{\numberline {4.5}{\ignorespaces Nucleosome occupancy, determined by MNase-seq, in bins of 10bp, +/- 1000bp around 79'957 CTCF binding sites in GM12878 cells. \textbf {A} MNaseI-seq read density around the CTCF binding sites. ChIP-seq peak summits are aligned at position 0. The regions (rows) are ordered according the their resemblance (correlation) to the overall aggregation pattern. \textbf {B} SPar-K data partition. The number of clusters (4) was determined using the elbow method (Supplemental Figure \ref {fig_s06}). The cluster labels are indicated by the color ribbons on the left. Within each cluster, the data have been realigned according to the shift and flip informations returned by SPar-K and the regions have been ordered according the their resemblance (correlation) to the cluster aggregation pattern. Because of the realignment, ChIP-seq peak summits are not anymore aligned at position 0. \textbf {C} Corresponding DNaseI hypersensitivity measured by DNaseI-seq at the same loci and realigned as in B. \textbf {D} CTCF motif occurrences predicted using a motif scan, at the same loci and realigned as in B. Each predicted binding site, +/- 1kb around a peak, is represented as a point. \textbf {E} Transcription start site (TSS) density at the same loci and realigned as in B. \textbf {F} Cluster 1 (red) aggregation profiles. The original peak coordinates were modified accordingly to the shift and flip values returned by SPar-K and the read densities the different data types were measured using ChIP-Cor \citep {ambrosini_chip-seq_2016}. For the TSSs and the transcription initiation (CAGE), only the data mapping on the negative strand were used to monitor transcription firing towards the nucleosome array (towards the left). \textbf {G} Proportions of regions having at least one CTCF motif +/- 1kb (same motifs as in D), for each cluster. \textbf {H} Proportions of regions having at least one TSS +/- 1kb (same TSSs as in E), for each cluster.\relax }}{59}{figure.caption.28}} +\newlabel{spark_ctcf}{{4.5}{59}{Nucleosome occupancy, determined by MNase-seq, in bins of 10bp, +/- 1000bp around 79'957 CTCF binding sites in GM12878 cells. \textbf {A} MNaseI-seq read density around the CTCF binding sites. ChIP-seq peak summits are aligned at position 0. The regions (rows) are ordered according the their resemblance (correlation) to the overall aggregation pattern. \textbf {B} SPar-K data partition. The number of clusters (4) was determined using the elbow method (Supplemental Figure \ref {fig_s06}). The cluster labels are indicated by the color ribbons on the left. Within each cluster, the data have been realigned according to the shift and flip informations returned by SPar-K and the regions have been ordered according the their resemblance (correlation) to the cluster aggregation pattern. Because of the realignment, ChIP-seq peak summits are not anymore aligned at position 0. \textbf {C} Corresponding DNaseI hypersensitivity measured by DNaseI-seq at the same loci and realigned as in B. \textbf {D} CTCF motif occurrences predicted using a motif scan, at the same loci and realigned as in B. Each predicted binding site, +/- 1kb around a peak, is represented as a point. \textbf {E} Transcription start site (TSS) density at the same loci and realigned as in B. \textbf {F} Cluster 1 (red) aggregation profiles. The original peak coordinates were modified accordingly to the shift and flip values returned by SPar-K and the read densities the different data types were measured using ChIP-Cor \citep {ambrosini_chip-seq_2016}. For the TSSs and the transcription initiation (CAGE), only the data mapping on the negative strand were used to monitor transcription firing towards the nucleosome array (towards the left). \textbf {G} Proportions of regions having at least one CTCF motif +/- 1kb (same motifs as in D), for each cluster. \textbf {H} Proportions of regions having at least one TSS +/- 1kb (same TSSs as in E), for each cluster.\relax }{figure.caption.28}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {4.6}{\ignorespaces Partitioning of DNaseI hypersensitivity profiles around SP1 binding sites in K562 cells. The optimal number of clusters was determined using the elbow method. \textbf {A.} Input data based on peak summits provided by ENCODE. \textbf {B.} Same regions clustered, re-aligned and oriented by SPar-K. Clusters 1, 2 and 3 are indicated by colored bars in red, blue, and green, respectively. \textbf {C.} MNase-seq read densities for the same regions, ordered, aligned and oriented as in B. \textbf {D.} Predicted SP1 binding motifs for the same regions, ordered, aligned and oriented as in B. \textbf {E.} Proportion of binding sites within each cluster having a confirmed promoter-associated TSS within +/- 300bp. \textbf {F.} Aggregations profiles for DNase-seq (red), MNase-seq (blue), promoter TSS (green) and CAGE-seq data (violet) for cluster 2 (aligned and oriented as in B). \textbf {G.} Motifs found by MEME-ChIP and Tomtom in the narrow footprints of each cluster. (*) known SP1 interactor, (c) central enrichment. Cluster 2 left and right refer to the left and right footprints seen in \textbf {B}. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }}{60}{figure.caption.29}} +\newlabel{spark_dnase}{{4.6}{60}{Partitioning of DNaseI hypersensitivity profiles around SP1 binding sites in K562 cells. The optimal number of clusters was determined using the elbow method. \textbf {A.} Input data based on peak summits provided by ENCODE. \textbf {B.} Same regions clustered, re-aligned and oriented by SPar-K. Clusters 1, 2 and 3 are indicated by colored bars in red, blue, and green, respectively. \textbf {C.} MNase-seq read densities for the same regions, ordered, aligned and oriented as in B. \textbf {D.} Predicted SP1 binding motifs for the same regions, ordered, aligned and oriented as in B. \textbf {E.} Proportion of binding sites within each cluster having a confirmed promoter-associated TSS within +/- 300bp. \textbf {F.} Aggregations profiles for DNase-seq (red), MNase-seq (blue), promoter TSS (green) and CAGE-seq data (violet) for cluster 2 (aligned and oriented as in B). \textbf {G.} Motifs found by MEME-ChIP and Tomtom in the narrow footprints of each cluster. (*) known SP1 interactor, (c) central enrichment. Cluster 2 left and right refer to the left and right footprints seen in \textbf {B}. Figure and legend taken and adapted from \citep {groux_spar-k:_2019}.\relax }{figure.caption.29}{}} +\citation{groux_spar-k:_2019} +\citation{bailey_meme_2009} +\citation{groux_spar-k:_2019} +\citation{kundaje_ubiquitous_2012} +\@writefile{toc}{\contentsline {section}{\numberline {4.3}Conclusions}{61}{section.4.3}} +\@setckpt{main/ch_spark}{ +\setcounter{page}{62} +\setcounter{equation}{1} +\setcounter{enumi}{13} +\setcounter{enumii}{0} +\setcounter{enumiii}{0} +\setcounter{enumiv}{0} +\setcounter{footnote}{0} +\setcounter{mpfootnote}{0} +\setcounter{part}{0} +\setcounter{chapter}{4} +\setcounter{section}{3} +\setcounter{subsection}{0} +\setcounter{subsubsection}{0} +\setcounter{paragraph}{0} +\setcounter{subparagraph}{0} +\setcounter{figure}{6} +\setcounter{table}{0} +\setcounter{NAT@ctr}{0} +\setcounter{FBcaption@count}{0} +\setcounter{ContinuedFloat}{0} +\setcounter{KVtest}{0} +\setcounter{subfigure}{0} +\setcounter{subfigure@save}{0} +\setcounter{lofdepth}{1} +\setcounter{subtable}{0} +\setcounter{subtable@save}{0} +\setcounter{lotdepth}{1} +\setcounter{lips@count}{2} +\setcounter{lstnumber}{1} +\setcounter{Item}{13} +\setcounter{Hfootnote}{0} +\setcounter{bookmark@seq@number}{0} +\setcounter{AM@survey}{0} +\setcounter{ttlp@side}{0} +\setcounter{myparts}{0} +\setcounter{parentequation}{0} +\setcounter{AlgoLine}{28} +\setcounter{algocfline}{1} +\setcounter{algocfproc}{1} +\setcounter{algocf}{1} +\setcounter{float@type}{8} +\setcounter{nlinenum}{0} +\setcounter{lstlisting}{0} +\setcounter{section@level}{0} +} diff --git a/main/ch_spark.log b/main/ch_spark.log new file mode 100644 index 0000000..d44798c --- /dev/null +++ b/main/ch_spark.log @@ -0,0 +1,6452 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.12.12) 16 DEC 2019 16:30 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**ch_spark.tex +(./ch_spark.tex +LaTeX2e <2017-04-15> +Babel <3.18> and hyphenation patterns for 84 language(s) loaded. +! 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+! Undefined control sequence. +l.9 ...an adapted from the original article \citep + {groux_spar-k:_2019}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +! Missing $ inserted. + + $ +l.9 ...ted from the original article \citep{groux_ + spar-k:_2019}. +I've inserted a begin-math/end-math symbol since I think +you left one out. 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Undefined control sequence. +l.11 ... relationship. However, as noted in \citep + {kundaje_ubiquitous_2012},... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no k in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no e in font nullfont! +! Missing $ inserted. + + $ +l.11 ...ship. However, as noted in \citep{kundaje_ + ubiquitous_2012}, chromati... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.11 ...s noted in \citep{kundaje_ubiquitous_2012} + , chromatin patterns tend ... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.12 ...es, CAGT and ChIP-Partitioning, see \citep + {nair_probabilistic_2014} ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.13 + +I've inserted a begin-math/end-math symbol since I think +you left one out. 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Undefined control sequence. +l.14 \section + {Algorithm} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.14 \section{A + lgorithm} +You're in trouble here. 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Undefined control sequence. +l.17 ...r is summarized a vector of length $L\geqW + $ that contains the averag... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.20 T + he input data are stored as a $N$ rows and $L$ columns matrix $R$. The... + +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.23 S + Par-K optimizes the alignments by minimizing the sum of squares errors... + +You're in trouble here. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.26 T + he distance between any two regions is computed a modified correlation... + +You're in trouble here. 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+Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 1 in font nullfont! 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+Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.26 ...st and vice-versa), resulting in $2\timesS + ^{2}$ values. Eventually, ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +! Undefined control sequence. +l.26 ...e $S^{2}$ (without flipping) or $2\timesS + ^{2}$ (with flipping) valu... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ( in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 26--27 +[] + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (29.34724pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 W$$L$$S$$\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (15.24301pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 s \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (38.37494pt too wide) in paragraph at lines 26--27 +\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2\OML/cmm/m/it/10 ; :::; S$ + + [] + + +Overfull \hbox (11.19444pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 S[]$ + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 26--27 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (47.8195pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 cor\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[]; Y[]\OT1/cmr/m/n/10 ) +$ + [] + + +Overfull \hbox (11.61401pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 X[]$ + [] + + +Overfull \hbox (10.01912pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (22.02443pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 i; j \OMS/cmsy/m/n/10 2 + [] + + +Overfull \hbox (4.6875pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 s$ + [] + + +Overfull \hbox (11.19444pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 S[]$ + [] + + +Overfull \hbox (10.01912pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (10.01912pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (9.48615pt too wide) in paragraph at lines 26--27 +\OT1/cmr/m/n/10 2[]$ + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (11.19444pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 S[]$ + [] + + +Overfull \hbox (9.48615pt too wide) in paragraph at lines 26--27 +\OT1/cmr/m/n/10 2[]$ + [] + + +Overfull \hbox (3.44513pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 i$ + [] + + +Overfull \hbox (4.69049pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 j$ + [] + + +Overfull \hbox (10.01912pt too wide) in paragraph at lines 26--27 +\OML/cmm/m/it/10 Y[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 S + Par-K is initialized by choosing $K$ regions to become the initial clu... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.29 ...ng the K-means++ sampling procedure \citep + {arthur_k-means++:_2007}. ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +! Missing $ inserted. + + $ +l.29 ...-means++ sampling procedure \citep{arthur_ + k-means++:_2007}. Then, ea... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.29 ...g procedure \citep{arthur_k-means++:_2007} + . Then, each regions is al... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +Missing character: There is no N in font nullfont! +! Missing $ inserted. + + $ +l.30 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 29--30 +[] + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 29--30 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 29--30 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (12.69797pt too wide) in paragraph at lines 29--30 +[] \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (37.18994pt too wide) in paragraph at lines 29--30 +\OML/cmm/m/it/10 means \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (17.81943pt too wide) in paragraph at lines 29--30 +\OT1/cmr/m/n/10 + :[] + [] + + +Overfull \hbox (1160.70155pt too wide) in paragraph at lines 29--30 +\OT1/cmr/m/n/10 007\OML/cmm/m/it/10 :Then; eachregionsisalignedagainsteachclust +eraggregationanassignedtotheclustertowhichithasthesmallestdistancewith:Onceall$ +$regionshavebeenalignedtoacluster; theclusteraggregationsareupdatedbycomputedth +eaveragesignalateachpositioninthealignment:$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.31 T + his procedure and is then iteratively repeated until i) reaching the m... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.40 E + ach of the $K$ cluster is represented by an aggregation of length $L$ ... + +You're in trouble here. 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Undefined control sequence. +l.40 ...ation of length $L$ (remember that $L\geqW + $). +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 40--41 +[] + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (3.44513pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 i$ + [] + + +Overfull \hbox (4.69049pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 j$ + [] + + +Overfull \hbox (10.83334pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 W$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 40--41 +\OML/cmm/m/it/10 L$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 E + ach of the $K$ cluster is an alignment of regions slices of length $W$... + +You're in trouble here. 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Undefined control sequence. +l.42 ...$ against an aggregation of length $L\geqW + $. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 42--43 +[] + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 42--43 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (10.83334pt too wide) in paragraph at lines 42--43 +\OML/cmm/m/it/10 W$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 42--43 +\OML/cmm/m/it/10 L$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. + \includegraphics + [scale=0.4]{images/ch_lab_resources/spark_figure... +l.51 ...mages/ch_lab_resources/spark_figure1.pdf}} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.51 ...mages/ch_lab_resources/spark_figure1.pdf}} + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. + .../ch_lab_resources/spark_figure1.pdf} + +l.51 ...mages/ch_lab_resources/spark_figure1.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +\centerline #1->\@@line {\hss #1\hss } + +l.51 ...mages/ch_lab_resources/spark_figure1.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.52 \caption + {Partitioning of DNaseI hypersensitivity profiles around SP1 bi... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Undefined control sequence. +l.53 ...e and legend taken and adapted from \citep + {groux_spar-k:_2019}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.55 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.55 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.55 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.55 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Undefined control sequence. +l.58 \subsection + {Methods} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.58 \subsection{M + ethods} +You're in trouble here. 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+Missing character: There is no a in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! 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+Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.62 ... in Figure \ref{lab_resources_spark_dnase} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 62. + +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 58--63 +[] + [] + + +Overfull \hbox (9.12497pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 N$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (9.12497pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 N$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (32.12503pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 W$$L$$S \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 58--63 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 58--63 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 58--63 +[] + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.65 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. + \includegraphics + [scale=0.4]{images/ch_lab_resources/spark_supple... +l.66 ...resources/spark_supplemental_figure2.pdf}} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.66 ...resources/spark_supplemental_figure2.pdf}} + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. + ...rces/spark_supplemental_figure2.pdf} + +l.66 ...resources/spark_supplemental_figure2.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +\centerline #1->\@@line {\hss #1\hss } + +l.66 ...resources/spark_supplemental_figure2.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.67 \caption + {\textbf{Clustering accuracy using random seeding :} to compare... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Undefined control sequence. +l.68 ...e and legend taken and adapted from \citep + {groux_spar-k:_2019}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.70 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.70 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.70 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.70 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.73 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. + \includegraphics + [scale=0.4]{images/ch_lab_resources/spark_supple... +l.74 ...resources/spark_supplemental_figure4.pdf}} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.74 ...resources/spark_supplemental_figure4.pdf}} + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. + ...rces/spark_supplemental_figure4.pdf} + +l.74 ...resources/spark_supplemental_figure4.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +\centerline #1->\@@line {\hss #1\hss } + +l.74 ...resources/spark_supplemental_figure4.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.75 \caption + {\textbf{Median SSE :} for the simulated ChIP-seq dataset conta... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Undefined control sequence. +l.76 ...e and legend taken and adapted from \citep + {groux_spar-k:_2019}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.78 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.78 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.78 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.78 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.81 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. + \includegraphics + [scale=0.4]{images/ch_lab_resources/spark_supple... +l.82 ...resources/spark_supplemental_figure5.pdf}} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.82 ...resources/spark_supplemental_figure5.pdf}} + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. + ...rces/spark_supplemental_figure5.pdf} + +l.82 ...resources/spark_supplemental_figure5.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +\centerline #1->\@@line {\hss #1\hss } + +l.82 ...resources/spark_supplemental_figure5.pdf}} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.83 \caption + {\textbf{Running times :} to compare the run times of each prog... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Undefined control sequence. +l.84 ...e and legend taken and adapted from \citep + {groux_spar-k:_2019}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.86 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.86 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.86 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.86 \end{figure} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Undefined control sequence. +l.89 \subsection + {Results} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.89 \subsection{R + esults} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! 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+Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.90 ...asets (see Supplemental Figure 1 in \citep + {groux_spar-k:_2019}) exhi... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +! Missing $ inserted. + + $ +l.90 ...see Supplemental Figure 1 in \citep{groux_ + spar-k:_2019}) exhibiting ... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.90 ...tal Figure 1 in \citep{groux_spar-k:_2019} + ) exhibiting properties th... +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. + ..._resources_spark_ari' on page \thepage + \space undefined\on@line . +l.90 ... (see Figure \ref{lab_resources_spark_ari} + and Supplemental Figure 3... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_ari' on page undefined on input +line 90. + +! Undefined control sequence. +l.90 ...k_ari} and Supplemental Figure 3 in \citep + {groux_spar-k:_2019}) and ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. + ..._resources_spark_sse' on page \thepage + \space undefined\on@line . +l.90 ...thod (Figure \ref{lab_resources_spark_sse} + ). As expected, regular K-... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_sse' on page undefined on input +line 90. + +! Undefined control sequence. + ...resources_spark_time' on page \thepage + \space undefined\on@line . +l.90 ... 20 (Figure \ref{lab_resources_spark_time} + ).\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_time' on page undefined on input + line 90. + +Missing character: There is no K in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 3 in font nullfont! +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ...ls (Figure \ref{lab_resources_spark_dnase} + A). The results revealed t... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ...rs (Figure \ref{lab_resources_spark_dnase} + B). To validate these foot... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ...es (Figure \ref{lab_resources_spark_dnase} + C) and SP1 binding motifs ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ...fs (Figure \ref{lab_resources_spark_dnase} + D), which was indeed the c... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ... in Figure \ref{lab_resources_spark_dnase} + B with MEME-ChIP and Tomto... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. +l.91 ...k_dnase}B with MEME-ChIP and Tomtom \citep + {bailey_meme_2009} discove... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.91 ...fs (Figure \ref{lab_resources_spark_dnase} + G) the latter two reported... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 91. + +! Undefined control sequence. + ...esources_spark_dnase' on page \thepage + \space undefined\on@line . +l.92 ...gs (Figure \ref{lab_resources_spark_dnase} + E and F). Finally, the sym... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `lab_resources_spark_dnase' on page undefined on inpu +t line 92. + +\citation{groux_spar-k:_2019} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.93 ...ntal Figure 8 in \cite{groux_spar-k:_2019} + ). Overall, the results co... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `groux_spar-k:_2019' on page undefined on input line 9 +3. + +! Undefined control sequence. +l.93 ...s confirm observations published by \citep + {kundaje_ubiquitous_2012}.... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.94 + +I've inserted a begin-math/end-math symbol since I think +you left one out. 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theresultsconfirmobservationspublishedby[]:Strongnucleosomearraysbecamevis +ibleinallclassesafterrealignment; withthreeoutoffourshowingstrongasymmetryinadd +ition:$ + [] + +! 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Emergency stop. +<*> ch_spark.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 18 strings out of 492982 + 344 string characters out of 6134895 + 73361 words of memory out of 5000000 + 3683 multiletter control sequences out of 15000+600000 + 3948 words of font info for 15 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 18i,5n,21p,1137b,104s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/main/ch_spark.tex b/main/ch_spark.tex index a8a889c..fab7427 100644 --- a/main/ch_spark.tex +++ b/main/ch_spark.tex @@ -1,67 +1,119 @@ \cleardoublepage \chapter{SPar-K} \label{spark} \markboth{SPar-K}{SPar-K} \addcontentsline{chapter}{toc}{SPar-K} -\section{SPar-K} +This chapter describes SPar-K (Signal Partitioning with K-means), a modification of the K-means algorithm to cluster genomic regions based on their chromatin organization, defined by by their sequencing profiles. -This section describes SPar-K (Signal Partitioning with K-means), a modification of the K-means algorithm to cluster genomic regions based on their chromatin organization, defined by by their sequencing profiles. +I developed, implemented and benchmark this algorithm and produced all the figures that are shown in this chapter. The content of this section is taken an adapted from the original article \citep{groux_spar-k:_2019}. -My contribution to this work is major. I developed the algorithm, implemented it and run all the benchmark and other analyses. +Due to the wealth of sequencing data, it is common to analyze positional correlations between chromatin features, e.g. the position of nucleosomes (revealed by MNase-seq) relative to transcription factor binding regions (mapped by ChIP-seq) in order to shed light on their functional relationship. However, as noted in \citep{kundaje_ubiquitous_2012}, chromatin patterns tend to be heterogeneous and often asymmetric. Furthermore, limited mapping precision leading to moderate misalignment between functionally equivalent regions can also obscure a chromatin pattern. -The content of this section is taken an adapted from the original article \citep{groux_spar-k:_2019}. I produced all the figures presented in this section. +Several methods and software have been developed for discovering chromatin pattern by clustering and/or realignment of signal profiles for genomic regions, including ChromaSig, CATCHProfiles, CAGT and ChIP-Partitioning, see \citep{nair_probabilistic_2014} and references therein. All of these programs have some limitations. Some do not realign, others are restricted to count data or lack an efficient implementation. To fill this gap, I developed SPar-K (Signal Partitioning with K-means). -\subsection{Introduction} -The sequence-specific binding of transcription factors (TFs) to target sites and the associated changes in chromatin state are considered key events in gene regulatory processes that turn on or off genes. The advent of powerful assays to characterize chromatin features genome-wide (e.g. ChIP-seq, DNase-seq, MNase-seq) and the large-scale application of these technologies to many cell types by consortia such as ENCODE \citep{consortium_integrated_2012} have created a wealth of data. To gain knowledge from such data, it is common to analyze positional correlations between chromatin features, e.g. the position of nucleosomes (revealed by MNase-seq) relative to transcription factor binding regions (mapped by ChIP-seq). However, as noted in \citep{kundaje_ubiquitous_2012}, chromatin patterns tend to be heterogeneous and often asymmetric. The latter is a problem if the orientation of a given functional region is not defined by experiments. Furthermore, limited mapping precision leading to moderate misalignment between functionally equivalent regions can also obscure a chromatin pattern.\\ -Several methods and software tools have been developed for discovering chromatin pattern by clustering and/or realignment of signal profiles for genomic regions, including ChromaSig, CATCHProfiles, CAGT and ChIP-Partitioning, see \citep{nair_probabilistic_2014} and references therein. All of these programs have some limitations. Some do not realign, others are restricted to count data or lack an efficient implementation. To fill this gap, we developed SPar-K (Signal Partitioning with K-means). +\section{Algorithm} + +% summary +SPar-K algorithm (Algorithm \ref{algo_spark}) is a modified version of the regular K-means algorithm during which a set of $N$ regions of size $L$ are partitioned into $K$ clusters, using an iterative optimization procedure. Each cluster is composed of an alignment of regions sub-parts of length $W$ assigned to this cluster and the cluster is summarized a vector of length $L \geq W$ that contains the average signal at each position in the alignment. + +% input +The input data are stored as a $N$ rows and $L$ columns matrix $R$. The signal resolution may be at single-base or at a larger bin size. The regions are typically defined by relative positions to an anchor point, e.g. a ChIP-seq peak summit. If the signal is noisy, a data smoothing step can be undertaken to average out outlier values (Algorithm \ref{algo_smooth_outliers}) and ease the partitioning procedure. + +% objective function +SPar-K optimizes the alignments by minimizing the sum of squares errors. That is, the sum of the squares distances of each point to the cluster aggregation they are assigned to. + +% distances +The distance between any two regions is computed a modified correlation distance. Let us assume two regions $X$ and $Y$ of length $L$ and a shifting freedom $S$. Consequently, $X$ and $Y$ will be sub-divided in $S$ slices of length $W$=$L-S-1$ starting at all possible offsets $s=1,2,...,S$. All $S^{2}$ pairwise comparisons between any slice of $X$ and $Y$ are computed using $1-cor(X_{i},Y_{j})$ where $X_{i}$ and $Y_{j}$ are the slices starting at offsets $i,j \in s$. If flipping is allowed, another set of $S^{2}$ comparisons is performed by flipping $Y_{j}$ (that is, the 1st position in $Y_{j}$ becomes the last and vice-versa), resulting in $2 \times S^{2}$ values. Eventually, the distance between $X$ and $Y$ is the minimum of the $S^{2}$ (without flipping) or $2 \times S^{2}$ (with flipping) values. For each distance, the indices $i$ and $j$ and whether $Y_{j}$ was flipped in the best comparison are remembered. The naive algorithm for this step is $\Theta(S^{2} \times W)$ in time however I could design a faster algorithm which is $\Theta(S \times W)$ by using a dynamic programming approach (see algorithm \ref{algo_distance_fast}). + +% iteration walk-through +SPar-K is initialized by choosing $K$ regions to become the initial cluster aggregations of length $L$ either i) randomly (Algorithm \ref{algo_seed_random}) or ii) using the K-means++ sampling procedure (Algorithm \ref{algo_seed_kmeans++}, \cite{arthur_k-means++:_2007}). Then, each regions is aligned against each cluster aggregation an assigned to the cluster to which it has the smallest distance with. Once all $N$ regions have been aligned to a cluster, the cluster aggregations are updated by computed the average signal at each position in the alignment. + +This procedure and is then iteratively repeated until i) reaching the maximum number of iterations or ii) achieving convergence. -% figure 1 from article -\begin{figure} -\centerline{\includegraphics[scale=0.4]{images/ch_lab_resources/spark_figure1.pdf}} -\caption{Partitioning of DNaseI hypersensitivity profiles around SP1 binding sites in K562 cells. The optimal number of clusters was determined using the elbow method. \textbf{A.} Input data based on peak summits provided by ENCODE. \textbf{B.} Same regions clustered, re-aligned and oriented by SPar-K. Clusters 1, 2 and 3 are indicated by colored bars in red, blue, and green, respectively. \textbf{C.} MNase-seq read densities for the same regions, ordered, aligned and oriented as in B. \textbf{D.} Predicted SP1 binding motifs for the same regions, ordered, aligned and oriented as in B. \textbf{E.} Proportion of binding sites within each cluster having a confirmed promoter-associated TSS within +/- 300bp. \textbf{F.} Aggregations profiles for DNase-seq (red), MNase-seq (blue), promoter TSS (green) and CAGE-seq data (violet) for cluster 2 (aligned and oriented as in B). \textbf{G.} Motifs found by MEME-ChIP and Tomtom in the narrow footprints of each cluster. (*) known SP1 interactor, (c) central enrichment. Cluster 2 left and right refer to the left and right footprints seen in \textbf{B}. -Figure and legend taken and adapted from \citep{groux_spar-k:_2019}.} -\label{lab_resources_spark_dnase} -\end{figure} +\subsection{Implementation} +SPar-K algorithm has been implemented as a stand-alone, fully multithreaded, C++ program. Regarding the parallellization, the computations at each step are independent of each other, leading to an ”embarrassingly parallel” situation. Thus, at each step, the computations are split into equal amounts and distributed over a pool of worker threads. Eventually, the program returns a table listing for each region the cluster assignment, the shift state and the orientation. The software distribution also includes R scripts for visualizing the data as heatmaps as shown in Figure \ref{spark_dnase}. The software source code is available from Github \url{https://github.com/romaingroux/SPar-K} and as Docker container \url{https://hub.docker.com/r/rgroux/spar-k}. -\subsection{Methods} -SPar-K is a modified K-means algorithm which iteratively partitions, aligns and orients a set of genomic regions based on their signal density profiles obtained by a chromatin profiling assay (or in some other way). SPar-K is implemented as a stand-alone, fully multithreaded, C++ program. A brief description of its overall design follows. Details can be found in the Supplementary Material where all the algorithms are described.\\ -Input data are the signal over $N$ regions of length $L$ stored as a $N$ rows and $L$ columns matrix. The signal resolution may be at single-base or at a larger bin size. The regions are typically defined by relative positions to an anchor point, e.g. a ChIP-seq peak summit.\\ -The user sets via command-line options the number of clusters to find $K$, the shifting freedom $S$, whether flipping is allowed, the maximum number of iterations, whether outlier smoothing should be performed, the seeding strategy, and optionally a seed for the random number generator. The shifting freedom is specified as the maximal number of positions two regions may be shifted relative to each other ($S$), or pattern width ($W$=$L$-$S-1$). The partitioning is initialized by choosing $K$ rows from the input matrix according to the specified seeding strategy. These regions define the initial class centers (signal profiles). During iterative optimization, each region is compared to the current class centers in all possible alignments (shifting states) and orientations and assigned to the closest one in terms of correlation distance. The class centers are then updated by aggregation of the optimally aligned regions of its members. The process stops after a convergence criterion or the maximal number of iterations is reached.\\ -The program returns a table listing for each region the cluster assignment, the shift state and the orientation. The software distribution includes R scripts for visualizing the data as heatmaps as shown in Figure \ref{lab_resources_spark_dnase}. +\section{Results} + +\begin{figure}[H] + \centerline{\includegraphics[scale=0.4]{images/ch_spark/supplemental_figure1.pdf}} + \caption{Synthethic datasets : \textbf{A} The class signal densities, as described in section \ref{methods_simulated_data}. \textbf{B} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 0\% noise ($p_{s}$=1, $p_{b}$=0) and \textbf{C} one of the corresponding SPar-K partition, with shifting and flipping. The color ribbons on the side indicate the cluster assignments. \textbf{D} A synthetic dataset with a mean coverage of a 100 reads per region in average ($c$=100) and 90\% noise ($p_{s}$=0.1, $p_{b}$=0.9) and \textbf{E} one of the corresponding SPar-K partition, with shifting and flipping.}. + \label{spark_simulated_data} +\end{figure} % supplemental figure 2 from article \begin{figure} -\centerline{\includegraphics[scale=0.4]{images/ch_lab_resources/spark_supplemental_figure2.pdf}} +\centerline{\includegraphics[scale=0.4]{images/ch_spark/spark_supplemental_figure2.pdf}} \caption{\textbf{Clustering accuracy using random seeding :} to compare the clustering accuracies of the different methods, several simulated dataset containing 3 classes, different coverages (10, 50 and 100 reads per region indicated as "cov10", "cov50" and "cov100") and noise proportions (no noise, 10\% noise, 50\% noise and 90\% noise indicated as "0.0", "0.1", "0.5" and "0.9") were generated. Each dataset was clustered 50 times with each method. The Adjusted Rand Index (ARI) was computed for each partition. The ARI values are displayed as boxplots. SPar-K and ChIPPartitioning were run allowing flipping and shifting. The ARI was measured on each of the resulting data partitions. For SPar-K, "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. "R" stands for "random" and indicates the ARI values obtained when comparing the true cluster labels with a randomly shuffled version of it, 100 times. Figure and legend taken and adapted from \citep{groux_spar-k:_2019}.} -\label{lab_resources_spark_ari} +\label{spark_ari} \end{figure} % supplemental figure 4 from article \begin{figure} -\centerline{\includegraphics[scale=0.4]{images/ch_lab_resources/spark_supplemental_figure4.pdf}} +\centerline{\includegraphics[scale=0.4]{images/ch_spark/spark_supplemental_figure4.pdf}} \caption{\textbf{Median SSE :} for the simulated ChIP-seq dataset containing 3 classes, with coverage 100 and no noise, partitioned into 2 to 5 clusters. To judge whether the elbow method could be used to estimate the optimal number of clusters, this dataset was partitioned with SPar-K, allowing flip and shifting, into 2 to 5 clusters, 50 times for each set of parameters. For each number of clusters, the median SSE is shown, +/- 1 standard deviation (bars). \textbf{A} Seeding done at random, \textbf{B} seeding done at random and outlier smoothing \textbf{C} seeding done with the K-means++ method \textbf{D} seeding done with the K-means++ method and outlier smoothing. In all cases, the optimal number of clusters seemed to be 3 (which was the expected value). Figure and legend taken and adapted from \citep{groux_spar-k:_2019}.} -\label{lab_resources_spark_sse} +\label{spark_sse} \end{figure} % supplemental figure 4 from article \begin{figure} -\centerline{\includegraphics[scale=0.4]{images/ch_lab_resources/spark_supplemental_figure5.pdf}} +\centerline{\includegraphics[scale=0.4]{images/ch_spark/spark_supplemental_figure5.pdf}} \caption{\textbf{Running times :} to compare the run times of each program, the synthetic dataset with coverage 100 and no noise was partitioned 20 times with each program. The run times (wall clock) in second were measured. For all SPar-K and the regular K-means, the partitions were initialized using a random and K-means++ (indicated as "k++"). For ChIPPartitioning, only a random seeding was used. The partitions were then optimized for 30 iterations at most. For SPar-K and ChIPPartitioning, a shifting of 71 bins and flipping were allowed. For SPar-K, only one thread was used and "smooth" indicates outlier smoothing. For the regular K-means, "eucl." and "corr." refer to the euclidean and correlation distances. Figure and legend taken and adapted from \citep{groux_spar-k:_2019}.} -\label{lab_resources_spark_time} +\label{spark_time} \end{figure} +\begin{figure}[H] + \centerline{\includegraphics[scale=0.4]{images/ch_spark/supplemental_figure8.pdf}} + \caption{Nucleosome occupancy, determined by MNase-seq, in bins of 10bp, +/- 1000bp around 79'957 CTCF binding sites in GM12878 cells. \textbf{A} MNaseI-seq read density around the CTCF binding sites. ChIP-seq peak summits are aligned at position 0. The regions (rows) are ordered according the their resemblance (correlation) to the overall aggregation pattern. \textbf{B} SPar-K data partition. The number of clusters (4) was determined using the elbow method (Supplemental Figure \ref{fig_s06}). The cluster labels are indicated by the color ribbons on the left. Within each cluster, the data have been realigned according to the shift and flip informations returned by SPar-K and the regions have been ordered according the their resemblance (correlation) to the cluster aggregation pattern. Because of the realignment, ChIP-seq peak summits are not anymore aligned at position 0. \textbf{C} Corresponding DNaseI hypersensitivity measured by DNaseI-seq at the same loci and realigned as in B. \textbf{D} CTCF motif occurrences predicted using a motif scan, at the same loci and realigned as in B. Each predicted binding site, +/- 1kb around a peak, is represented as a point. \textbf{E} Transcription start site (TSS) density at the same loci and realigned as in B. \textbf{F} Cluster 1 (red) aggregation profiles. The original peak coordinates were modified accordingly to the shift and flip values returned by SPar-K and the read densities the different data types were measured using ChIP-Cor \citep{ambrosini_chip-seq_2016}. For the TSSs and the transcription initiation (CAGE), only the data mapping on the negative strand were used to monitor transcription firing towards the nucleosome array (towards the left). \textbf{G} Proportions of regions having at least one CTCF motif +/- 1kb (same motifs as in D), for each cluster. \textbf{H} Proportions of regions having at least one TSS +/- 1kb (same TSSs as in E), for each cluster.} + \label{spark_ctcf} +\end{figure} -\subsection{Results} -First we compared SPar-K, regular K-means and ChIP-partitioning on synthetic datasets (see Supplemental Figure 1 in \citep{groux_spar-k:_2019}) exhibiting properties that are plausible for ChIP-seq profiles for genomic regions: count vectors, 3 classes with different shapes, limited misalignment, random orientation and various amounts of background noise. Performance was assessed by the Adjusted Rand index (see Figure \ref{lab_resources_spark_ari} and Supplemental Figure 3 in \citep{groux_spar-k:_2019}) and the optimal number of classes was estimated by the elbow method (Figure \ref{lab_resources_spark_sse}). As expected, regular K-means performed poorly. On the contrary, SPar-K was equally accurate as ChIP-Partitioning except for the lowest coverage class. Considering speed, Spar-K outperformed ChIP-partitioning by a factor of at least 20 (Figure \ref{lab_resources_spark_time}).\\ -We applied SPar-K with $K=3$ to DNaseI accessibility profiles (2bp resolution) around 7'206 ChIP-seq SP1-binding peaks (+/-300bp relative to peak summit) in K562 cells (Figure \ref{lab_resources_spark_dnase}A). The results revealed the presence of clear footprints in all the clusters (Figure \ref{lab_resources_spark_dnase}B). To validate these footprints, we checked whether they are consistent with to location of nucleosomes (Figure \ref{lab_resources_spark_dnase}C) and SP1 binding motifs (Figure \ref{lab_resources_spark_dnase}D), which was indeed the case. De novo motif analysis of the narrow footprints seen in Figure \ref{lab_resources_spark_dnase}B with MEME-ChIP and Tomtom \citep{bailey_meme_2009} discovered SP1-related, NFYA/B and GATA motifs (Figure \ref{lab_resources_spark_dnase}G) the latter two reportedly being interaction partners of SP1. Taken together, these results suggest that SPar-K is able to precisely refocus initially misaligned DNaseI profiles around SP1 binding sites.\\ -The partitioning of SP1 binding regions reveals distinct chromatin landscapes. Cluster 1 (red) groups binding sites lying between two closely spaced nucleosomes. Cluster 2 (blue) shows strong asymmetry suggestive of promoter regions, an interpretation supported by the presence of promoter-associated transcription starts sites (TSSs) and CAGE tags (Figure \ref{lab_resources_spark_dnase}E and F). Finally, the symmetrical cluster 3 (green) contains binding sites located on large nucleosome-free regions reminiscent of enhancer regions.\\ -As a second example, we ran the same type of analysis on nucleosome profiles around CTCF binding sites (see Supplemental Figure 8 in \cite{groux_spar-k:_2019}). Overall, the results confirm observations published by \citep{kundaje_ubiquitous_2012}. Strong nucleosome arrays became visible in all classes after realignment, with three out of four showing strong asymmetry in addition. +% figure 1 from article +\begin{figure} +\centerline{\includegraphics[scale=0.4]{images/ch_spark/spark_figure1.pdf}} +\caption{Partitioning of DNaseI hypersensitivity profiles around SP1 binding sites in K562 cells. The optimal number of clusters was determined using the elbow method. \textbf{A.} Input data based on peak summits provided by ENCODE. \textbf{B.} Same regions clustered, re-aligned and oriented by SPar-K. Clusters 1, 2 and 3 are indicated by colored bars in red, blue, and green, respectively. \textbf{C.} MNase-seq read densities for the same regions, ordered, aligned and oriented as in B. \textbf{D.} Predicted SP1 binding motifs for the same regions, ordered, aligned and oriented as in B. \textbf{E.} Proportion of binding sites within each cluster having a confirmed promoter-associated TSS within +/- 300bp. \textbf{F.} Aggregations profiles for DNase-seq (red), MNase-seq (blue), promoter TSS (green) and CAGE-seq data (violet) for cluster 2 (aligned and oriented as in B). \textbf{G.} Motifs found by MEME-ChIP and Tomtom in the narrow footprints of each cluster. (*) known SP1 interactor, (c) central enrichment. Cluster 2 left and right refer to the left and right footprints seen in \textbf{B}. +Figure and legend taken and adapted from \citep{groux_spar-k:_2019}.} +\label{spark_dnase} +\end{figure} + + +First we compared SPar-K, regular K-means and ChIP-partitioning on synthetic datasets (see Supplemental Figure 1 in \citep{groux_spar-k:_2019}) exhibiting properties that are plausible for ChIP-seq profiles for genomic regions: count vectors, 3 classes with different shapes, limited misalignment, random orientation and various amounts of background noise. + + + + + +For benchmarking purposes, we generated several synthetic datasets. Each dataset contained 1000 regions of 2001bp (+/- 1kb around a central position), equally distributed over 3 classes. The signal over a region was modeled as a mixture of class specific signal and of background signal. The class specific signal was modeled by a 1902 element density vector. The background signal was modeled using a second 1902 element density vector containing a uniform density. The first class density vector contained a Gaussian density with mean 951 and standard deviation 40 (Figure \ref{fig_s01}A upper panel). The second class density was a Gaussian density of mean 950 and standard deviation 40. To create an asymmetric signal class, the values at positions 950 to 1902 (comprised) were set to the minimal value found in the original density (Figure \ref{fig_s01}A middle panel). The last class contained a rectangular function with a step corresponding to the elements 830 to 1070 (Figure \ref{fig_s01}A lower panel). Finally, all the densities were normalized such that the sum of each vector was 1. From these densities, the $\lambda$ values for a class $k$ were computed using the following formula : + +\begin{equation} +lambdas_{k} = signal_{k} * c * p_{s} + background * c * p_{b} +\end{equation} + +where $signal_{k}$ is the class characteristic signal density, $background$ a uniform density, $c$ the coverage factor, $p_{s}$ the overall signal proportion and $p_{b}$ the overall background proportion, with the constraint $p_{s} + p_{b} = 1$.\\ + +% generations +For each region, a read signal of 1902bp long was randomly sampled from Poisson distributions with the $lambdas$ values as function parameters. Then, the signal vector was introduced, in a 2001 element long vector filled of 0's, at a given offset, in a given orientation. The offset was randomly sampled from 1 to 100 . The orientation was randomly sampled with a probability of 0.3 to be in the reversed orientation. Finally, the resulting 2001bp vectors were binned using a 10bp window, that is, the signal was summed up every 10 columns leading to the creation of 201 bin long vectors. At the end of the process, a dataset was stored as a matrix of 1000 rows and 201 columns. Two examples of synthetic datasets are shown in Figure \ref{fig_s01}B and D.\\ + + + + + + + + +Performance was assessed by the Adjusted Rand index (see Figure \ref{spark_ari} and Supplemental Figure 3 in \citep{groux_spar-k:_2019}) and the optimal number of classes was estimated by the elbow method (Figure \ref{spark_sse}). As expected, regular K-means performed poorly. On the contrary, SPar-K was equally accurate as ChIP-Partitioning except for the lowest coverage class. Considering speed, Spar-K outperformed ChIP-partitioning by a factor of at least 20 (Figure \ref{spark_time}). + +We applied SPar-K with $K=3$ to DNaseI accessibility profiles (2bp resolution) around 7'206 ChIP-seq SP1-binding peaks (+/-300bp relative to peak summit) in K562 cells (Figure \ref{spark_dnase}A). The results revealed the presence of clear footprints in all the clusters (Figure \ref{spark_dnase}B). To validate these footprints, we checked whether they are consistent with to location of nucleosomes (Figure \ref{spark_dnase}C) and SP1 binding motifs (Figure \ref{spark_dnase}D), which was indeed the case. De novo motif analysis of the narrow footprints seen in Figure \ref{spark_dnase}B with MEME-ChIP and Tomtom \citep{bailey_meme_2009} discovered SP1-related, NFYA/B and GATA motifs (Figure \ref{spark_dnase}G) the latter two reportedly being interaction partners of SP1. Taken together, these results suggest that SPar-K is able to precisely refocus initially misaligned DNaseI profiles around SP1 binding sites. + +The partitioning of SP1 binding regions reveals distinct chromatin landscapes. Cluster 1 (red) groups binding sites lying between two closely spaced nucleosomes. Cluster 2 (blue) shows strong asymmetry suggestive of promoter regions, an interpretation supported by the presence of promoter-associated transcription starts sites (TSSs) and CAGE tags (Figure \ref{spark_dnase}E and F). Finally, the symmetrical cluster 3 (green) contains binding sites located on large nucleosome-free regions reminiscent of enhancer regions. + +As a second example, we ran the same type of analysis on nucleosome profiles around CTCF binding sites (see Supplemental Figure 8 in \cite{groux_spar-k:_2019}). Overall, the results confirm observations published by \citep{kundaje_ubiquitous_2012}. Strong nucleosome arrays became visible in all classes after realignment, with three out of four showing strong asymmetry in addition. -\subsection{Conclusion} +\section{Conclusions} SPar-K is a useful partitioning method for moderately misaligned and randomly oriented chromatin regions. 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(/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.greek.cod e.tex File: chemmacros.module.greek.code.tex 2017/08/28 v5.8b chemmacros module `gree k' 2015/06/09 upright greek symbols (/usr/share/texlive/texmf-dist/tex/latex/chemgreek/chemgreek.sty Package: chemgreek 2016/12/20 v1.1 interfaceforuprightgreeklettersforuseinchemi stry (CN) \l__chemgreek_tmpa_int=\count338 \g__chemgreek_tmpa_int=\count339 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \newchemgreekmapping with sig. 'O{}mm' on line 336. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \renewchemgreekmapping with sig. 'O{}mm' on line 339. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \declarechemgreekmapping with sig. 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LaTeX info: "xparse/define-command" . . Defining command \chemgreekmappingsymbol with sig. 'mm' on line 477. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \activatechemgreekmapping with sig. 'sm' on line 486. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \selectchemgreekmapping with sig. 'm' on line 491. ................................................. )) (chemmacros) Loading module `chemformula'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.chemformu la.code.tex File: chemmacros.module.chemformula.code.tex 2017/08/28 v5.8b chemmacros module `chemformula' 2016/05/03 integration of chemical formulas (chemmacros) Loading module `charges'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.charges.c ode.tex File: chemmacros.module.charges.code.tex 2017/08/28 v5.8b chemmacros module `ch arges' 2015/07/30 charges ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemCharge with sig. 'mm' on line 122. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemCharge with sig. 'mm' on line 122. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemCharge with sig. 'mm' on line 122. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemCharge with sig. 'mm' on line 122. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemPartialCharge with sig. 'mm' on line 125. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemPartialCharge with sig. 'mm' on line 125. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemPartialCharge with sig. 'mm' on line 125. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemPartialCharge with sig. 'mm' on line 125. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \mch with sig. 'o' on line 146. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \pch with sig. 'o' on line 147. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \fmch with sig. 'o' on line 148. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \fpch with sig. 'o' on line 149. ................................................. )) (chemmacros) Loading module `acid-base'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.acid-base .code.tex File: chemmacros.module.acid-base.code.tex 2017/08/28 v5.8b chemmacros module ` acid-base' 2016/05/31 acid/base ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemEqConstant with sig. 'mmm' on line 87. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemEqConstant with sig. 'mmm' on line 87. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemEqConstant with sig. 'mmm' on line 87. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemEqConstant with sig. 'mmm' on line 87. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \p with sig. 'm' on line 119. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \pH with sig. '' on line 120. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \pOH with sig. '' on line 121. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \pKa with sig. 'o' on line 130. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \pKb with sig. 'o' on line 139. ................................................. ) (chemmacros) Loading module `symbols'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.symbols.c ode.tex File: chemmacros.module.symbols.code.tex 2017/08/28 v5.8b chemmacros module `sy mbols' 2015/06/09 symbols ................................................. . LaTeX info: "xparse/define-command" . . Defining command \standardstate with sig. '' on line 67. ................................................. ) (chemmacros) Loading module `particles'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.particles .code.tex File: chemmacros.module.particles.code.tex 2017/08/28 v5.8b chemmacros module ` particles' 2016/04/02 particles ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemParticle with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemParticle with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemParticle with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemParticle with sig. 'mm' on line 45. ................................................. \l__chemmacros_nucleophile_dim=\dimen308 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemNucleophile with sig. 'mm' on line 111. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemNucleophile with sig. 'mm' on line 111. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemNucleophile with sig. 'mm' on line 111. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemNucleophile with sig. 'mm' on line 111. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \Nuc with sig. 'o' on line 130. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ba with sig. 'o' on line 131. ................................................. ) (chemmacros) Loading module `phases'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.phases.co de.tex File: chemmacros.module.phases.code.tex 2017/08/28 v5.8b chemmacros module `pha ses' 2016/05/31 phase descriptors \l__chemmacros_phases_space_dim=\dimen309 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemPhase with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemPhase with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemPhase with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemPhase with sig. 'mm' on line 45. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \phase with sig. 'm' on line 93. ................................................. ................................................. . LaTeX info: "xparse/redefine-command" . . Redefining command \sld with sig. 'o' on line 95. ................................................. ................................................. . LaTeX info: "xparse/redefine-command" . . Redefining command \lqd with sig. 'o' on line 96. ................................................. ................................................. . LaTeX info: "xparse/redefine-command" . . Redefining command \gas with sig. 'o' on line 97. ................................................. ................................................. . LaTeX info: "xparse/redefine-command" . . Redefining command \aq with sig. 'o' on line 98. ................................................. ) (chemmacros) Loading module `nomenclature'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.nomenclat ure.code.tex File: chemmacros.module.nomenclature.code.tex 2017/08/28 v5.8b chemmacros modul e `nomenclature' 2017/06/11 chemical names (chemmacros) Loading module `tikz'... (/usr/share/texlive/texmf-dist/tex/latex/chemmacros/chemmacros.module.tikz.code .tex File: chemmacros.module.tikz.code.tex 2017/08/28 v5.8b chemmacros module `tikz' 2015/10/26 upright greek symbols (/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik zlibrarycalc.code.tex File: tikzlibrarycalc.code.tex 2013/07/15 v3.0.1a (rcs-revision 1.9) ) (/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik zlibrarydecorations.pathmorphing.code.tex (/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik zlibrarydecorations.code.tex (/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduledecorations.cod e.tex \pgfdecoratedcompleteddistance=\dimen310 \pgfdecoratedremainingdistance=\dimen311 \pgfdecoratedinputsegmentcompleteddistance=\dimen312 \pgfdecoratedinputsegmentremainingdistance=\dimen313 \pgf@decorate@distancetomove=\dimen314 \pgf@decorate@repeatstate=\count340 \pgfdecorationsegmentamplitude=\dimen315 \pgfdecorationsegmentlength=\dimen316 ) \tikz@lib@dec@box=\box73 ) (/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary decorations.pathmorphing.code.tex)) \l__chemmacros_el_length_dim=\dimen317 ) ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemIUPAC with sig. 'mm' on line 209. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemIUPAC with sig. 'mm' on line 212. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemIUPAC with sig. 'mm' on line 215. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemIUPAC with sig. 'mm' on line 218. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \LetChemIUPAC with sig. 'mm' on line 221. ................................................. \l__chemmacros_cip_kern_dim=\dimen318 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \Sconf with sig. 'O{S}' on line 349. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \Rconf with sig. 'O{R}' on line 350. ................................................. \l__chemmacros_iupac_hyphen_pre_dim=\dimen319 \l__chemmacros_iupac_hyphen_post_dim=\dimen320 \l__chemmacros_iupac_break_dim=\dimen321 \l__chemmacros_iupac_break_skip=\skip102 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemIUPACShorthand with sig. 'mm' on line 604. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemIUPACShorthand with sig. 'mm' on line 611. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemIUPACShorthand with sig. 'mm' on line 617. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemIUPACShorthand with sig. 'mm' on line 624. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RemoveChemIUPACShorthand with sig. 'm' on line 627. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \iupac with sig. 'O{}m' on line 673. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemLatin with sig. 'mm' on line 755. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemLatin with sig. 'mm' on line 755. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemLatin with sig. 'mm' on line 755. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemLatin with sig. 'mm' on line 755. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \latin with sig. 'O{}m' on line 826. ................................................. )))) ................................................. . chemmacros info: "default-formula-method" . . You haven't chosen a formula method so I'm assuming the default method . `chemformula'. ................................................. (/usr/share/texlive/texmf-dist/tex/latex/chemformula/chemformula.sty (/usr/share/texlive/texmf-dist/tex/latex/l3packages/xfrac/xfrac.sty (/usr/share/texlive/texmf-dist/tex/latex/l3packages/xtemplate/xtemplate.sty Package: xtemplate 2018/02/21 L3 Experimental prototype document functions \l__xtemplate_tmp_dim=\dimen322 \l__xtemplate_tmp_int=\count341 \l__xtemplate_tmp_muskip=\muskip18 \l__xtemplate_tmp_skip=\skip103 ) Package: xfrac 2018/02/21 L3 Experimental split-level fractions \l__xfrac_slash_box=\box74 \l__xfrac_tmp_box=\box75 \l__xfrac_denominator_bot_sep_dim=\dimen323 \l__xfrac_numerator_bot_sep_dim=\dimen324 \l__xfrac_numerator_top_sep_dim=\dimen325 \l__xfrac_slash_left_sep_dim=\dimen326 \l__xfrac_slash_right_sep_dim=\dimen327 \l__xfrac_slash_left_muskip=\muskip19 \l__xfrac_slash_right_muskip=\muskip20 ................................................. . xtemplate info: "declare-object-type" . . Declaring object type 'xfrac' taking 3 argument(s) on line 80. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \sfrac with sig. 'omom' on line 420. ................................................. ) (/usr/share/texlive/texmf-dist/tex/latex/units/nicefrac.sty Package: nicefrac 1998/08/04 v0.9b Nice fractions \L@UnitsRaiseDisplaystyle=\skip104 \L@UnitsRaiseTextstyle=\skip105 \L@UnitsRaiseScriptstyle=\skip106 ) (/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta. code.tex File: pgflibraryarrows.meta.code.tex 2015/05/13 v3.0.1a (rcs-revision 1.13) \pgfarrowinset=\dimen328 \pgfarrowlength=\dimen329 \pgfarrowwidth=\dimen330 \pgfarrowlinewidth=\dimen331 ) Package: chemformula 2017/03/23 v4.15e typeset chemical compounds and reactions (CN) \l__chemformula_tmpa_dim=\dimen332 \l__chemformula_tmpb_dim=\dimen333 \l__chemformula_tmpc_dim=\dimen334 \l__chemformula_tmpa_int=\count342 \l__chemformula_tmpb_int=\count343 \l__chemformula_tmpc_int=\count344 \l__chemformula_tmpa_box=\box76 \l__chemformula_tmpb_box=\box77 \l__chemformula_arrow_length_dim=\dimen335 \l__chemformula_arrow_label_height_dim=\dimen336 \l__chemformula_arrow_label_offset_dim=\dimen337 \l__chemformula_arrow_minimum_length_dim=\dimen338 \l__chemformula_arrow_shortage_dim=\dimen339 \l__chemformula_arrow_offset_dim=\dimen340 \l__chemformula_arrow_yshift_dim=\dimen341 \l__chemformula_radical_radius_dim=\dimen342 \l__chemformula_radical_hshift_dim=\dimen343 \l__chemformula_radical_vshift_dim=\dimen344 \l__chemformula_radical_space_dim=\dimen345 \l__chemformula_arrow_head_dim=\dimen346 \l__chemformula_name_dim=\dimen347 \l__chemformula_adduct_space_dim=\dimen348 \l__chemformula_charge_shift_dim=\dimen349 \l__chemformula_subscript_shift_dim=\dimen350 \l__chemformula_superscript_shift_dim=\dimen351 \l__chemformula_subscript_dim=\dimen352 \l__chemformula_superscript_dim=\dimen353 \l__chemformula_bond_dim=\dimen354 \l__chemformula_bond_space_dim=\dimen355 \l__chemformula_elspec_pair_distance_dim=\dimen356 \l__chemformula_elspec_pair_line_length_dim=\dimen357 \l__chemformula_elspec_pair_width_dim=\dimen358 \l__chemformula_kroegervink_positive_radius_dim=\dimen359 \l__chemformula_kroegervink_positive_hshift_dim=\dimen360 \l__chemformula_kroegervink_positive_vshift_dim=\dimen361 \l__chemformula_kroegervink_positive_space_dim=\dimen362 \l__chemformula_stoich_space_skip=\skip107 \l__chemformula_math_space_skip=\skip108 \l__chemformula_count_tokens_int=\count345 \g__chemformula_lewis_int=\count346 \l__chemformula_arrow_arg_i_box=\box78 \l__chemformula_arrow_arg_ii_box=\box79 \l__chemformula_superscript_box=\box80 \l__chemformula_subscript_box=\box81 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \charrow with sig. 'mO{}O{}' on line 823. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemArrow with sig. 'mm' on line 896. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemArrow with sig. 'mm' on line 904. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemArrow with sig. 'mm' on line 911. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemArrow with sig. 'mm' on line 921. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ShowChemArrow with sig. 'm' on line 931. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ch with sig. 'O{}m' on line 1176. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \chcpd with sig. 'O{}m' on line 1198. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \chname with sig. 'R(){}R(){}' on line 1276. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemCompoundProperty with sig. 'mm' on line 1361. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemCompoundProperty with sig. 'mm' on line 1364. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemCompoundProperty with sig. 'mm' on line 1367. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemCompoundProperty with sig. 'mm' on line 1370. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RemoveChemCompoundProperty with sig. 'm' on line 1373. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemBond with sig. 'mm' on line 1571. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemBond with sig. 'mm' on line 1574. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemBond with sig. 'mm' on line 1577. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemBond with sig. 'mm' on line 1580. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemBondAlias with sig. 'mm' on line 1583. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemBondAlias with sig. 'mm' on line 1586. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ShowChemBond with sig. 'm' on line 1589. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \bond with sig. 'm' on line 1592. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \chstoich with sig. 'm' on line 2191. ................................................. \l__chemformula_additions_symbol_space_skip=\skip109 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemAdditionSymbol with sig. 'mmm' on line 2697. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemAdditionSymbol with sig. 'mmm' on line 2706. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemAdditionSymbol with sig. 'mmm' on line 2715. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemAdditionSymbol with sig. 'mmm' on line 2718. ................................................. \l__chemformula_plus_space_skip=\skip110 \l__chemformula_minus_space_skip=\skip111 ................................................. . LaTeX info: "xparse/define-command" . . Defining command \NewChemSymbol with sig. 'mm' on line 2763. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \ProvideChemSymbol with sig. 'mm' on line 2769. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \RenewChemSymbol with sig. 'mm' on line 2776. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \DeclareChemSymbol with sig. 'mm' on line 2779. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \chlewis with sig. 'O{}mm' on line 3334. ................................................. ................................................. . LaTeX info: "xparse/define-command" . . Defining command \setchemformula with sig. 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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \input{head/settings_epfl_template.tex} \input{head/settings_custom.tex} % place your custom packages, etc... in this file! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% HEAD: Book-Begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \setlength{\parindent}{0pt} \setlength{\parskip}{0pt} %(needs to be before titlepage and frontmatter to keep the table of contents lists short) \frontmatter \input{head/titlepage.tex} \include{head/dedication} \setcounter{page}{0} \include{head/acknowledgements} \include{head/preface} \include{head/abstracts} \cleardoublepage \pdfbookmark{\contentsname}{toc} \tableofcontents % % Following content is OPTIONAL (List of figures + tables) % \cleardoublepage % \phantomsection % \addcontentsline{toc}{chapter}{List of Figures} % adds an entry to the table of contents % \listoffigures % % \cleardoublepage % \phantomsection % \addcontentsline{toc}{chapter}{List of Tables} % adds an entry to the table of contents % \listoftables % your list of symbols here, if needed. % space before each new paragraph according to the template guidelines. %(needs to be after titlepage and frontmatter to keep the table of contents lists short) \setlength{\parskip}{1em} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% MAIN: The chapters of the thesis %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \mainmatter \include{main/ch_introduction} \include{main/ch_lab_resources} \include{main/ch_encode_peaks} +\include{main/ch_spark} \include{main/ch_smile-seq} \include{main/ch_pwmscan} \include{main/ch_atac-seq} \include{main/ch_discussion} % use to end the last part if the thesis is composed of parts \addtocontents{toc}{\vspace{\normalbaselineskip}} \cleardoublepage \bookmarksetup{startatroot} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% TAIL: Bibliography, Appendix, CV %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \include{tail/appendix} \backmatter \include{tail/biblio} % Add your glossary here % Add your index here % Photographic credits (list of pictures&images that have been used with names of the person holding the copyright for them) \include{tail/cv} \end{document} diff --git a/my_thesis.toc b/my_thesis.toc index b486b7d..135cdd6 100644 --- a/my_thesis.toc +++ b/my_thesis.toc @@ -1,116 +1,121 @@ \babel@toc {english}{} \babel@toc {french}{} \babel@toc {english}{} \contentsline {chapter}{Acknowledgements}{i}{chapter*.1} \contentsline {chapter}{Preface}{iii}{chapter*.2} \contentsline {chapter}{Abstract (English/Fran\IeC {\c c}ais/Deutsch)}{v}{chapter*.3} \babel@toc {german}{} \babel@toc {english}{} \babel@toc {french}{} \babel@toc {english}{} \contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1} \contentsline {chapter}{Introduction}{1}{chapter.1} \contentsline {section}{\numberline {1.1}About chromatin}{1}{section.1.1} \contentsline {subsection}{\numberline {1.1.1}The chromatin structure}{1}{subsection.1.1.1} \contentsline {subsection}{\numberline {1.1.2}The chromatin is dynamic}{3}{subsection.1.1.2} \contentsline {subsection}{\numberline {1.1.3}Measuring nucleosome occupancy}{4}{subsection.1.1.3} \contentsline {section}{\numberline {1.2}About transcription factors}{5}{section.1.2} \contentsline {subsection}{\numberline {1.2.1}TF co-binding}{6}{subsection.1.2.1} \contentsline {subsection}{\numberline {1.2.2}Modeling sequence specificity}{7}{subsection.1.2.2} \contentsline {subsubsection}{Position weight matrix}{7}{subsection.1.2.2} \contentsline {subsubsection}{Predicting binding sites}{9}{equation.1.2.4} \contentsline {subsubsection}{Aligning binding sites}{10}{equation.1.2.6} \contentsline {subsection}{\numberline {1.2.3}Measuring TF binding in vivo}{10}{subsection.1.2.3} \contentsline {subsection}{\numberline {1.2.4}Measuring TF binding in vitro}{11}{subsection.1.2.4} \contentsline {section}{\numberline {1.3}About nucleosome positioning}{11}{section.1.3} \contentsline {section}{\numberline {1.4}Gene regulation in a nutshell}{14}{section.1.4} \contentsline {subsection}{\numberline {1.4.1}The chromatin barrier}{14}{subsection.1.4.1} \contentsline {subsection}{\numberline {1.4.2}TFs cooperative binding}{14}{subsection.1.4.2} \contentsline {subsection}{\numberline {1.4.3}Pioneer TFs}{15}{subsection.1.4.3} \contentsline {subsection}{\numberline {1.4.4}Regulatory elements}{15}{subsection.1.4.4} \contentsline {subsection}{\numberline {1.4.5}The genome goes 3D}{16}{subsection.1.4.5} \contentsline {subsection}{\numberline {1.4.6}Digital footprinting}{17}{subsection.1.4.6} \contentsline {chapter}{\numberline {2}Laboratory resources}{21}{chapter.2} \contentsline {chapter}{Laboratory resources}{21}{chapter.2} \contentsline {section}{\numberline {2.1}Mass Genome Annotation repository}{21}{section.2.1} \contentsline {subsection}{\numberline {2.1.1}MGA content and organization}{22}{subsection.2.1.1} \contentsline {subsection}{\numberline {2.1.2}Conclusions}{24}{subsection.2.1.2} \contentsline {section}{\numberline {2.2}Eukaryotic Promoter Database}{25}{section.2.2} \contentsline {subsection}{\numberline {2.2.1}EPDnew now annotates (some of) your mushrooms and vegetables}{26}{subsection.2.2.1} \contentsline {subsection}{\numberline {2.2.2}Increased mapping precision in human}{27}{subsection.2.2.2} \contentsline {subsection}{\numberline {2.2.3}Integration of EPDnew with other resources}{27}{subsection.2.2.3} \contentsline {subsection}{\numberline {2.2.4}Conclusions}{28}{subsection.2.2.4} \contentsline {subsection}{\numberline {2.2.5}Methods}{28}{subsection.2.2.5} \contentsline {subsubsection}{Motif occurrence profiles}{28}{subsection.2.2.5} \contentsline {chapter}{\numberline {3}ENCODE peaks analysis}{29}{chapter.3} \contentsline {chapter}{ENCODE peaks analysis}{29}{chapter.3} \contentsline {section}{\numberline {3.1}Data}{29}{section.3.1} \contentsline {section}{\numberline {3.2}ChIPPartitioning : an algorithm to identify chromatin architectures}{31}{section.3.2} \contentsline {subsection}{\numberline {3.2.1}Data realignment}{32}{subsection.3.2.1} \contentsline {section}{\numberline {3.3}Nucleosome organization around transcription factor binding sites}{33}{section.3.3} \contentsline {section}{\numberline {3.4}The case of CTCF, RAD21, SMC3, YY1 and ZNF143}{35}{section.3.4} \contentsline {section}{\numberline {3.5}CTCF and JunD interactomes}{39}{section.3.5} \contentsline {section}{\numberline {3.6}EBF1 binds nucleosomes}{43}{section.3.6} \contentsline {section}{\numberline {3.7}Discussion}{46}{section.3.7} \contentsline {section}{\numberline {3.8}Methods}{46}{section.3.8} \contentsline {subsection}{\numberline {3.8.1}Data and data processing}{46}{subsection.3.8.1} \contentsline {subsection}{\numberline {3.8.2}Classification of MNase patterns}{47}{subsection.3.8.2} \contentsline {subsection}{\numberline {3.8.3}Quantifying nucleosome array intensity from classification results}{48}{subsection.3.8.3} \contentsline {subsection}{\numberline {3.8.4}Peak colocalization}{49}{subsection.3.8.4} \contentsline {subsection}{\numberline {3.8.5}NDR detection}{50}{subsection.3.8.5} \contentsline {subsection}{\numberline {3.8.6}CTCF and JunD interactors}{52}{subsection.3.8.6} \contentsline {subsection}{\numberline {3.8.7}EBF1 and nucleosome}{53}{subsection.3.8.7} -\contentsline {chapter}{\numberline {4}SMiLE-seq data analysis}{55}{chapter.4} -\contentsline {chapter}{SMiLE-seq data analysis}{55}{chapter.4} -\contentsline {subsection}{\numberline {4.0.1}Introduction}{55}{subsection.4.0.1} -\contentsline {subsection}{\numberline {4.0.2}Hidden Markov Model Motif discovery}{57}{subsection.4.0.2} -\contentsline {subsection}{\numberline {4.0.3}Binding motif evaluation}{58}{subsection.4.0.3} -\contentsline {subsection}{\numberline {4.0.4}Results}{60}{subsection.4.0.4} -\contentsline {subsection}{\numberline {4.0.5}Conclusions}{62}{subsection.4.0.5} -\contentsline {chapter}{\numberline {5}PWMScan}{63}{chapter.5} -\contentsline {section}{\numberline {5.1}Algorithms}{63}{section.5.1} -\contentsline {subsection}{\numberline {5.1.1}Scanner algorithm}{64}{subsection.5.1.1} -\contentsline {subsection}{\numberline {5.1.2}Matches enumeration and mapping}{64}{subsection.5.1.2} -\contentsline {section}{\numberline {5.2}PMWScan architecture}{65}{section.5.2} -\contentsline {section}{\numberline {5.3}Benchmark}{67}{section.5.3} -\contentsline {section}{\numberline {5.4}Conclusions}{69}{section.5.4} -\contentsline {chapter}{\numberline {6}Chromatin accessibility of monocytes}{71}{chapter.6} -\contentsline {section}{\numberline {6.1}Monitoring TF binding}{71}{section.6.1} -\contentsline {section}{\numberline {6.2}The advent of single cell DGF}{72}{section.6.2} -\contentsline {section}{\numberline {6.3}Open issues}{72}{section.6.3} -\contentsline {section}{\numberline {6.4}Data}{72}{section.6.4} -\contentsline {section}{\numberline {6.5}Identifying over-represented signals}{73}{section.6.5} -\contentsline {subsection}{\numberline {6.5.1}ChIPPartitioning : an algorithm to identify over-represented read patterns}{73}{subsection.6.5.1} -\contentsline {subsection}{\numberline {6.5.2}EMSequence : an algorithm to identify over-represented sequences}{73}{subsection.6.5.2} -\contentsline {subsubsection}{without shift and flip}{75}{figure.caption.30} -\contentsline {subsubsection}{with shift and flip}{75}{equation.6.5.2} -\contentsline {subsection}{\numberline {6.5.3}EMJoint : an algorithm to identify over-represented sequences and chromatin architectures}{76}{subsection.6.5.3} -\contentsline {subsection}{\numberline {6.5.4}Data realignment}{77}{subsection.6.5.4} -\contentsline {section}{\numberline {6.6}Results}{78}{section.6.6} -\contentsline {subsection}{\numberline {6.6.1}Fragment size analysis}{80}{subsection.6.6.1} -\contentsline {subsection}{\numberline {6.6.2}Measuring open chromatin and nucleosome occupancy}{80}{subsection.6.6.2} -\contentsline {subsection}{\numberline {6.6.3}Evaluation of EMSequence and ChIPPartitioning}{82}{subsection.6.6.3} -\contentsline {subsubsection}{EMSequence}{83}{subsection.6.6.3} -\contentsline {subsubsection}{ChIPPartitioning}{85}{figure.caption.35} -\contentsline {section}{\numberline {6.7}Aligning the binding sites}{87}{section.6.7} -\contentsline {section}{\numberline {6.8}Exploring individual TF classes}{91}{section.6.8} -\contentsline {section}{\numberline {6.9}Discussions}{91}{section.6.9} -\contentsline {section}{\numberline {6.10}Perspectives}{92}{section.6.10} -\contentsline {section}{\numberline {6.11}Methods}{93}{section.6.11} -\contentsline {subsection}{\numberline {6.11.1}Partitioning programs}{93}{subsection.6.11.1} -\contentsline {subsection}{\numberline {6.11.2}Fragment classes}{93}{subsection.6.11.2} -\contentsline {subsection}{\numberline {6.11.3}Simulated sequences}{94}{subsection.6.11.3} -\contentsline {subsection}{\numberline {6.11.4}Realignment using JASPAR motifs}{94}{subsection.6.11.4} -\contentsline 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analysis}{63}{chapter.5} +\contentsline {chapter}{SMiLE-seq data analysis}{63}{chapter.5} +\contentsline {subsection}{\numberline {5.0.1}Introduction}{63}{subsection.5.0.1} +\contentsline {subsection}{\numberline {5.0.2}Hidden Markov Model Motif discovery}{65}{subsection.5.0.2} +\contentsline {subsection}{\numberline {5.0.3}Binding motif evaluation}{66}{subsection.5.0.3} +\contentsline {subsection}{\numberline {5.0.4}Results}{68}{subsection.5.0.4} +\contentsline {subsection}{\numberline {5.0.5}Conclusions}{70}{subsection.5.0.5} +\contentsline {chapter}{\numberline {6}PWMScan}{71}{chapter.6} +\contentsline {section}{\numberline {6.1}Algorithms}{71}{section.6.1} +\contentsline {subsection}{\numberline {6.1.1}Scanner algorithm}{72}{subsection.6.1.1} +\contentsline {subsection}{\numberline {6.1.2}Matches enumeration and mapping}{72}{subsection.6.1.2} +\contentsline {section}{\numberline {6.2}PMWScan architecture}{73}{section.6.2} +\contentsline {section}{\numberline {6.3}Benchmark}{75}{section.6.3} +\contentsline {section}{\numberline {6.4}Conclusions}{77}{section.6.4} +\contentsline {chapter}{\numberline {7}Chromatin accessibility of monocytes}{79}{chapter.7} +\contentsline {section}{\numberline {7.1}Monitoring TF binding}{79}{section.7.1} +\contentsline {section}{\numberline {7.2}The advent of single cell DGF}{80}{section.7.2} +\contentsline {section}{\numberline {7.3}Open issues}{80}{section.7.3} +\contentsline {section}{\numberline {7.4}Data}{80}{section.7.4} +\contentsline {section}{\numberline {7.5}Identifying over-represented signals}{81}{section.7.5} +\contentsline {subsection}{\numberline {7.5.1}ChIPPartitioning : an algorithm to identify over-represented read patterns}{81}{subsection.7.5.1} +\contentsline {subsection}{\numberline {7.5.2}EMSequence : an algorithm to identify over-represented sequences}{81}{subsection.7.5.2} +\contentsline {subsubsection}{without shift and flip}{83}{figure.caption.36} +\contentsline {subsubsection}{with shift and flip}{83}{equation.7.5.2} +\contentsline {subsection}{\numberline {7.5.3}EMJoint : an algorithm to identify over-represented sequences and chromatin architectures}{84}{subsection.7.5.3} +\contentsline {subsection}{\numberline {7.5.4}Data realignment}{85}{subsection.7.5.4} +\contentsline {section}{\numberline {7.6}Results}{86}{section.7.6} +\contentsline {subsection}{\numberline {7.6.1}Fragment size analysis}{88}{subsection.7.6.1} +\contentsline {subsection}{\numberline {7.6.2}Measuring open chromatin and nucleosome occupancy}{88}{subsection.7.6.2} +\contentsline {subsection}{\numberline {7.6.3}Evaluation of EMSequence and ChIPPartitioning}{90}{subsection.7.6.3} +\contentsline {subsubsection}{EMSequence}{91}{subsection.7.6.3} +\contentsline {subsubsection}{ChIPPartitioning}{93}{figure.caption.41} +\contentsline {section}{\numberline {7.7}Aligning the binding sites}{95}{section.7.7} +\contentsline {section}{\numberline {7.8}Exploring individual TF classes}{99}{section.7.8} +\contentsline {section}{\numberline {7.9}Discussions}{99}{section.7.9} +\contentsline {section}{\numberline {7.10}Perspectives}{100}{section.7.10} +\contentsline {section}{\numberline {7.11}Methods}{101}{section.7.11} +\contentsline {subsection}{\numberline {7.11.1}Partitioning programs}{101}{subsection.7.11.1} +\contentsline {subsection}{\numberline {7.11.2}Fragment classes}{101}{subsection.7.11.2} +\contentsline {subsection}{\numberline {7.11.3}Simulated sequences}{102}{subsection.7.11.3} +\contentsline {subsection}{\numberline {7.11.4}Realignment using JASPAR motifs}{102}{subsection.7.11.4} +\contentsline {subsection}{\numberline {7.11.5}Model extension}{104}{subsection.7.11.5} +\contentsline {subsection}{\numberline {7.11.6}Extracting data assigned to a class}{104}{subsection.7.11.6} +\contentsline {subsection}{\numberline {7.11.7}Peak processing}{107}{subsection.7.11.7} +\contentsline {subsection}{\numberline {7.11.8}Per TF classes}{107}{subsection.7.11.8} +\contentsline {subsection}{\numberline {7.11.9}Per TF sub-classes}{107}{subsection.7.11.9} +\contentsline {chapter}{\numberline {8}Discussion}{109}{chapter.8} +\contentsline {chapter}{Discussions}{109}{chapter.8} \vspace {\normalbaselineskip } -\contentsline {chapter}{\numberline {A}An appendix}{105}{appendix.A} -\contentsline {section}{\numberline {A.1}Supplementary figures}{105}{section.A.1} -\contentsline {chapter}{Bibliography}{123}{section*.60} -\contentsline {chapter}{Bibliography}{135}{appendix*.61} -\contentsline {chapter}{Curriculum Vitae}{137}{section*.62} +\contentsline {chapter}{\numberline {A}An appendix}{113}{appendix.A} +\contentsline {section}{\numberline {A.1}Supplementary figures}{113}{section.A.1} +\contentsline {chapter}{Bibliography}{145}{section*.66} +\contentsline {chapter}{Bibliography}{157}{appendix*.67} +\contentsline {chapter}{Curriculum Vitae}{159}{section*.68} diff --git a/scripts/ch_spark/get_figures.sh b/scripts/ch_spark/get_figures.sh new file mode 100644 index 0000000..047c335 --- /dev/null +++ b/scripts/ch_spark/get_figures.sh @@ -0,0 +1,15 @@ +dest_dir='/local/groux/phd_thesis/images/ch_spark' +script_dir='/local/groux/phd_thesis/scripts/ch_spark' +targ_dir='/local/groux/Kmeans_chipseq/results/article' + +mkdir -p $targ_dir + +cp $targ_dir/figure1.pdf $dest_dir +cp $targ_dir/supplemental_figure1.pdf $dest_dir +cp $targ_dir/supplemental_figure2.pdf $dest_dir +cp $targ_dir/supplemental_figure4.pdf $dest_dir +cp $targ_dir/supplemental_figure5.pdf $dest_dir +cp $targ_dir/supplemental_figure8.pdf $dest_dir + + + diff --git a/tail/appendix.aux b/tail/appendix.aux index b616505..87fee99 100644 --- a/tail/appendix.aux +++ b/tail/appendix.aux @@ -1,97 +1,112 @@ \relax \providecommand\hyper@newdestlabel[2]{} \citation{jolma_dna-binding_2013} \citation{jolma_dna-binding_2013} -\@writefile{toc}{\contentsline {chapter}{\numberline {A}An appendix}{105}{appendix.A}} +\@writefile{toc}{\contentsline {chapter}{\numberline {A}An appendix}{113}{appendix.A}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{loa}{\addvspace {10\p@ }} -\@writefile{toc}{\contentsline {section}{\numberline {A.1}Supplementary figures}{105}{section.A.1}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.1}{\ignorespaces \textbf {Predictive power of SMiLE-seq :} \textbf {A} binding models were derived de novo from HT-SELEX 1st cycle data using the HMM discovery method (labelled HT-SELEX cycle 1 HMM) and their performances were assessed using the AUC-ROC. AUC-ROC values for the corresponding TF models derived from SMiLe-seq data (labelled SMiLE-seq) and reported by Jolma and colleagues (labelled HT-SELEX reported matrices, \cite {jolma_dna-binding_2013}) are also displayed. \textbf {B} the predictive performances of CEBPb, CTCF and TCF7 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }}{105}{figure.caption.41}} -\newlabel{suppl_smileseq_auc_2}{{A.1}{105}{\textbf {Predictive power of SMiLE-seq :} \textbf {A} binding models were derived de novo from HT-SELEX 1st cycle data using the HMM discovery method (labelled HT-SELEX cycle 1 HMM) and their performances were assessed using the AUC-ROC. AUC-ROC values for the corresponding TF models derived from SMiLe-seq data (labelled SMiLE-seq) and reported by Jolma and colleagues (labelled HT-SELEX reported matrices, \cite {jolma_dna-binding_2013}) are also displayed. \textbf {B} the predictive performances of CEBPb, CTCF and TCF7 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }{figure.caption.41}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.2}{\ignorespaces \textbf {Chromatine architectures around CTCF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{106}{figure.caption.42}} -\newlabel{suppl_encode_peaks_em_ctcf}{{A.2}{106}{\textbf {Chromatine architectures around CTCF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.42}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.3}{\ignorespaces \textbf {Chromatine architectures around NRF1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{107}{figure.caption.43}} -\newlabel{suppl_encode_peaks_em_nrf1}{{A.3}{107}{\textbf {Chromatine architectures around NRF1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.43}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.4}{\ignorespaces \textbf {Chromatine architectures around cFOS binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{108}{figure.caption.44}} -\newlabel{suppl_encode_peaks_em_cfos}{{A.4}{108}{\textbf {Chromatine architectures around cFOS binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.44}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.5}{\ignorespaces \textbf {Chromatine architectures around max binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{109}{figure.caption.45}} -\newlabel{suppl_encode_peaks_em_max}{{A.5}{109}{\textbf {Chromatine architectures around max binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.45}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.6}{\ignorespaces \textbf {Chromatine architectures around BRCA1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{110}{figure.caption.46}} -\newlabel{suppl_encode_peaks_em_brca1}{{A.6}{110}{\textbf {Chromatine architectures around BRCA1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.46}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.7}{\ignorespaces \textbf {Nucleosome occupancy around CTCF peaks } measured by MNase-seq, in bins of 10bp. The nucleosome depleted region is displayed in blue.\relax }}{111}{figure.caption.47}} -\newlabel{suppl_encode_peaks_ctcf_ndr}{{A.7}{111}{\textbf {Nucleosome occupancy around CTCF peaks } measured by MNase-seq, in bins of 10bp. The nucleosome depleted region is displayed in blue.\relax }{figure.caption.47}{}} +\@writefile{toc}{\contentsline {section}{\numberline {A.1}Supplementary figures}{113}{section.A.1}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.1}{\ignorespaces \textbf {Predictive power of SMiLE-seq :} \textbf {A} binding models were derived de novo from HT-SELEX 1st cycle data using the HMM discovery method (labelled HT-SELEX cycle 1 HMM) and their performances were assessed using the AUC-ROC. AUC-ROC values for the corresponding TF models derived from SMiLe-seq data (labelled SMiLE-seq) and reported by Jolma and colleagues (labelled HT-SELEX reported matrices, \cite {jolma_dna-binding_2013}) are also displayed. \textbf {B} the predictive performances of CEBPb, CTCF and TCF7 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }}{113}{figure.caption.47}} +\newlabel{suppl_smileseq_auc_2}{{A.1}{113}{\textbf {Predictive power of SMiLE-seq :} \textbf {A} binding models were derived de novo from HT-SELEX 1st cycle data using the HMM discovery method (labelled HT-SELEX cycle 1 HMM) and their performances were assessed using the AUC-ROC. AUC-ROC values for the corresponding TF models derived from SMiLe-seq data (labelled SMiLE-seq) and reported by Jolma and colleagues (labelled HT-SELEX reported matrices, \cite {jolma_dna-binding_2013}) are also displayed. \textbf {B} the predictive performances of CEBPb, CTCF and TCF7 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.\relax }{figure.caption.47}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.2}{\ignorespaces \textbf {Chromatine architectures around CTCF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{114}{figure.caption.48}} +\newlabel{suppl_encode_peaks_em_ctcf}{{A.2}{114}{\textbf {Chromatine architectures around CTCF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.48}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.3}{\ignorespaces \textbf {Chromatine architectures around NRF1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{115}{figure.caption.49}} +\newlabel{suppl_encode_peaks_em_nrf1}{{A.3}{115}{\textbf {Chromatine architectures around NRF1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.49}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.4}{\ignorespaces \textbf {Chromatine architectures around cFOS binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{116}{figure.caption.50}} +\newlabel{suppl_encode_peaks_em_cfos}{{A.4}{116}{\textbf {Chromatine architectures around cFOS binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.50}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.5}{\ignorespaces \textbf {Chromatine architectures around max binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{117}{figure.caption.51}} +\newlabel{suppl_encode_peaks_em_max}{{A.5}{117}{\textbf {Chromatine architectures around max binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.51}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.6}{\ignorespaces \textbf {Chromatine architectures around BRCA1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }}{118}{figure.caption.52}} +\newlabel{suppl_encode_peaks_em_brca1}{{A.6}{118}{\textbf {Chromatine architectures around BRCA1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.\relax }{figure.caption.52}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.7}{\ignorespaces \textbf {Nucleosome occupancy around CTCF peaks } measured by MNase-seq, in bins of 10bp. The nucleosome depleted region is displayed in blue.\relax }}{119}{figure.caption.53}} +\newlabel{suppl_encode_peaks_ctcf_ndr}{{A.7}{119}{\textbf {Nucleosome occupancy around CTCF peaks } measured by MNase-seq, in bins of 10bp. The nucleosome depleted region is displayed in blue.\relax }{figure.caption.53}{}} \citation{khan_jaspar_2018} \citation{khan_jaspar_2018} -\@writefile{lof}{\contentsline {figure}{\numberline {A.8}{\ignorespaces \textbf {JunD motif association} measured around the binding sites of different TFs. For a each TF, its binding sites, +/- 500bp, were searched for the presence of i) the TF motif and ii) CTCF motif. For each TF, a 2x2 contingency table was created with the number of peaks having i) both motifs, ii) the TF motif only, iii) CTCF motif only and iv) no motif. \textbf {A} Odd ratio (OR) of the exact Fisher test performed on each TF contingency table. The ORs are displayed with their 95\% confidence interval (CI). ORs > 1 - that is, with 1 not part of the 95\%CI - are labeled in green and indicate an association of both motifs more frequent than expected by chance. ORs < 1 are labeled in red and indicate a repulsion of both motifs more frequence than expected by chance. The JunD and cFos dataset ORs are too high to be represented in this plot. \textbf {B} Density of JunD motif occurrence at the absolute distance of different TF binding sites (peak centers) which also have their own motif present (at distance 0). The rows were standardized and aggregated using the Euclidean distance. \textbf {C} Same as in (B) but for TF binding sites that does not have their own motif.\relax }}{112}{figure.caption.48}} -\newlabel{suppl_encode_peaks_jund_association}{{A.8}{112}{\textbf {JunD motif association} measured around the binding sites of different TFs. For a each TF, its binding sites, +/- 500bp, were searched for the presence of i) the TF motif and ii) CTCF motif. For each TF, a 2x2 contingency table was created with the number of peaks having i) both motifs, ii) the TF motif only, iii) CTCF motif only and iv) no motif. \textbf {A} Odd ratio (OR) of the exact Fisher test performed on each TF contingency table. The ORs are displayed with their 95\% confidence interval (CI). ORs > 1 - that is, with 1 not part of the 95\%CI - are labeled in green and indicate an association of both motifs more frequent than expected by chance. ORs < 1 are labeled in red and indicate a repulsion of both motifs more frequence than expected by chance. The JunD and cFos dataset ORs are too high to be represented in this plot. \textbf {B} Density of JunD motif occurrence at the absolute distance of different TF binding sites (peak centers) which also have their own motif present (at distance 0). The rows were standardized and aggregated using the Euclidean distance. \textbf {C} Same as in (B) but for TF binding sites that does not have their own motif.\relax }{figure.caption.48}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.9}{\ignorespaces \textbf {EBF1 binding sites} around the dyad of nucleosomes having an occupied EBF1 motif within 100bp (in red) and of all nucleosomes (in blue). The abrupt decrease of EBF1 motif frequency at +/- 100bp reflects the nucleosome selection process.\relax }}{113}{figure.caption.49}} -\newlabel{suppl_encode_peaks_ebf1_nucl}{{A.9}{113}{\textbf {EBF1 binding sites} around the dyad of nucleosomes having an occupied EBF1 motif within 100bp (in red) and of all nucleosomes (in blue). The abrupt decrease of EBF1 motif frequency at +/- 100bp reflects the nucleosome selection process.\relax }{figure.caption.49}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.10}{\ignorespaces \textbf {EBF1 logo} from JASPAR binding model MA0154.3 \citep {khan_jaspar_2018}.\relax }}{113}{figure.caption.50}} -\newlabel{suppl_encode_peaks_ebf1_logo}{{A.10}{113}{\textbf {EBF1 logo} from JASPAR binding model MA0154.3 \citep {khan_jaspar_2018}.\relax }{figure.caption.50}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.11}{\ignorespaces \textbf {EBF1 binding sites} chromatin features. \textbf {A} Chromatin accessibility around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {B} H3K4me2 deposition around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {C} Sequence conservation around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue).\relax }}{114}{figure.caption.51}} -\newlabel{suppl_encode_peaks_ebf1_chrom}{{A.11}{114}{\textbf {EBF1 binding sites} chromatin features. \textbf {A} Chromatin accessibility around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {B} H3K4me2 deposition around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {C} Sequence conservation around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue).\relax }{figure.caption.51}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.8}{\ignorespaces \textbf {JunD motif association} measured around the binding sites of different TFs. For a each TF, its binding sites, +/- 500bp, were searched for the presence of i) the TF motif and ii) CTCF motif. For each TF, a 2x2 contingency table was created with the number of peaks having i) both motifs, ii) the TF motif only, iii) CTCF motif only and iv) no motif. \textbf {A} Odd ratio (OR) of the exact Fisher test performed on each TF contingency table. The ORs are displayed with their 95\% confidence interval (CI). ORs > 1 - that is, with 1 not part of the 95\%CI - are labeled in green and indicate an association of both motifs more frequent than expected by chance. ORs < 1 are labeled in red and indicate a repulsion of both motifs more frequence than expected by chance. The JunD and cFos dataset ORs are too high to be represented in this plot. \textbf {B} Density of JunD motif occurrence at the absolute distance of different TF binding sites (peak centers) which also have their own motif present (at distance 0). The rows were standardized and aggregated using the Euclidean distance. \textbf {C} Same as in (B) but for TF binding sites that does not have their own motif.\relax }}{120}{figure.caption.54}} +\newlabel{suppl_encode_peaks_jund_association}{{A.8}{120}{\textbf {JunD motif association} measured around the binding sites of different TFs. For a each TF, its binding sites, +/- 500bp, were searched for the presence of i) the TF motif and ii) CTCF motif. For each TF, a 2x2 contingency table was created with the number of peaks having i) both motifs, ii) the TF motif only, iii) CTCF motif only and iv) no motif. \textbf {A} Odd ratio (OR) of the exact Fisher test performed on each TF contingency table. The ORs are displayed with their 95\% confidence interval (CI). ORs > 1 - that is, with 1 not part of the 95\%CI - are labeled in green and indicate an association of both motifs more frequent than expected by chance. ORs < 1 are labeled in red and indicate a repulsion of both motifs more frequence than expected by chance. The JunD and cFos dataset ORs are too high to be represented in this plot. \textbf {B} Density of JunD motif occurrence at the absolute distance of different TF binding sites (peak centers) which also have their own motif present (at distance 0). The rows were standardized and aggregated using the Euclidean distance. \textbf {C} Same as in (B) but for TF binding sites that does not have their own motif.\relax }{figure.caption.54}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.9}{\ignorespaces \textbf {EBF1 binding sites} around the dyad of nucleosomes having an occupied EBF1 motif within 100bp (in red) and of all nucleosomes (in blue). The abrupt decrease of EBF1 motif frequency at +/- 100bp reflects the nucleosome selection process.\relax }}{121}{figure.caption.55}} +\newlabel{suppl_encode_peaks_ebf1_nucl}{{A.9}{121}{\textbf {EBF1 binding sites} around the dyad of nucleosomes having an occupied EBF1 motif within 100bp (in red) and of all nucleosomes (in blue). The abrupt decrease of EBF1 motif frequency at +/- 100bp reflects the nucleosome selection process.\relax }{figure.caption.55}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.10}{\ignorespaces \textbf {EBF1 logo} from JASPAR binding model MA0154.3 \citep {khan_jaspar_2018}.\relax }}{121}{figure.caption.56}} +\newlabel{suppl_encode_peaks_ebf1_logo}{{A.10}{121}{\textbf {EBF1 logo} from JASPAR binding model MA0154.3 \citep {khan_jaspar_2018}.\relax }{figure.caption.56}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.11}{\ignorespaces \textbf {EBF1 binding sites} chromatin features. \textbf {A} Chromatin accessibility around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {B} H3K4me2 deposition around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {C} Sequence conservation around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue).\relax }}{122}{figure.caption.57}} +\newlabel{suppl_encode_peaks_ebf1_chrom}{{A.11}{122}{\textbf {EBF1 binding sites} chromatin features. \textbf {A} Chromatin accessibility around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {B} H3K4me2 deposition around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf {C} Sequence conservation around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue).\relax }{figure.caption.57}{}} +\newlabel{algo_spark}{{4}{124}{Supplementary figures}{algocfline.4}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {4}{\ignorespaces SPar-K algorithm.\relax }}{124}{algocf.4}} +\newlabel{algo_smooth_outliers}{{5}{125}{Supplementary figures}{algocfline.5}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {5}{\ignorespaces Smooth the data matrix by removing outliers.\relax }}{125}{algocf.5}} +\newlabel{algo_distance_fast}{{6}{127}{Supplementary figures}{algocfline.6}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {6}{\ignorespaces Fast algorithm to compute the correlation distance with shift and flip\relax }}{127}{algocf.6}} +\newlabel{initialize_algo}{{7}{128}{Supplementary figures}{algocfline.7}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {7}{\ignorespaces A routine of distanceFast() that initializes all the necessary variables. This function can access and modify variables in distanceFast().\relax }}{128}{algocf.7}} +\@writefile{loa}{\contentsline {algocf}{\numberline {8}{\ignorespaces A routine of distanceFast() computing all distances with $X$ having a shift of 0. This function can access and modify all variables declared in distanceFast().\relax }}{130}{algocf.8}} +\@writefile{loa}{\contentsline {algocf}{\numberline {9}{\ignorespaces A routine of distanceFast() computing all distances with $Y$ having a shift of 0. This function is can access and modify all variables declared in distanceFast().\relax }}{132}{algocf.9}} +\@writefile{loa}{\contentsline {algocf}{\numberline {10}{\ignorespaces A routine of distanceFast() computing all remaining distances between $X$ and $Y$. This function can access and modify all variables declared in distanceFast().\relax }}{134}{algocf.10}} +\newlabel{algo_seed_random}{{11}{135}{Supplementary figures}{algocfline.11}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {11}{\ignorespaces Random seeding algorithm\relax }}{135}{algocf.11}} +\newlabel{algo_seed_kmeans++}{{12}{136}{Supplementary figures}{algocfline.12}{}} +\@writefile{loa}{\contentsline {algocf}{\numberline {12}{\ignorespaces Kmeans++ seeding algorithm.\relax }}{136}{algocf.12}} \citation{ou_motifstack_2018} \citation{ou_motifstack_2018} -\@writefile{lof}{\contentsline {figure}{\numberline {A.12}{\ignorespaces \textbf {Open chromatin classes around SP1 motifs :} EMRead was run without shifing (+/- 10bp) but with flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }}{115}{figure.caption.52}} -\newlabel{suppl_emread_sp1_noshift_flip}{{A.12}{115}{\textbf {Open chromatin classes around SP1 motifs :} EMRead was run without shifing (+/- 10bp) but with flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }{figure.caption.52}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.13}{\ignorespaces \textbf {Open chromatin classes around SP1 motifs :} EMRead was run with shifing (+/- 10bp) flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }}{115}{figure.caption.53}} -\newlabel{suppl_emread_sp1_shift_flip}{{A.13}{115}{\textbf {Open chromatin classes around SP1 motifs :} EMRead was run with shifing (+/- 10bp) flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }{figure.caption.53}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.14}{\ignorespaces \textbf {Simulated data motifs :} motifs used for the data generation (labeled "True motif") and the best scoring - based on the AUC - partition motifs (labeled "Found motif"). The partition with EMSequence was run such that it was searching for motifs of 11bp, slightly longer than those used for the data generation. "RC" stands for reverse complement. The motifs tree and alignment was build using the motifStack R package \citep {ou_motifstack_2018}.\relax }}{116}{figure.caption.54}} -\newlabel{suppl_atac_seq_emseq_best_motifs}{{A.14}{116}{\textbf {Simulated data motifs :} motifs used for the data generation (labeled "True motif") and the best scoring - based on the AUC - partition motifs (labeled "Found motif"). The partition with EMSequence was run such that it was searching for motifs of 11bp, slightly longer than those used for the data generation. "RC" stands for reverse complement. The motifs tree and alignment was build using the motifStack R package \citep {ou_motifstack_2018}.\relax }{figure.caption.54}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.15}{\ignorespaces \textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }}{117}{figure.caption.55}} -\newlabel{suppl_emseq_sp1_10class}{{A.15}{117}{\textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }{figure.caption.55}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.16}{\ignorespaces \textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }}{118}{figure.caption.56}} -\newlabel{suppl_emseq_sp1_10class}{{A.16}{118}{\textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }{figure.caption.56}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.17}{\ignorespaces \textbf {Extended sequence and chromatin models} found in 10'000 monocytes regulatory regions. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{119}{figure.caption.57}} -\newlabel{suppl_atac_seq_23class}{{A.17}{119}{\textbf {Extended sequence and chromatin models} found in 10'000 monocytes regulatory regions. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }{figure.caption.57}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.18}{\ignorespaces \textbf {PU.1 sub-classes} obtained by extracting PU.1 class data and subjecting them to a ChIPPartitioning classification into 2 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{120}{figure.caption.58}} -\newlabel{suppl_atac_seq_pu1_subclass}{{A.18}{120}{\textbf {PU.1 sub-classes} obtained by extracting PU.1 class data and subjecting them to a ChIPPartitioning classification into 2 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }{figure.caption.58}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {A.19}{\ignorespaces \textbf {AP1 sub-classes} obtained by extracting AP1 class data and subjecting them to a ChIPPartitioning classification into 3 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{121}{figure.caption.59}} -\newlabel{suppl_atac_seq_ap1_subclass}{{A.19}{121}{\textbf {AP1 sub-classes} obtained by extracting AP1 class data and subjecting them to a ChIPPartitioning classification into 3 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }{figure.caption.59}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.12}{\ignorespaces \textbf {Open chromatin classes around SP1 motifs :} EMRead was run without shifing (+/- 10bp) but with flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }}{137}{figure.caption.58}} +\newlabel{suppl_emread_sp1_noshift_flip}{{A.12}{137}{\textbf {Open chromatin classes around SP1 motifs :} EMRead was run without shifing (+/- 10bp) but with flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }{figure.caption.58}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.13}{\ignorespaces \textbf {Open chromatin classes around SP1 motifs :} EMRead was run with shifing (+/- 10bp) flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }}{137}{figure.caption.59}} +\newlabel{suppl_emread_sp1_shift_flip}{{A.13}{137}{\textbf {Open chromatin classes around SP1 motifs :} EMRead was run with shifing (+/- 10bp) flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.\relax }{figure.caption.59}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.14}{\ignorespaces \textbf {Simulated data motifs :} motifs used for the data generation (labeled "True motif") and the best scoring - based on the AUC - partition motifs (labeled "Found motif"). The partition with EMSequence was run such that it was searching for motifs of 11bp, slightly longer than those used for the data generation. "RC" stands for reverse complement. The motifs tree and alignment was build using the motifStack R package \citep {ou_motifstack_2018}.\relax }}{138}{figure.caption.60}} +\newlabel{suppl_atac_seq_emseq_best_motifs}{{A.14}{138}{\textbf {Simulated data motifs :} motifs used for the data generation (labeled "True motif") and the best scoring - based on the AUC - partition motifs (labeled "Found motif"). The partition with EMSequence was run such that it was searching for motifs of 11bp, slightly longer than those used for the data generation. "RC" stands for reverse complement. The motifs tree and alignment was build using the motifStack R package \citep {ou_motifstack_2018}.\relax }{figure.caption.60}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.15}{\ignorespaces \textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }}{139}{figure.caption.61}} +\newlabel{suppl_emseq_sp1_10class}{{A.15}{139}{\textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }{figure.caption.61}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.16}{\ignorespaces \textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }}{140}{figure.caption.62}} +\newlabel{suppl_emseq_sp1_10class}{{A.16}{140}{\textbf {SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.\relax }{figure.caption.62}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.17}{\ignorespaces \textbf {Extended sequence and chromatin models} found in 10'000 monocytes regulatory regions. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{141}{figure.caption.63}} +\newlabel{suppl_atac_seq_23class}{{A.17}{141}{\textbf {Extended sequence and chromatin models} found in 10'000 monocytes regulatory regions. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }{figure.caption.63}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.18}{\ignorespaces \textbf {PU.1 sub-classes} obtained by extracting PU.1 class data and subjecting them to a ChIPPartitioning classification into 2 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{142}{figure.caption.64}} +\newlabel{suppl_atac_seq_pu1_subclass}{{A.18}{142}{\textbf {PU.1 sub-classes} obtained by extracting PU.1 class data and subjecting them to a ChIPPartitioning classification into 2 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }{figure.caption.64}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {A.19}{\ignorespaces \textbf {AP1 sub-classes} obtained by extracting AP1 class data and subjecting them to a ChIPPartitioning classification into 3 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.\relax }}{143}{figure.caption.65}} +\newlabel{suppl_atac_seq_ap1_subclass}{{A.19}{143}{\textbf {AP1 sub-classes} obtained by extracting AP1 class data and subjecting them to a ChIPPartitioning classification into 3 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \section{S + upplementary figures} +You're in trouble here. 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \begin{figure}[ + H] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 11--12 +[] + [] + +! Undefined control sequence. +l.13 \includegraphics + [scale=0.3]{images/ch_smile-seq/figure_s4_reproduced.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.13 \includegraphics[scale=0.3]{images/ch_ + smile-seq/figure_s4_reproduced.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 13. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 13. +! Extra }, or forgotten $. +l.13 ...ges/ch_smile-seq/figure_s4_reproduced.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.14 \captionof + {figure}{\textbf{Predictive power of SMiLE-seq :} \textbf{A}... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\citation{jolma_dna-binding_2013} +! Undefined control sequence. + ...: Citation `\@citeb ' on page \thepage + \space undefined\on@line . +l.14 ...ed matrices, \cite{jolma_dna-binding_2013} + ) are also displayed. \tex... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Citation `jolma_dna-binding_2013' on page undefined on input li +ne 14. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.16 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.16 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (32.11423pt too wide) in paragraph at lines 13--18 +[]\OML/cmm/m/it/10 mile \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (3780.76639pt too wide) in paragraph at lines 13--18 +\OML/cmm/m/it/10 seq=figure[]\OT1/cmr/m/n/10 4[]\OML/cmm/m/it/10 eproduced:png[ +][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 29--30 +[] + [] + +! Undefined control sequence. +l.31 \includegraphics + [scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsUwGm... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.31 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/wgEncodeAwgTfbsUwGm... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.31 ...12878_allpeaks_EM_4class_15shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.32 \captionof + {figure}{\textbf{Chromatine architectures around CTCF bindin... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.34 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.34 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.34 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.34 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.34 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.35 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (3780.66936pt too wide) in paragraph at lines 31--36 +[]\OML/cmm/m/it/10 ncode[]eaks=wgEncodeAwgTfbsUwGm\OT1/cmr/m/n/10 12878\OML/cmm +/m/it/10 CtcfUniPk[]Nase[]M\OT1/cmr/m/n/10 12878[]\OML/cmm/m/it/10 llpeaks[]M[] +class[]\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 shift[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.37 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 37--38 +[] + [] + +! Undefined control sequence. +l.39 \includegraphics + [scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydh... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.39 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/wgEncodeAwgTfbsSydh... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.39 ...12878_allpeaks_EM_4class_15shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.40 \captionof + {figure}{\textbf{Chromatine architectures around NRF1 bindin... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.42 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.42 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.43 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (3824.7662pt too wide) in paragraph at lines 39--44 +[]\OML/cmm/m/it/10 ncode[]eaks=wgEncodeAwgTfbsSydhGm\OT1/cmr/m/n/10 12878\OML/c +mm/m/it/10 Nrf\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 IggmusUniPk[]Nase[]M\OT1/cmr/m/ +n/10 12878[]\OML/cmm/m/it/10 llpeaks[]M[]class[]\OT1/cmr/m/n/10 5\OML/cmm/m/it/ +10 shift[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.45 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 45--46 +[] + [] + +! Undefined control sequence. +l.47 \includegraphics + [scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydh... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.47 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/wgEncodeAwgTfbsSydh... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.47 ...12878_allpeaks_EM_4class_15shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.48 \captionof + {figure}{\textbf{Chromatine architectures around cFOS bindin... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.50 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.50 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.50 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.51 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (3785.06384pt too wide) in paragraph at lines 47--52 +[]\OML/cmm/m/it/10 ncode[]eaks=wgEncodeAwgTfbsSydhGm\OT1/cmr/m/n/10 12878\OML/c +mm/m/it/10 CfosUniPk[]Nase[]M\OT1/cmr/m/n/10 12878[]\OML/cmm/m/it/10 llpeaks[]M +[]class[]\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 shift[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.53 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 53--54 +[] + [] + +! Undefined control sequence. +l.55 \includegraphics + [scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydh... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.55 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/wgEncodeAwgTfbsSydh... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.55 ...12878_allpeaks_EM_4class_15shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.56 \captionof + {figure}{\textbf{Chromatine architectures around max binding... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.58 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.58 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.58 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.58 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.58 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.59 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (3812.30438pt too wide) in paragraph at lines 55--60 +[]\OML/cmm/m/it/10 ncode[]eaks=wgEncodeAwgTfbsSydhGm\OT1/cmr/m/n/10 12878\OML/c +mm/m/it/10 MaxIggmusUniPk[]Nase[]M\OT1/cmr/m/n/10 12878[]\OML/cmm/m/it/10 llpea +ks[]M[]class[]\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 shift[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.61 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 61--62 +[] + [] + +! Undefined control sequence. +l.63 \includegraphics + [scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydh... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.63 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/wgEncodeAwgTfbsSydh... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.63 ...12878_allpeaks_EM_4class_15shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.64 \captionof + {figure}{\textbf{Chromatine architectures around BRCA1 bindi... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.66 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.66 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.66 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.66 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.66 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.67 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (3856.28012pt too wide) in paragraph at lines 63--68 +[]\OML/cmm/m/it/10 ncode[]eaks=wgEncodeAwgTfbsSydhGm\OT1/cmr/m/n/10 12878\OML/c +mm/m/it/10 Brca\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 a\OT1/cmr/m/n/10 300\OML/cmm/m +/it/10 IggmusUniPk[]Nase[]M\OT1/cmr/m/n/10 12878[]\OML/cmm/m/it/10 llpeaks[]M[] +class[]\OT1/cmr/m/n/10 5\OML/cmm/m/it/10 shift[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.69 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 69--70 +[] + [] + +! Undefined control sequence. +l.71 \includegraphics + [scale=0.8]{images/ch_encode_peaks/ctcf_ndr.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 8 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.71 \includegraphics[scale=0.8]{images/ch_ + encode_peaks/ctcf_ndr.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.71 ...=0.8]{images/ch_encode_peaks/ctcf_ndr.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.72 \captionof + {figure}{\textbf{Nucleosome occupancy around CTCF peaks } me... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.74 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.74 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.74 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.74 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.74 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.75 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (760.43195pt too wide) in paragraph at lines 71--76 +[]\OML/cmm/m/it/10 ncode[]eaks=ctcf[]dr:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.77 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 77--78 +[] + [] + +! Undefined control sequence. +l.79 \includegraphics + [scale=0.4]{images/ch_encode_peaks/jund_motif_associat... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.79 \includegraphics[scale=0.4]{images/ch_ + encode_peaks/jund_motif_associat... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.79 ...h_encode_peaks/jund_motif_association.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.80 \captionof + {figure}{\textbf{JunD motif association} measured around the... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.82 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.82 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.82 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.82 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.82 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.83 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (4923.26454pt too wide) in paragraph at lines 79--84 +[]\OML/cmm/m/it/10 ncode[]eaks=jund[]otif[]ssociation:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.85 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 86--86 +[] + [] + +! Undefined control sequence. +l.87 \includegraphics + [scale=0.4]{images/ch_encode_peaks/ebf1_haib_3.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.87 \includegraphics[scale=0.4]{images/ch_ + encode_peaks/ebf1_haib_3.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.87 ...4]{images/ch_encode_peaks/ebf1_haib_3.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.88 \captionof + {figure}{\textbf{EBF1 binding sites} around the dyad of nucl... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.90 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.90 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.90 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.90 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.90 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.91 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (1171.53302pt too wide) in paragraph at lines 87--92 +[]\OML/cmm/m/it/10 ncode[]eaks=ebf\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 aib[]:png +[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.93 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 93--94 +[] + [] + +! Undefined control sequence. +l.95 \includegraphics + [scale=0.5]{images/ch_encode_peaks/MA0154_3.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.95 \includegraphics[scale=0.5]{images/ch_ + encode_peaks/MA0154_3.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.95 ...=0.5]{images/ch_encode_peaks/MA0154_3.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.96 \captionof + {figure}{\textbf{EBF1 logo} from JASPAR binding model MA0154... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.96 ... from JASPAR binding model MA0154.3 \citep + {khan_jaspar_2018}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.98 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.98 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.98 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.98 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.98 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.99 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (451.17548pt too wide) in paragraph at lines 95--100 +[]\OML/cmm/m/it/10 ncode[]eaks=MA\OT1/cmr/m/n/10 0154[]\OML/cmm/m/it/10 :png[][ +][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.101 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 102--102 +[] + [] + +! Undefined control sequence. +l.103 \includegraphics + [scale=0.4]{images/ch_encode_peaks/ebf1_haib_2.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.103 \includegraphics[scale=0.4]{images/ch_ + encode_peaks/ebf1_haib_2.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.103 ...]{images/ch_encode_peaks/ebf1_haib_2.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.104 \captionof + {figure}{\textbf{EBF1 binding sites} chromatin features. \t... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.106 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.106 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.106 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.106 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.106 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.107 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (1878.18787pt too wide) in paragraph at lines 103--108 +[]\OML/cmm/m/it/10 ncode[]eaks=ebf\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 aib[]:png +[][][]$ + [] + +! Undefined control sequence. +l.114 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{void SPar-K}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +LaTeX Font Info: Try loading font information for OMS+cmr on input line 114. + +(/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd +File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available +(Font) Font shape `OMS/cmsy/m/n' tried instead on input line 114. + +! Undefined control sequence. +l.114 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{void SPar-K}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no K in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.115 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.117 \Fn + {\Function{R, K, S, I}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.117 \Fn{\Function + {R, K, S, I}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no I in font nullfont! +! Undefined control sequence. +l.119 \KwData + {$R$ a 2D matrix of numericals of dimension $N \times L$; $K$... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no ; in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ; in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ; in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +! Undefined control sequence. +l.120 \KwResult + {5 vectors of length $N$ with the cluster labels, the data ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 5 in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 114--121 +[]\OMS/cmsy/m/n/10 f + [] + + +Overfull \hbox (7.67015pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 R$ + [] + + +Overfull \hbox (16.90277pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 N \OMS/cmsy/m/n/10 ^^B + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (5.18054pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 I$ + [] + + +Overfull \hbox (9.12497pt too wide) in paragraph at lines 114--121 +\OML/cmm/m/it/10 N$ + [] + +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +! Missing $ inserted. + + $ +l.122 $CLUSTER =$ vector of 0 of size $N$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no N in font nullfont! +! Missing $ inserted. + + $ +l.127 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (82.71103pt too wide) in paragraph at lines 122--127 +[]$\OML/cmm/m/it/10 CLUSTER \OT1/cmr/m/n/10 =$ + [] + + +Overfull \hbox (9.12497pt too wide) in paragraph at lines 122--127 +\OML/cmm/m/it/10 N$ + [] + + +Overfull \hbox (74.73344pt too wide) in paragraph at lines 122--127 +\OML/cmm/m/it/10 vectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (74.73344pt too wide) in paragraph at lines 122--127 +\OML/cmm/m/it/10 vectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (74.73344pt too wide) in paragraph at lines 122--127 +\OML/cmm/m/it/10 vectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $ + [] + + +Overfull \hbox (74.73344pt too wide) in paragraph at lines 122--127 +\OML/cmm/m/it/10 vectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $ + [] + +! Undefined control sequence. +l.128 \If + {smoothing} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no ) in font nullfont! +! Missing $ inserted. + + $ +l.129 { smoothOutliers($R$) \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.129 { smoothOutliers($R$) \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.130 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 128--130 +[] + [] + + +Overfull \hbox (7.67015pt too wide) in paragraph at lines 128--130 +\OML/cmm/m/it/10 R$ + [] + +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +! Missing $ inserted. + + $ +l.131 ... $ a matrix of $K$ rows and $L$ columns\; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no K in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no R in font nullfont! +! Missing $ inserted. + + $ +l.133 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (54.00343pt too wide) in paragraph at lines 131--133 +[]$\OML/cmm/m/it/10 REF \OT1/cmr/m/n/10 =$ + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 131--133 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 131--133 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (322.8392pt too wide) in paragraph at lines 131--133 +\OML/cmm/m/it/10 select$$rowsof$$andcopythemin$$usingseedingRandom\OT1/cmr/m/n/ +10 ($$\OML/cmm/m/it/10 ;$$\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 orseedingKmeans \OT +1/cmr/m/n/10 + + [] + + +Overfull \hbox (21.1111pt too wide) in paragraph at lines 131--133 +\OT1/cmr/m/n/10 +($$\OML/cmm/m/it/10 ;$$\OT1/cmr/m/n/10 ) $ + [] + +! Missing $ inserted. + + $ +l.134 $n\_iter = 1$\; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +! Missing $ inserted. + + $ +l.136 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (53.05974pt too wide) in paragraph at lines 134--136 +[]$\OML/cmm/m/it/10 n[]iter \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (7.77773pt too wide) in paragraph at lines 134--136 +\OT1/cmr/m/n/10 1$$ $ + [] + +! Undefined control sequence. +l.137 \While + {$n\_iter != I$ or not $converged$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.139 \For + {$i=0$ to $N-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +! Missing $ inserted. + + $ +l.140 { $D =$ a vector 0 of size $K$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no K in font nullfont! +! Undefined control sequence. +l.144 \For + {$k=0$ to $K-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.144 \For{$ + k=0$ to $K-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no k in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.144 \For{$k=0$ to $K-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.145 { $ + D_{k},S\_REF_{k},S\_DAT_{k}, F\_DAT_{k} =$ distanceFast($REF_{k... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no D in font nullfont! +! Missing $ inserted. + + $ +l.145 { $D_ + {k},S\_REF_{k},S\_DAT_{k}, F\_DAT_{k} =$ distanceFast($REF_{k... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no ) in font nullfont! +! Missing $ inserted. + + $ +l.145 ...distanceFast($REF_{k,}$, $R{i,}$, $S$) \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.145 ...stanceFast($REF_{k,}$, $R{i,}$, $S$) \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no R in font nullfont! +! Missing $ inserted. + + $ +l.147 $CLUSTER_ + {i} = D_{j}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.147 $CLUSTER_{i} = D_{j}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +! Missing $ inserted. + + $ +l.148 $SHIFT\_REF_ + {i} = S\_REF_{j}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.148 $SHIFT\_REF_{i} = S\_REF_{j}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.149 $SHIFT\_DAT_ + {i} = S\_DAT_{j}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.149 $SHIFT\_DAT_{i} = S\_DAT_{j}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no F in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.150 $FLIP\_DAT_ + {i} = F\_DAT_{j}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.150 $FLIP\_DAT_{i} = F\_DAT_{j}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no D in font nullfont! +! Missing $ inserted. + + $ +l.151 $DISTANCE\_{i} = D_ + {j}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.151 $DISTANCE\_{i} = D_{j}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.152 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.153 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (55.83752pt too wide) in paragraph at lines 137--153 +[]$\OML/cmm/m/it/10 n[]iter\OT1/cmr/m/n/10 ! = + [] + + +Overfull \hbox (5.18054pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 I$ + [] + + +Overfull \hbox (44.81837pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 converged$ + [] + + +Overfull \hbox (14.00064pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 137--153 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (16.90277pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 N \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 137--153 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (19.11246pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 D \OT1/cmr/m/n/10 =$ + [] + + +Overfull \hbox (9.20833pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 K$ + [] + + +Overfull \hbox (69.19984pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 avector\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (69.19984pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 avector\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (208.32413pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 avector\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ []$$to$$[]$$ +[]; S[]REF[]; S[]DAT[]; F[]DAT[] \OT1/cmr/m/n/10 =$ + [] + + +Overfull \hbox (29.35419pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 REF[]$ + [] + + +Overfull \hbox (13.89307pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 R[]$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (130.96426pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 indexofminimumvaluein$$ $$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.49272pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 D[]$ + [] + + +Overfull \hbox (13.8848pt too wide) in paragraph at lines 137--153 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (32.9809pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 S[]REF[]$ + [] + + +Overfull \hbox (13.8848pt too wide) in paragraph at lines 137--153 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (32.82259pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 S[]DAT[]$ + [] + + +Overfull \hbox (13.8848pt too wide) in paragraph at lines 137--153 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (33.93373pt too wide) in paragraph at lines 137--153 +\OML/cmm/m/it/10 F[]DAT[]$ + [] + + +Overfull \hbox (4.21356pt too wide) in paragraph at lines 137--153 +[]$ + [] + +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no ) in font nullfont! +! Missing $ inserted. + + $ +l.154 ...HIFT\_REF$, $SHIFT\_DAT$, $FLIP\_DAT$) \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.155 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (54.00343pt too wide) in paragraph at lines 154--155 +[]$\OML/cmm/m/it/10 REF \OT1/cmr/m/n/10 =$ + [] + + +Overfull \hbox (7.67015pt too wide) in paragraph at lines 154--155 +\OML/cmm/m/it/10 R$ + [] + + +Overfull \hbox (52.15552pt too wide) in paragraph at lines 154--155 +\OML/cmm/m/it/10 CLUSTER$ + [] + + +Overfull \hbox (59.51385pt too wide) in paragraph at lines 154--155 +\OML/cmm/m/it/10 SHIFT[]REF$ + [] + + +Overfull \hbox (59.35555pt too wide) in paragraph at lines 154--155 +\OML/cmm/m/it/10 SHIFT[]DAT$ + [] + + +Overfull \hbox (50.90422pt too wide) in paragraph at lines 154--155 +\OML/cmm/m/it/10 FLIP[]DAT$ + [] + +! Undefined control sequence. +l.156 \If + {$n\_iter > 1$ and at least one value of $CLUSTER$ changed since... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.157 { $converged = false$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.157 { $converged = false$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.158 \Else + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.159 { $ + converged = true$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +! Extra }, or forgotten $. +l.159 { $converged = true$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. +l.161 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.162 \Return + {$CLUSTER, SHIFT\_REF, SHIFT\_DAT, FLIP, DISTANCE$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.162 \Return{$ + CLUSTER, SHIFT\_REF, SHIFT\_DAT, FLIP, DISTANCE$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no C in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no E in font nullfont! +! Extra }, or forgotten $. + } + +l.162 ... SHIFT\_REF, SHIFT\_DAT, FLIP, DISTANCE$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.163 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.164 \caption + {SPar-K algorithm.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.165 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.165 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (53.05974pt too wide) in paragraph at lines 156--166 +[]$\OML/cmm/m/it/10 n[]iter > + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 156--166 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (52.15552pt too wide) in paragraph at lines 156--166 +\OML/cmm/m/it/10 CLUSTER$ + [] + + +Overfull \hbox (55.37389pt too wide) in paragraph at lines 156--166 +\OML/cmm/m/it/10 converged \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (23.78249pt too wide) in paragraph at lines 156--166 +\OML/cmm/m/it/10 false$ + [] + + +Overfull \hbox (93.63034pt too wide) in paragraph at lines 156--166 +[]$ + [] + +! Undefined control sequence. +l.168 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{MATRIX smoothOutliers}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.168 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{MATRIX smoothOutliers}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.169 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.171 \Fn + {\Function{MATRIX}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.171 \Fn{\Function + {MATRIX}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no X in font nullfont! +! Undefined control sequence. +l.173 \KwData + {$MATRIX$ a 2D matrix of numericals of dimensions $N \times L$.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +! Undefined control sequence. +l.174 \KwResult + {a 2D matrix of numericals of dimensions $N \times L$. with... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 168--175 +[]\OMS/cmsy/m/n/10 f + [] + + +Overfull \hbox (47.44444pt too wide) in paragraph at lines 168--175 +\OML/cmm/m/it/10 MATRIX$ + [] + + +Overfull \hbox (16.90277pt too wide) in paragraph at lines 168--175 +\OML/cmm/m/it/10 N \OMS/cmsy/m/n/10 ^^B + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 168--175 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (16.90277pt too wide) in paragraph at lines 168--175 +\OML/cmm/m/it/10 N \OMS/cmsy/m/n/10 ^^B + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 168--175 +\OML/cmm/m/it/10 L$ + [] + +! Undefined control sequence. +l.176 \ForEach + {$ROW$ in MATRIX} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +! Missing $ inserted. + + $ +l.177 { $m$ = mean of $ROW$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no s in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +! Undefined control sequence. +l.181 \ForEach + {$value$ in $ROW$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.181 \ForEach{$ + value$ in $ROW$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no W in font nullfont! +! Extra }, or forgotten $. + } + +l.181 \ForEach{$value$ in $ROW$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.182 { \If + {$value < lower$ or $value > upper$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.182 { \If{$ + value < lower$ or $value > upper$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.182 { \If{$ + value < lower$ or $value > upper$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no < in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no > in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +! Extra }, or forgotten $. + } + +l.182 { \If{$value < lower$ or $value > upper$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.183 { \If + {$value$ has a left neighbor $l$ and a right neighbor $r$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.183 { \If{$ + value$ has a left neighbor $l$ and a right neighbor $r$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.183 { \If{$ + value$ has a left neighbor $l$ and a right neighbor $r$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no r in font nullfont! +! Extra }, or forgotten $. + } + +l.183 ...ft neighbor $l$ and a right neighbor $r$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.184 { $ + value$ = ($l$ + $r$) / 2 \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no r in font nullfont! +! Extra }, or forgotten $. +l.184 { $value$ = ($l$ + $r$) / 2 \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.185 \ElseIf + {$value$ has two left neighbors $l1$ and $l2$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.185 \ElseIf{$ + value$ has two left neighbors $l1$ and $l2$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 2 in font nullfont! +! Extra }, or forgotten $. + } + +l.185 ...ue$ has two left neighbors $l1$ and $l2$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.186 { $ + value$ = ($l1$ + $l2$) / 2 \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 2 in font nullfont! +! Extra }, or forgotten $. +l.186 { $value$ = ($l1$ + $l2$) / 2 \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.187 \ElseIf + {$value$ has two right neighbors $r1$ and $r2$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.187 \ElseIf{$ + value$ has two right neighbors $r1$ and $r2$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 2 in font nullfont! +! Extra }, or forgotten $. + } + +l.187 ...e$ has two right neighbors $r1$ and $r2$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.188 { $ + value$ = ($r1$ + $r2$) / 2 \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no 2 in font nullfont! +! Extra }, or forgotten $. +l.188 { $value$ = ($r1$ + $r2$) / 2 \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.189 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.190 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.191 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.192 \Return + {$MATRIX$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.192 \Return{$ + MATRIX$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no X in font nullfont! +! Extra }, or forgotten $. + } + +l.192 \Return{$MATRIX$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.193 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.194 \caption + {Smooth the data matrix by removing outliers.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.195 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.195 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.195 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.195 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (46.40904pt too wide) in paragraph at lines 176--196 +[]$\OML/cmm/m/it/10 ROW$ + [] + + +Overfull \hbox (8.78014pt too wide) in paragraph at lines 176--196 +\OML/cmm/m/it/10 m$ + [] + + +Overfull \hbox (26.40904pt too wide) in paragraph at lines 176--196 +\OML/cmm/m/it/10 ROW$ + [] + + +Overfull \hbox (7.7778pt too wide) in paragraph at lines 176--196 +\OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (161.48718pt too wide) in paragraph at lines 176--196 +\OML/cmm/m/it/10 standarddeviationof$$ $$\OT1/cmr/m/n/10 =$$\OMS/cmsy/m/n/10 ^^ +@\OT1/cmr/m/n/10 3\OMS/cmsy/m/n/10 ^^C$$ $$\OT1/cmr/m/n/10 =$$+3\OMS/cmsy/m/n/1 +0 ^^C$$ []$$\OML/cmm/m/it/10 in$$[]$ + [] + + +Overfull \hbox (9.6366pt too wide) in paragraph at lines 176--196 +\OML/cmm/m/it/10 or$ + [] + + +Overfull \hbox (168.5776pt too wide) in paragraph at lines 176--196 +[]$$\OML/cmm/m/it/10 hasaleftneighbor$$andarightneighbor$$[]$$\OT1/cmr/m/n/10 = + + [] + + +Overfull \hbox (145.25557pt too wide) in paragraph at lines 176--196 +\OT1/cmr/m/n/10 ($$+$$)\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 2 []$$\OML/cmm/m/it/10 + hastwoleftneighbors$$and$$[]$$\OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (150.57101pt too wide) in paragraph at lines 176--196 +\OT1/cmr/m/n/10 ($$+$$)\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 2 []$$\OML/cmm/m/it/10 + hastworightneighbors$$and$$[]$$\OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (218.06032pt too wide) in paragraph at lines 176--196 +\OT1/cmr/m/n/10 ($$+$$)\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 2 []$$[]$ + [] + +! Undefined control sequence. +l.199 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{d,s\_xf,s\_y,f\_y dista... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.199 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{d,s\_xf,s\_y,f\_y dista... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.200 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.202 \Fn + {\Function{X,Y,S}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.202 \Fn{\Function + {X,Y,S}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no X in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +! Undefined control sequence. +l.203 { \KwData + {$X$ and $Y$ two vectors of size $L$ and $S$ the allowed shi... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +! Undefined control sequence. +l.204 \KwResult + {the distance between $X$ and $Y$, the shift of $X$ and $Y$... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +! Undefined control sequence. +l.205 \tcc + {initialize all variables and data structures} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no ) in font nullfont! +! Missing $ inserted. + + $ +l.206 initialize() \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.207 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 199--207 +[]\OMS/cmsy/m/n/10 f[][][] + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (6.80557pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 L$ + [] + + +Overfull \hbox (6.70831pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 S$ + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 199--207 +\OML/cmm/m/it/10 Y$ + [] + +! Undefined control sequence. +l.208 \For + {$i=0$ to $n-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +! Undefined control sequence. +l.209 { $SUM\_X_0 \pluseq + X_i $ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.209 { $SUM\_X_0 \pluseq X_i $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no 2 in font nullfont! +! Missing $ inserted. + + $ +l.210 $SUM\_X2_ + 0 \pluseq X_i^2$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.210 $SUM\_X2_0 \pluseq + X_i^2$ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.210 $SUM\_X2_0 \pluseq X_i^2$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.211 $SUM\_Y_ + 0 \pluseq Y_i $ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.211 $SUM\_Y_0 \pluseq + Y_i $ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.211 $SUM\_Y_0 \pluseq Y_i $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no 2 in font nullfont! +! Missing $ inserted. + + $ +l.212 $SUM\_Y2_ + 0 \pluseq Y_i^2$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.212 $SUM\_Y2_0 \pluseq + Y_i^2$ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.212 $SUM\_Y2_0 \pluseq Y_i^2$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.213 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +Missing character: There is no i in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.215 \For + {$s=1$ to $s=S-1$ } +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.215 \For{$ + s=1$ to $s=S-1$ } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no s in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. +l.215 \For{$s=1$ to $s=S-1$ } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.216 { $ + SUM\_X_{s} = SUM\_X_{s-1} + X_{i-n} + X_{i} $ \; +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +! Missing $ inserted. + + $ +l.216 { $SUM\_X_ + {s} = SUM\_X_{s-1} + X_{i-n} + X_{i} $ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.216 ... SUM\_X_{s-1} + X_{i-n} + X_{i} $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no 2 in font nullfont! +! Missing $ inserted. + + $ +l.217 $SUM\_X2_ + {s} = SUM\_X2_{s-1} + X_{i-n}^{2} + X_{i}^{2}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.217 ...M\_X2_{s-1} + X_{i-n}^{2} + X_{i}^{2}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.218 $SUM\_Y_ + {s} = SUM\_Y_{s-1} + Y_{i-n} + Y_{i} $ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.218 ... SUM\_Y_{s-1} + Y_{i-n} + Y_{i} $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no 2 in font nullfont! +! Missing $ inserted. + + $ +l.219 $SUM\_Y2_ + {s} = SUM\_Y2_{s-1} + Y_{i-n}^{2} + Y_{i}^{2}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.219 ...M\_Y2_{s-1} + Y_{i-n}^{2} + Y_{i}^{2}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no i in font nullfont! +! Undefined control sequence. +l.220 $i \pluseq + 1$ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. +l.221 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.222 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.00064pt too wide) in paragraph at lines 208--222 +[]$\OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 208--222 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (13.78015pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 208--222 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (49.80287pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 SUM[]X[]X[]$ + [] + + +Overfull \hbox (18.04169pt too wide) in paragraph at lines 208--222 +[]$[]\OML/cmm/m/it/10 X[]$ + [] + + +Overfull \hbox (13.62097pt too wide) in paragraph at lines 208--222 +[]$[]\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (17.00005pt too wide) in paragraph at lines 208--222 +[]$[]\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (23.28818pt too wide) in paragraph at lines 208--222 +[]$$\OML/cmm/m/it/10 to$$[]$[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (55.991pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 SUM[]X[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (30.58516pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 X[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (11.61401pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 X[]$ + [] + + +Overfull \hbox (14.82983pt too wide) in paragraph at lines 208--222 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (61.77571pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 SUM[]X\OT1/cmr/m/n/10 2[] + + [] + + +Overfull \hbox (30.58516pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 X[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (13.55556pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 X[]$ + [] + + +Overfull \hbox (14.82983pt too wide) in paragraph at lines 208--222 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (53.51183pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 SUM[]Y[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (28.10599pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 Y[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (9.13484pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (14.82983pt too wide) in paragraph at lines 208--222 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (60.73407pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 SUM[]Y\OT1/cmr/m/n/10 2[] + + [] + + +Overfull \hbox (28.10599pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 Y[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (12.51392pt too wide) in paragraph at lines 208--222 +\OML/cmm/m/it/10 Y[]$ + [] + +! Undefined control sequence. +l.223 \tcc + {compute all distances with $X$ having a shift of 0, $Y$ having ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no ) in font nullfont! +! Missing $ inserted. + + $ +l.224 fillFirstRow() \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.227 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 223--227 +[] + [] + + +Overfull \hbox (9.06943pt too wide) in paragraph at lines 223--227 +\OML/cmm/m/it/10 X$ + [] + + +Overfull \hbox (8.02779pt too wide) in paragraph at lines 223--227 +\OML/cmm/m/it/10 Y$ + [] + + +Overfull \hbox (146.50739pt too wide) in paragraph at lines 223--227 +\OML/cmm/m/it/10 fillFirstColl\OT1/cmr/m/n/10 () \OML/cmm/m/it/10 fillRemaining +\OT1/cmr/m/n/10 () $ + [] + +! Undefined control sequence. +l.228 \tcc + {if more than one, find the minimal distance which also minimize... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Missing $ inserted. + + $ +l.229 ...t\_s\_x = best\_s\_y = best\_f\_y = 0$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.230 \For + {$tripplet$ in $MIN\_DIST$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.230 \For{$ + tripplet$ in $MIN\_DIST$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. + } + +l.230 \For{$tripplet$ in $MIN\_DIST$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.231 { $ + s\_x = tripplet_{0}$ \; +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no s in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Missing $ inserted. + + $ +l.231 { $s\_x = tripplet_ + {0}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.231 { $s\_x = tripplet_{0}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Missing $ inserted. + + $ +l.232 $s\_y = tripplet_ + {1}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.232 $s\_y = tripplet_{1}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +! Missing $ inserted. + + $ +l.233 $f\_y = tripplet_ + {2}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.233 $f\_y = tripplet_{2}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +! Missing $ inserted. + + $ +l.234 $min\_score = \infty + $ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.234 $min\_score = \infty$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.235 \If + {$SCORES_{s\_x,s\_y} < min\_score$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.235 \If{$ + SCORES_{s\_x,s\_y} < min\_score$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no S in font nullfont! +! Missing $ inserted. + + $ +l.235 \If{$SCORES_ + {s\_x,s\_y} < min\_score$} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.236 { $min\_score = SCORES_{s\_x,s\_y}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.240 $best\_d = DIST_ + {s\_x,s\_y,f\_y}$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.240 $best\_d = DIST_{s\_x,s\_y,f\_y}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.241 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.242 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.243 \Return + {$best\_d,best\_s\_x,best\_s\_y,best\_f\_y$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.243 \Return{$ + best\_d,best\_s\_x,best\_s\_y,best\_f\_y$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no y in font nullfont! +! Extra }, or forgotten $. + } + +l.243 ...est\_d,best\_s\_x,best\_s\_y,best\_f\_y$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.244 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 228--244 +[] + [] + + +Overfull \hbox (32.46492pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 best[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (38.20482pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 best[]s[]x \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (37.75114pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 best[]s[]y \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (39.0359pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 best[]f[]y \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 228--244 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (9.44748pt too wide) in paragraph at lines 228--244 +[]$$\OML/cmm/m/it/10 in$[]$[]$[] + [] + + +Overfull \hbox (4.48613pt too wide) in paragraph at lines 228--244 +[]$ + [] + + +Overfull \hbox (4.48613pt too wide) in paragraph at lines 228--244 +[]$ + [] + + +Overfull \hbox (4.48613pt too wide) in paragraph at lines 228--244 +[]$ + [] + + +Overfull \hbox (10.00002pt too wide) in paragraph at lines 228--244 +\OMS/cmsy/m/n/10 1$ + [] + + +Overfull \hbox (29.82063pt too wide) in paragraph at lines 228--244 +[]$$[] \OML/cmm/m/it/10 < + [] + + +Overfull \hbox (41.53554pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 min[]score$ + [] + + +Overfull \hbox (52.09105pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 min[]score \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (63.50188pt too wide) in paragraph at lines 228--244 +\OML/cmm/m/it/10 SCORES[]$ + [] + + +Overfull \hbox (2.77771pt too wide) in paragraph at lines 228--244 +[]$ $[][] + [] + + +Overfull \hbox (2.77771pt too wide) in paragraph at lines 228--244 +[]$ $[][] + [] + + +Overfull \hbox (2.77771pt too wide) in paragraph at lines 228--244 +[]$ $[] + [] + + +Overfull \hbox (30.63095pt too wide) in paragraph at lines 228--244 +[]$ + [] + + +! LaTeX Error: The font size command \normalsize is not defined: + there is probably something wrong with the class file. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.244 + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} +! Undefined control sequence. + ...abel{suppl_smileseq_auc_2}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_smileseq_auc_2}{{}{}} +! Undefined control sequence. + ...uppl_encode_peaks_em_ctcf}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_em_ctcf}{{}{}} +! Undefined control sequence. + ...uppl_encode_peaks_em_nrf1}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_em_nrf1}{{}{}} +! Undefined control sequence. + ...uppl_encode_peaks_em_cfos}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_em_cfos}{{}{}} +! Undefined control sequence. + ...suppl_encode_peaks_em_max}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_em_max}{{}{}} +! Undefined control sequence. + ...ppl_encode_peaks_em_brca1}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_em_brca1}{{}{}} +! Undefined control sequence. + ...ppl_encode_peaks_ctcf_ndr}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_ctcf_ndr}{{}{}} +! Undefined control sequence. + ...de_peaks_jund_association}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_jund_association}{{}{}} +! Undefined control sequence. + ...pl_encode_peaks_ebf1_nucl}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_ebf1_nucl}{{}{}} +! Undefined control sequence. + ...pl_encode_peaks_ebf1_logo}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_ebf1_logo}{{}{}} +! Undefined control sequence. + ...l_encode_peaks_ebf1_chrom}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{suppl_encode_peaks_ebf1_chrom}{{}{}} +! Undefined control sequence. + \newlabel{algo_spark}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{algo_spark}{{}{}} +! Undefined control sequence. + ...abel{algo_smooth_outliers}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{algo_smooth_outliers}{{}{}} +! Undefined control sequence. + \newlabel{algo_distance_fast}{{}{\thepage + }} +l.244 + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +\newlabel{algo_distance_fast}{{}{}} +] + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.246 \caption + {Fast algorithm to compute the correlation distance with shif... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no F in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.247 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing } inserted. + + } +l.247 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 246--248 +[] + [] + +! Undefined control sequence. +l.251 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{initialize}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.251 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{initialize}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.252 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.254 \Fn + {\Function{}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.254 \Fn{\Function + {}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 251--256 +[]\OMS/cmsy/m/n/10 f + [] + +! Missing $ inserted. + + $ +l.257 $l\_half = L / 2$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no n in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 3 in font nullfont! +! Extra }, or forgotten $. +l.276 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.277 \caption + {A routine of distanceFast() that initializes all the necessa... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.278 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.278 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.278 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (53.93639pt too wide) in paragraph at lines 257--279 +[]$\OML/cmm/m/it/10 l[]half \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (16.8056pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 L=\OT1/cmr/m/n/10 2$ + [] + + +Overfull \hbox (126.35902pt too wide) in paragraph at lines 257--279 +\OT1/cmr/m/n/10 3\OML/cmm/m/it/10 Dmatrixof\OT1/cmr/m/n/10 3\OML/cmm/m/it/10 of +dimensions$$ $[] + [] + + +Overfull \hbox (126.35902pt too wide) in paragraph at lines 257--279 +\OT1/cmr/m/n/10 3\OML/cmm/m/it/10 Dmatrixof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 of +dimensions$$ $[] + [] + + +Overfull \hbox (80.01933pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 avectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (80.01933pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 avectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (80.01933pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 avectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $[] + [] + + +Overfull \hbox (80.01933pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 avectorof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 ofsize$$ $ + [] + + +Overfull \hbox (131.64491pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 a\OT1/cmr/m/n/10 2\OML/cmm/m/it/10 Dmatrixof\OT1/cmr/m/n/10 0\ +OML/cmm/m/it/10 ofdimensions$$ $[] + [] + + +Overfull \hbox (100.16243pt too wide) in paragraph at lines 257--279 +\OML/cmm/m/it/10 anemptylistoftriplets $[] + [] + + +Overfull \hbox (570.10634pt too wide) in paragraph at lines 257--279 +[]$ + [] + +! Undefined control sequence. +l.282 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{void fillFirstRow}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.282 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{void fillFirstRow}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no w in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.283 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.284 \Fn + {\Function{}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.284 \Fn{\Function + {}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.287 $from\_x = 0$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.289 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 282--289 +[]\OMS/cmsy/m/n/10 f + [] + + +Overfull \hbox (40.65977pt too wide) in paragraph at lines 282--289 +\OML/cmm/m/it/10 from[]x \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 282--289 +\OT1/cmr/m/n/10 0$ + [] + +! Undefined control sequence. +l.290 \For + {$i = 0$ to $S-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +! Undefined control sequence. +l.291 { \tcc + {forward orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.292 $from\_y = i$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.294 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.00064pt too wide) in paragraph at lines 290--294 +[]$\OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 290--294 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (14.48611pt too wide) in paragraph at lines 290--294 +\OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 290--294 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (40.2061pt too wide) in paragraph at lines 290--294 +\OML/cmm/m/it/10 from[]y \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (3.44513pt too wide) in paragraph at lines 290--294 +\OML/cmm/m/it/10 i$ + [] + +! Missing $ inserted. + + $ +l.295 $SUM_XY{from\_x,from\_y,0} = 0$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.296 \For + {$j = 0$ to $n-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.296 \For{$ + j = 0$ to $n-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.296 \For{$j = 0$ to $n-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.297 { $ + SUM\_XY_{from\_x,from\_y,0} \pluseq X_{from\_x+j} * Y_{from\_y+... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.297 { $SUM\_XY_ + {from\_x,from\_y,0} \pluseq X_{from\_x+j} * Y_{from\_y+... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.297 { $SUM\_XY_{from\_x,from\_y,0} \pluseq + X_{from\_x+j} * Y_{from\_y+... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.297 ...pluseq X_{from\_x+j} * Y_{from\_y+j}$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.297 ...useq X_{from\_x+j} * Y_{from\_y+j}$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.298 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (144.15685pt too wide) in paragraph at lines 295--298 +[]$\OML/cmm/m/it/10 SUM[]Y[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 295--298 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (113.67491pt too wide) in paragraph at lines 295--298 +\OML/cmm/m/it/10 to$$[]$[]$[]X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (40.12045pt too wide) in paragraph at lines 295--298 +\OML/cmm/m/it/10 Y[]$ + [] + +! Missing $ inserted. + + $ +l.301 ...Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.302 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.303 { $ + c = 0$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no c in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +! Extra }, or forgotten $. +l.303 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.304 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.88307pt too wide) in paragraph at lines 300--304 +[]$\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (255.66486pt too wide) in paragraph at lines 300--304 +[]$ + [] + + +Overfull \hbox (89.5034pt too wide) in paragraph at lines 300--304 +[][]$ + [] + +! Missing $ inserted. + + $ +l.306 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.307 $DIST_ + {from\_x,from\_y,0} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.307 $DIST_{from\_x,from\_y,0} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.308 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 306--308 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 306--308 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 306--308 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 306--308 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 306--308 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.310 $SCORES_{from\_x,from\_y} = \abs + {l\_half - (n\_half + from\_x)} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.311 \abs + {l\_half - (n\_half + fro... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.311 ... \abs{l\_half - (n\_half + from\_y)}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.312 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.312 \If{$ + d < min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no < in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.312 \If{$d < min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.313 { $ + min\_distance = d$ \; +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.315 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.316 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.316 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.316 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.317 { append a triplet $ + (from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.317 ...from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.318 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (125.82008pt too wide) in paragraph at lines 310--318 +[]$\OML/cmm/m/it/10 SCORES[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (119.68767pt too wide) in paragraph at lines 310--318 +[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (111.45619pt too wide) in paragraph at lines 310--318 +[]$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 310--318 +\OML/cmm/m/it/10 appendatriplet$[][] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 310--318 +\OML/cmm/m/it/10 to$[]$ []$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 310--318 +[]$[]$[][] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 310--318 +\OML/cmm/m/it/10 to$[]$ $ + [] + +! Undefined control sequence. +l.319 \tcc + {reverse orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.320 $SUM_XY{from\_x,from\_y,1} = 0$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.321 \For + {$j = 0$ to $n-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.321 \For{$ + j = 0$ to $n-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.321 \For{$j = 0$ to $n-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.322 { $ + SUM\_XY_{from\_x,from\_y,1} \pluseq X_{from\_x+j} * Y_{to\_y-j-... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.322 { $SUM\_XY_ + {from\_x,from\_y,1} \pluseq X_{from\_x+j} * Y_{to\_y-j-... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.322 { $SUM\_XY_{from\_x,from\_y,1} \pluseq + X_{from\_x+j} * Y_{to\_y-j-... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.322 ...pluseq X_{from\_x+j} * Y_{to\_y-j-1}$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.322 ...useq X_{from\_x+j} * Y_{to\_y-j-1}$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.323 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 319--323 +[] + [] + + +Overfull \hbox (124.15685pt too wide) in paragraph at lines 319--323 +\OML/cmm/m/it/10 SUM[]Y[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 319--323 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (113.67491pt too wide) in paragraph at lines 319--323 +\OML/cmm/m/it/10 to$$[]$[]$[]X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (37.78009pt too wide) in paragraph at lines 319--323 +\OML/cmm/m/it/10 Y[]$ + [] + +! Missing $ inserted. + + $ +l.326 ...Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.327 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.328 { $ + c = 0$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no c in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +! Extra }, or forgotten $. +l.328 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.329 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.88307pt too wide) in paragraph at lines 325--329 +[]$\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (255.66486pt too wide) in paragraph at lines 325--329 +[]$ + [] + + +Overfull \hbox (89.5034pt too wide) in paragraph at lines 325--329 +[][]$ + [] + +! Missing $ inserted. + + $ +l.331 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.332 $DIST_ + {from\_x,from\_y,1} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.332 $DIST_{from\_x,from\_y,1} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.333 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 331--333 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 331--333 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 331--333 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 331--333 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 331--333 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.334 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.335 { $min\_distance = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.337 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.338 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.338 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.338 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.339 { append a triplet $ + (from\_x,from\_y, 1)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.339 ...from\_x,from\_y, 1)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.340 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.341 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.342 \caption + {A routine of distanceFast() computing all distances with $X$... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.342 ...anceFast() computing all distances with $ + X$ having a shift of 0. Th... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no X in font nullfont! +! Extra }, or forgotten $. +l.342 ...ll variables declared in distanceFast().} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.343 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.343 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.343 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.343 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.343 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 334--344 +[]$\OML/cmm/m/it/10 d < + [] + + +Overfull \hbox (35.17622pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 min[]dist$ + [] + + +Overfull \hbox (66.0038pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 min[]distance \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 d$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 appendatriplet$[][] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 to$[]$ []$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 334--344 +[]$[]$[][] + [] + + +Overfull \hbox (650.9838pt too wide) in paragraph at lines 334--344 +\OML/cmm/m/it/10 to$[]$ []$$havingashiftof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 :Th +isfunctioncanaccessandmodifyallvariablesdeclaredindistanceFast\OT1/cmr/m/n/10 ( +)\OML/cmm/m/it/10 :$ + [] + +! Undefined control sequence. +l.347 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{void fillFirstCol}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.347 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{void fillFirstCol}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.348 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.349 \Fn + {\Function{}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.349 \Fn{\Function + {}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no ; in font nullfont! +! Missing $ inserted. + + $ +l.351 ... = 0$ ; $to\_y = from\_y + n$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.354 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 347--354 +[]\OMS/cmsy/m/n/10 f + [] + + +Overfull \hbox (40.2061pt too wide) in paragraph at lines 347--354 +\OML/cmm/m/it/10 from[]y \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 347--354 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (24.27545pt too wide) in paragraph at lines 347--354 +\OML/cmm/m/it/10 to[]y \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (37.42839pt too wide) in paragraph at lines 347--354 +\OML/cmm/m/it/10 from[]y \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (6.00235pt too wide) in paragraph at lines 347--354 +\OML/cmm/m/it/10 n$ + [] + +! Undefined control sequence. +l.355 \For + {$i=0$ to $S-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +! Missing $ inserted. + + $ +l.356 { $from\_x = i$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.358 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.00064pt too wide) in paragraph at lines 355--358 +[]$\OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 355--358 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (14.48611pt too wide) in paragraph at lines 355--358 +\OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 355--358 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (40.65977pt too wide) in paragraph at lines 355--358 +\OML/cmm/m/it/10 from[]x \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (3.44513pt too wide) in paragraph at lines 355--358 +\OML/cmm/m/it/10 i$ + [] + +! Undefined control sequence. +l.359 \tcc + {forward orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.360 $SUM\_XY_{from\_x,from\_y,0} = 0 $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.361 \For + {$j=0$ to $n-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.361 \For{$ + j=0$ to $n-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.361 \For{$j=0$ to $n-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.362 { $ + SUM\_XY{from\_x,from\_y,0} \pluseq X_{from\_x+j}*Y_{from\_y+j} $... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +! Undefined control sequence. +l.362 { $SUM\_XY{from\_x,from\_y,0} \pluseq + X_{from\_x+j}*Y_{from\_y+j} $... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no X in font nullfont! +! Missing $ inserted. + + $ +l.362 { $SUM\_XY{from\_x,from\_y,0} \pluseq X_ + {from\_x+j}*Y_{from\_y+j} $... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.362 ... \pluseq X_{from\_x+j}*Y_{from\_y+j} $ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.362 ...pluseq X_{from\_x+j}*Y_{from\_y+j} $ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.363 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 359--363 +[] + [] + + +Overfull \hbox (108.23744pt too wide) in paragraph at lines 359--363 +\OML/cmm/m/it/10 SUM[]XY[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 359--363 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (8.45834pt too wide) in paragraph at lines 359--363 +[]$$\OML/cmm/m/it/10 to$$[]$[][][] + [] + + +Overfull \hbox (39.5429pt too wide) in paragraph at lines 359--363 +[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (40.12045pt too wide) in paragraph at lines 359--363 +\OML/cmm/m/it/10 Y[]$ + [] + +! Missing $ inserted. + + $ +l.365 ...Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.366 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.367 { $ + c = 0$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no c in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +! Extra }, or forgotten $. +l.367 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.368 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.88307pt too wide) in paragraph at lines 364--368 +[]$\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (255.66486pt too wide) in paragraph at lines 364--368 +[]$ + [] + + +Overfull \hbox (89.5034pt too wide) in paragraph at lines 364--368 +[][]$ + [] + +! Missing $ inserted. + + $ +l.370 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.371 $DIST_ + {from\_x,from\_y,0} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.371 $DIST_{from\_x,from\_y,0} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.372 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 370--372 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 370--372 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 370--372 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 370--372 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 370--372 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.374 $SCORES_{from\_x,from\_y} = \abs + {l\_half - (n\_half + from\_x)} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.375 \abs + {l\_half - (n\_half + from\_y)}$ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.375 ... \abs{l\_half - (n\_half + from\_y)}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.376 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.376 \If{$ + d < min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no < in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.376 \If{$d < min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.377 { $ + min\_distance = d$ \; +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.379 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.380 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.380 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.380 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.381 { append a triplet $ + (from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.381 ...from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.382 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (125.82008pt too wide) in paragraph at lines 374--382 +[]$\OML/cmm/m/it/10 SCORES[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (119.68767pt too wide) in paragraph at lines 374--382 +[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (111.45619pt too wide) in paragraph at lines 374--382 +[]$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 374--382 +\OML/cmm/m/it/10 appendatriplet$[][] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 374--382 +\OML/cmm/m/it/10 to$[]$ []$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 374--382 +[]$[]$[][] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 374--382 +\OML/cmm/m/it/10 to$[]$ $ + [] + +! Undefined control sequence. +l.383 \tcc + {reverse orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.384 $SUM\_XY_{from\_x,S-1,1} = 0$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.385 \For + {$j=0$ to $n-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.385 \For{$ + j=0$ to $n-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.385 \For{$j=0$ to $n-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.386 { $ + SUM\_XY_{from\_x,S-1,1} \pluseq X_{from\_x+j} * Y_{to\_y\_rev-1-... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.386 { $SUM\_XY_ + {from\_x,S-1,1} \pluseq X_{from\_x+j} * Y_{to\_y\_rev-1-... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.386 { $SUM\_XY_{from\_x,S-1,1} \pluseq + X_{from\_x+j} * Y_{to\_y\_rev-1-... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.386 ...eq X_{from\_x+j} * Y_{to\_y\_rev-1-j}$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.386 ... X_{from\_x+j} * Y_{to\_y\_rev-1-j}$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.387 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 383--387 +[] + [] + + +Overfull \hbox (99.80424pt too wide) in paragraph at lines 383--387 +\OML/cmm/m/it/10 SUM[]XY[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 383--387 +\OT1/cmr/m/n/10 0$ + [] + + +Overfull \hbox (105.24171pt too wide) in paragraph at lines 383--387 +[]$$\OML/cmm/m/it/10 to$$[]$[]$[]X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (49.75365pt too wide) in paragraph at lines 383--387 +\OML/cmm/m/it/10 Y[]$ + [] + +! Missing $ inserted. + + $ +l.389 ...{n*SUM\_Y2_{S-1} - SUM\_Y_{S-1}^{2}}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.390 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.391 { $ + c = 0$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no c in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +! Extra }, or forgotten $. +l.391 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.392 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.88307pt too wide) in paragraph at lines 388--392 +[]$\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (238.65317pt too wide) in paragraph at lines 388--392 +[]$ + [] + + +Overfull \hbox (89.5034pt too wide) in paragraph at lines 388--392 +[][]$ + [] + +! Missing $ inserted. + + $ +l.394 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.395 $DIST_ + {from\_x,from\_y,1} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.395 $DIST_{from\_x,from\_y,1} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.396 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 394--396 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 394--396 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 394--396 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 394--396 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 394--396 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.397 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.398 { $min\_distance = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.400 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.401 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.401 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.401 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.402 { append a triplet $ + (from\_x,S-1, 1)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.402 ...t $(from\_x,S-1, 1)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.403 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.404 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.405 \caption + {A routine of distanceFast() computing all distances with $Y$... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.405 ...anceFast() computing all distances with $ + Y$ having a shift of 0. Th... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no Y in font nullfont! +! Extra }, or forgotten $. +l.405 ...ll variables declared in distanceFast().} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.406 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.406 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.406 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.406 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.406 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 397--407 +[]$\OML/cmm/m/it/10 d < + [] + + +Overfull \hbox (35.17622pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 min[]dist$ + [] + + +Overfull \hbox (66.0038pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 min[]distance \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 d$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 appendatriplet$[] + [] + + +Overfull \hbox (11.23605pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 to$[]$ []$ + [] + + +Overfull \hbox (64.82257pt too wide) in paragraph at lines 397--407 +[]$[]$[] + [] + + +Overfull \hbox (659.11642pt too wide) in paragraph at lines 397--407 +\OML/cmm/m/it/10 to$[]$ []$$havingashiftof\OT1/cmr/m/n/10 0\OML/cmm/m/it/10 :Th +isfunctioniscanaccessandmodifyallvariablesdeclaredindistanceFast\OT1/cmr/m/n/10 + ()\OML/cmm/m/it/10 :$ + [] + +! Undefined control sequence. +l.410 \SetKwProg + {Fn}{}{\{}{}\SetKwFunction{Function}{void fillRemaining}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no n in font nullfont! +! Undefined control sequence. +l.410 \SetKwProg{Fn}{}{\{}{}\SetKwFunction + {Function}{void fillRemaining}% +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no F in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! + +! LaTeX Error: Environment algorithm undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.411 \begin{algorithm} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.412 \Fn + {\Function{}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.412 \Fn{\Function + {}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.413 { \For + {$i=1$ to $S-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no ; in font nullfont! +! Missing $ inserted. + + $ +l.414 ...rom\_x = i$ ; $to\_x = from\_x + n $ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Undefined control sequence. +l.415 \For + {$j=1$ to $S-1$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.415 \For{$ + j=1$ to $S-1$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no j in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. + } + +l.415 \For{$j=1$ to $S-1$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.416 { $ + from\_y = j$ \; +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.418 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (25.00002pt too wide) in paragraph at lines 410--418 +[]\OMS/cmsy/m/n/10 f + [] + + +Overfull \hbox (14.00064pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 410--418 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (14.48611pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 410--418 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (40.65977pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 from[]x \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (3.44513pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 i$ + [] + + +Overfull \hbox (24.72913pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 to[]x \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (37.88206pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 from[]x \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (6.00235pt too wide) in paragraph at lines 410--418 +\OML/cmm/m/it/10 n$ + [] + + +Overfull \hbox (8.45834pt too wide) in paragraph at lines 410--418 +[]$$\OML/cmm/m/it/10 to$$[]$[] + [] + +! Undefined control sequence. +l.419 \tcc + {forward orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.420 ..._{from\_y-1} + X_{to\_x-1}*Y{to\_y-1}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no c in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no * in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no Y in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +! Missing $ inserted. + + $ +l.422 ...*SUM\_Y2_{from\_Y} - SUM\_Y_{from\_Y}^2}} + $ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +\frac #1#2->{\begingroup #1\endgroup \over #2} + +l.422 ...*SUM\_Y2_{from\_Y} - SUM\_Y_{from\_Y}^2}} + $ \; +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.422 ...\_Y2_{from\_Y} - SUM\_Y_{from\_Y}^2}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.423 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 419--423 +[] + [] + + +Overfull \hbox (108.23744pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 SUM[]XY[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (125.93202pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 SUM[]XY[] \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (48.21129pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (48.28192pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 Y[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (35.52368pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (38.96988pt too wide) in paragraph at lines 419--423 +\OML/cmm/m/it/10 Y[]$ + [] + + +Overfull \hbox (259.02142pt too wide) in paragraph at lines 419--423 +[][][][]$[]$ + [] + +! Undefined control sequence. +l.424 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +! Missing $ inserted. + + $ +l.425 { $c = 0$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.425 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.426 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 424--426 +[] + [] + + +Overfull \hbox (14.88307pt too wide) in paragraph at lines 424--426 +\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 424--426 +\OT1/cmr/m/n/10 0$ + [] + +! Missing $ inserted. + + $ +l.427 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.428 $DIST_ + {from\_x,from\_y,0} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.428 $DIST_{from\_x,from\_y,0} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.429 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 427--429 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 427--429 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 427--429 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 427--429 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 427--429 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.431 $SCORES_{from\_x,from\_y} = \abs + {l\_half - (n\_half + from\_x)} + +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.432 \abs + {l\_half - (n\_half + from\_y)}$ \; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.432 ... \abs{l\_half - (n\_half + from\_y)}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.433 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (125.82008pt too wide) in paragraph at lines 431--433 +[]$\OML/cmm/m/it/10 SCORES[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (119.68767pt too wide) in paragraph at lines 431--433 +[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (111.45619pt too wide) in paragraph at lines 431--433 +[]$ + [] + +! Undefined control sequence. +l.434 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.435 { $min\_distance = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.437 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.438 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.438 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.438 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.439 { append a triplet $ + (from\_x,from\_y,0)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.439 ...(from\_x,from\_y,0)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.440 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 434--440 +[]$\OML/cmm/m/it/10 d < + [] + + +Overfull \hbox (35.17622pt too wide) in paragraph at lines 434--440 +\OML/cmm/m/it/10 min[]dist$ + [] + + +Overfull \hbox (66.0038pt too wide) in paragraph at lines 434--440 +\OML/cmm/m/it/10 min[]distance \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 434--440 +\OML/cmm/m/it/10 d$ + [] + + +Overfull \hbox (76.05862pt too wide) in paragraph at lines 434--440 +\OML/cmm/m/it/10 appendatriplet$[][]$to$[]$ []$ + [] + + +Overfull \hbox (76.05862pt too wide) in paragraph at lines 434--440 +[]$[]$[][]$\OML/cmm/m/it/10 to$[]$ $ + [] + +! Undefined control sequence. +l.441 \tcc + {reverse orientation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +! Missing $ inserted. + + $ +l.442 $j\_rev = S - j - 1$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no + in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no U in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +! Missing $ inserted. + + $ +l.445 $SUM\_XY_ + {from\_x,from\_y\_rev,1} = SUM\_XY_{from\_x-1,from\_y\_re... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.445 ...y\_rev} + X_{to\_x-1}*Y{from\_y\_rev}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.446 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 441--446 +[] + [] + + +Overfull \hbox (29.89764pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 j[]rev \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (14.48611pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (12.46829pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 j \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 441--446 +\OT1/cmr/m/n/10 1$ + [] + + +Overfull \hbox (2.77771pt too wide) in paragraph at lines 441--446 +[]$ $[][] + [] + + +Overfull \hbox (79.91801pt too wide) in paragraph at lines 441--446 +[]$[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (137.79448pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 SUM[]XY[] \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (48.21129pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (37.33173pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 Y[] \OT1/cmr/m/n/10 + + [] + + +Overfull \hbox (35.52368pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 X[] \OMS/cmsy/m/n/10 ^^C + [] + + +Overfull \hbox (52.33002pt too wide) in paragraph at lines 441--446 +\OML/cmm/m/it/10 Y[]$ + [] + +! Missing $ inserted. + + $ +l.448 ...m\_y\_rev} - SUM\_Y_{from\_y_rev}^2}}$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.449 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (34.88307pt too wide) in paragraph at lines 447--449 +[]$\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (277.39697pt too wide) in paragraph at lines 447--449 +[]$ + [] + +! Undefined control sequence. +l.450 \If + {division by 0 occurred} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +! Missing $ inserted. + + $ +l.451 { $c = 0$ \; + } +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.451 { $c = 0$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.452 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 450--452 +[] + [] + + +Overfull \hbox (14.88307pt too wide) in paragraph at lines 450--452 +\OML/cmm/m/it/10 c \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 450--452 +\OT1/cmr/m/n/10 0$ + [] + +! Missing $ inserted. + + $ +l.453 $d = 1 - c$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.454 $DIST_ + {from\_x,from\_y,1} = d$ \; +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.454 $DIST_{from\_x,from\_y,1} = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing $ inserted. + + $ +l.455 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 453--455 +[]$\OML/cmm/m/it/10 d \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (12.77782pt too wide) in paragraph at lines 453--455 +\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (4.32756pt too wide) in paragraph at lines 453--455 +\OML/cmm/m/it/10 c$ + [] + + +Overfull \hbox (67.94446pt too wide) in paragraph at lines 453--455 +[] \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 453--455 +\OML/cmm/m/it/10 d$ + [] + +! Undefined control sequence. +l.456 \If + {$d < min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing $ inserted. + + $ +l.457 { $min\_distance = d$ \; + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.459 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.460 \ElseIf + {$d = min\_dist$} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.460 \ElseIf{$ + d = min\_dist$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no d in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +! Extra }, or forgotten $. + } + +l.460 \ElseIf{$d = min\_dist$} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing } inserted. + + } +l.461 { append a triplet $ + (from\_x,from\_y\_rev,1)$ to $MIN\_DIST$ \; } +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no ( in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no ) in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no T in font nullfont! +! Extra }, or forgotten $. +l.461 ...\_x,from\_y\_rev,1)$ to $MIN\_DIST$ \; } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.462 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.463 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Extra }, or forgotten $. +l.464 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.465 \caption + {A routine of distanceFast() computing all remaining distance... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.465 ...mputing all remaining distances between $ + X$ and $Y$. This function ... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no X in font nullfont! +Missing character: There is no Y in font nullfont! +! Extra }, or forgotten $. +l.465 ...ll variables declared in distanceFast().} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \begin{document} ended by \end{algorithm}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.466 \end{algorithm} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.466 \end{algorithm} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (35.76038pt too wide) in paragraph at lines 456--467 +[]$\OML/cmm/m/it/10 d < + [] + + +Overfull \hbox (35.17622pt too wide) in paragraph at lines 456--467 +\OML/cmm/m/it/10 min[]dist$ + [] + + +Overfull \hbox (66.0038pt too wide) in paragraph at lines 456--467 +\OML/cmm/m/it/10 min[]distance \OT1/cmr/m/n/10 = + [] + + +Overfull \hbox (5.20486pt too wide) in paragraph at lines 456--467 +\OML/cmm/m/it/10 d$ + [] + + +Overfull \hbox (76.05862pt too wide) in paragraph at lines 456--467 +\OML/cmm/m/it/10 appendatriplet$[][][]$to$[]$ []$ + [] + + +Overfull \hbox (719.47824pt too wide) in paragraph at lines 456--467 +[]$[]$[][][]$\OML/cmm/m/it/10 to$[]$ []$$and$$:Thisfunctioncanaccessandmodifyal +lvariablesdeclaredindistanceFast\OT1/cmr/m/n/10 ()\OML/cmm/m/it/10 :$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.471 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 471--472 +[] + [] + +! Undefined control sequence. +l.473 \includegraphics + [scale=0.3]{images/ch_atac-seq/sp1_motifs_6class_nosh... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.473 \includegraphics[scale=0.3]{images/ch_ + atac-seq/sp1_motifs_6class_nosh... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.473 ...c-seq/sp1_motifs_6class_noshift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.474 \captionof + {figure}{\textbf{Open chromatin classes around SP1 motifs :... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.476 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.476 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.476 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.476 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.476 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.477 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 473--478 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (2546.62112pt too wide) in paragraph at lines 473--478 +\OML/cmm/m/it/10 seq=sp\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 otifs[]class[]oshift +[]lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.479 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 479--480 +[] + [] + +! Undefined control sequence. +l.481 \includegraphics + [scale=0.3]{images/ch_atac-seq/sp1_motifs_6class_shif... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.481 \includegraphics[scale=0.3]{images/ch_ + atac-seq/sp1_motifs_6class_shif... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.481 ...tac-seq/sp1_motifs_6class_shift_flip.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.482 \captionof + {figure}{\textbf{Open chromatin classes around SP1 motifs :... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.484 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.484 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.484 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.484 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.484 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.485 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 481--486 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (2487.86104pt too wide) in paragraph at lines 481--486 +\OML/cmm/m/it/10 seq=sp\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 otifs[]class[]hift[] +lip:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.487 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 487--488 +[] + [] + +! Undefined control sequence. +l.489 \includegraphics + [scale=0.4]{images/ch_atac-seq/simulated_sequences_2c... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.489 \includegraphics[scale=0.4]{images/ch_ + atac-seq/simulated_sequences_2c... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.489 ...ed_sequences_2class_flip_best_motifs.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.490 \captionof + {figure}{\textbf{Simulated data motifs :} motifs used for t... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.490 ...ild using the motifStack R package \citep + {ou_motifstack_2018}.} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.492 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.492 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.492 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.492 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.492 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.493 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 489--494 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (2097.5392pt too wide) in paragraph at lines 489--494 +\OML/cmm/m/it/10 seq=simulated[]equences[]class[]lip[]est[]otifs:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.495 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 495--496 +[] + [] + +! Undefined control sequence. +l.497 \includegraphics + [scale=0.35]{images/ch_atac-seq/sp1_motifs_10class.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.497 \includegraphics[scale=0.35]{images/ch_ + atac-seq/sp1_motifs_10class.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.497 ...mages/ch_atac-seq/sp1_motifs_10class.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.498 \captionof + {figure}{\textbf{SP1 motifs :} partition of 15'883 801bp se... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.498 ...arch for 10 different 30bp long motifs ($ + 801 - 30 = 771$ of shiftin... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no 8 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 7 in font nullfont! +Missing character: There is no 7 in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. +l.498 ...head-to-tail arrangements of SP1 motifs.} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.500 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.500 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.500 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.500 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.500 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.501 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 497--502 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (954.1467pt too wide) in paragraph at lines 497--502 +\OML/cmm/m/it/10 seq=sp\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 otifs[]\OT1/cmr/m/n/ +10 0\OML/cmm/m/it/10 class:png[][]$ + [] + + +Overfull \hbox (736.07962pt too wide) in paragraph at lines 497--502 +\OML/cmm/m/it/10 ofshiftingfreedom\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 :Theoptimiz +ationwasrunfor\OT1/cmr/m/n/10 20\OML/cmm/m/it/10 iterations:Thedifferentclasses +areorderedbydecreasingoverallprobability:Arrowsatopofthemotifsindicateshead \OM +S/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (16.23615pt too wide) in paragraph at lines 497--502 +\OML/cmm/m/it/10 to \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (143.65567pt too wide) in paragraph at lines 497--502 +\OML/cmm/m/it/10 tailarrangementsofSP\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 motifs:[ +]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.503 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 503--504 +[] + [] + +! Undefined control sequence. +l.505 \includegraphics + [scale=0.35]{images/ch_atac-seq/sp1_motifs_10class.png} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.505 \includegraphics[scale=0.35]{images/ch_ + atac-seq/sp1_motifs_10class.png} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.505 ...mages/ch_atac-seq/sp1_motifs_10class.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.506 \captionof + {figure}{\textbf{SP1 motifs :} partition of 15'883 801bp se... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Missing } inserted. + + } +l.506 ...arch for 10 different 30bp long motifs ($ + 801 - 30 = 771$ of shiftin... +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no 8 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 7 in font nullfont! +Missing character: There is no 7 in font nullfont! +Missing character: There is no 1 in font nullfont! +! Extra }, or forgotten $. +l.506 ...head-to-tail arrangements of SP1 motifs.} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.508 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.508 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.508 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.508 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.508 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.509 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 505--510 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (954.1467pt too wide) in paragraph at lines 505--510 +\OML/cmm/m/it/10 seq=sp\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 otifs[]\OT1/cmr/m/n/ +10 0\OML/cmm/m/it/10 class:png[][]$ + [] + + +Overfull \hbox (736.07962pt too wide) in paragraph at lines 505--510 +\OML/cmm/m/it/10 ofshiftingfreedom\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 :Theoptimiz +ationwasrunfor\OT1/cmr/m/n/10 20\OML/cmm/m/it/10 iterations:Thedifferentclasses +areorderedbydecreasingoverallprobability:Arrowsatopofthemotifsindicateshead \OM +S/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (16.23615pt too wide) in paragraph at lines 505--510 +\OML/cmm/m/it/10 to \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (143.65567pt too wide) in paragraph at lines 505--510 +\OML/cmm/m/it/10 tailarrangementsofSP\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 motifs:[ +]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.511 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 512--512 +[] + [] + +! Undefined control sequence. +l.513 \includegraphics + [scale=0.30]{images/ch_atac-seq/peaks_rmsk_sampled_se... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.513 \includegraphics[scale=0.30]{images/ch_ + atac-seq/peaks_rmsk_sampled_se... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.513 ...peaks_rmsk_sampled_sequences_23class.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.514 \captionof + {figure}{\textbf{Extended sequence and chromatin models} fo... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.516 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.516 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.516 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.516 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.516 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.517 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 513--518 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (1969.94185pt too wide) in paragraph at lines 513--518 +\OML/cmm/m/it/10 seq=peaks[]msk[]ampled[]equences[]\OT1/cmr/m/n/10 3\OML/cmm/m/ +it/10 class:png[][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.519 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 520--520 +[] + [] + +! Undefined control sequence. +l.521 \includegraphics + [scale=0.30]{images/ch_atac-seq/data_classPU1_2class.... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.521 \includegraphics[scale=0.30]{images/ch_ + atac-seq/data_classPU1_2class.... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.521 ...ges/ch_atac-seq/data_classPU1_2class.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.522 \captionof + {figure}{\textbf{PU.1 sub-classes} obtained by extracting P... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.524 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.524 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.524 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.524 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.524 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.525 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (25.84001pt too wide) in paragraph at lines 521--526 +[]\OML/cmm/m/it/10 tac \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (2035.30466pt too wide) in paragraph at lines 521--526 +\OML/cmm/m/it/10 seq=data[]lassPU\OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 class:png[ +][][]$ + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.527 \begin{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 528--528 +[] + [] + +! Undefined control sequence. +l.529 \includegraphics + [scale=0.30]{images/ch_atac-seq/data_classjun_3class.... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +! Missing $ inserted. + + $ +l.529 \includegraphics[scale=0.30]{images/ch_ + atac-seq/data_classjun_3class.... +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.529 ...ges/ch_atac-seq/data_classjun_3class.png} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Undefined control sequence. +l.530 \captionof + {figure}{\textbf{AP1 sub-classes} obtained by extracting AP... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Command \end{center} invalid in math mode. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.532 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.532 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.532 \end{center} + +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing $ inserted. + + $ +l.532 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.532 \end{center} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.533 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +) +! Emergency stop. +<*> appendix.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 35 strings out of 492982 + 580 string characters out of 6134895 + 85860 words of memory out of 5000000 + 3695 multiletter control sequences out of 15000+600000 + 3948 words of font info for 15 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 18i,7n,21p,1230b,134s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/tail/appendix.tex b/tail/appendix.tex index 2d2e92d..b9e4b1d 100644 --- a/tail/appendix.tex +++ b/tail/appendix.tex @@ -1,173 +1,596 @@ \appendix % \beginsupplement \chapter{An appendix} \section{Supplementary figures} % ======================================= SMiLE-seq figures ======================================= \begin{figure}[H] \begin{center} \includegraphics[scale=0.3]{images/ch_smile-seq/figure_s4_reproduced.png} \captionof{figure}{\textbf{Predictive power of SMiLE-seq :} \textbf{A} binding models were derived de novo from HT-SELEX 1st cycle data using the HMM discovery method (labelled HT-SELEX cycle 1 HMM) and their performances were assessed using the AUC-ROC. AUC-ROC values for the corresponding TF models derived from SMiLe-seq data (labelled SMiLE-seq) and reported by Jolma and colleagues (labelled HT-SELEX reported matrices, \cite{jolma_dna-binding_2013}) are also displayed. \textbf{B} the predictive performances of CEBPb, CTCF and TCF7 binding models were assessed using subsets of binding sites of decreasing affinities. Inside each peak list, the peaks were ranked by score and subsets of 500 peaks were selected. Peaks 1-500 have the highest affinity, then peaks 501-1000, and so on. The boxplots indicate the distribution of AUC-ROC obtained over all available peak-lists.} \label{suppl_smileseq_auc_2} \end{center} \end{figure} % ===================================== encode peaks figures ===================================== % \begin{figure}[H] % \begin{center} % \includegraphics[scale=0.25]{images/ch_encode_peaks/em_examples.png} % \captionof{figure}{\textbf{Nucleosome architectures around TF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. Partitions for \textbf{A} CTCF, \textbf{B} NRF1, \textbf{C} FOS and \textbf{D} max are displayed. The first row always contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} % \label{suppl_encode_peaks_em_examples} % % \end{center} % \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsUwGm12878CtcfUniPk_MNase_GM12878_allpeaks_EM_4class_15shift_flip.png} \captionof{figure}{\textbf{Chromatine architectures around CTCF binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} \label{suppl_encode_peaks_em_ctcf} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydhGm12878Nrf1IggmusUniPk_MNase_GM12878_allpeaks_EM_4class_15shift_flip.png} \captionof{figure}{\textbf{Chromatine architectures around NRF1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} \label{suppl_encode_peaks_em_nrf1} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydhGm12878CfosUniPk_MNase_GM12878_allpeaks_EM_4class_15shift_flip.png} \captionof{figure}{\textbf{Chromatine architectures around cFOS binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} \label{suppl_encode_peaks_em_cfos} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydhGm12878MaxIggmusUniPk_MNase_GM12878_allpeaks_EM_4class_15shift_flip.png} \captionof{figure}{\textbf{Chromatine architectures around max binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} \label{suppl_encode_peaks_em_max} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/wgEncodeAwgTfbsSydhGm12878Brca1a300IggmusUniPk_MNase_GM12878_allpeaks_EM_4class_15shift_flip.png} \captionof{figure}{\textbf{Chromatine architectures around BRCA1 binding sites} discovered using ChIPPartitioning. The partition was done with respect to the MNase reads (red), +/- 1kb around the peaks, in bins of 10bp, that were allowed to be shifted and flipped. DNaseI (blue), TSS density (violet) and sequence conservation (green) were realigned according to MNase classification and overlaid. The y-axis scale represent the proportion of the highest signal for each chromatin pattern. The first row contains the aggregated signal over all sites. The number of binding sites (peaks) is indicated in parenthesis. The following rows contains the 4 classes discovered. Their overall probability is indicated atop of the class signal, on the right. The y-axis indicates the min/max signal for all densities.} \label{suppl_encode_peaks_em_brca1} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.8]{images/ch_encode_peaks/ctcf_ndr.png} \captionof{figure}{\textbf{Nucleosome occupancy around CTCF peaks } measured by MNase-seq, in bins of 10bp. The nucleosome depleted region is displayed in blue.} \label{suppl_encode_peaks_ctcf_ndr} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.4]{images/ch_encode_peaks/jund_motif_association.png} \captionof{figure}{\textbf{JunD motif association} measured around the binding sites of different TFs. For a each TF, its binding sites, +/- 500bp, were searched for the presence of i) the TF motif and ii) CTCF motif. For each TF, a 2x2 contingency table was created with the number of peaks having i) both motifs, ii) the TF motif only, iii) CTCF motif only and iv) no motif. \textbf{A} Odd ratio (OR) of the exact Fisher test performed on each TF contingency table. The ORs are displayed with their 95\% confidence interval (CI). ORs > 1 - that is, with 1 not part of the 95\%CI - are labeled in green and indicate an association of both motifs more frequent than expected by chance. ORs < 1 are labeled in red and indicate a repulsion of both motifs more frequence than expected by chance. The JunD and cFos dataset ORs are too high to be represented in this plot. \textbf{B} Density of JunD motif occurrence at the absolute distance of different TF binding sites (peak centers) which also have their own motif present (at distance 0). The rows were standardized and aggregated using the Euclidean distance. \textbf{C} Same as in (B) but for TF binding sites that does not have their own motif.} \label{suppl_encode_peaks_jund_association} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=0.4]{images/ch_encode_peaks/ebf1_haib_3.png} \captionof{figure}{\textbf{EBF1 binding sites} around the dyad of nucleosomes having an occupied EBF1 motif within 100bp (in red) and of all nucleosomes (in blue). The abrupt decrease of EBF1 motif frequency at +/- 100bp reflects the nucleosome selection process.} \label{suppl_encode_peaks_ebf1_nucl} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.5]{images/ch_encode_peaks/MA0154_3.png} \captionof{figure}{\textbf{EBF1 logo} from JASPAR binding model MA0154.3 \citep{khan_jaspar_2018}.} \label{suppl_encode_peaks_ebf1_logo} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=0.4]{images/ch_encode_peaks/ebf1_haib_2.png} \captionof{figure}{\textbf{EBF1 binding sites} chromatin features. \textbf{A} Chromatin accessibility around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf{B} H3K4me2 deposition around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue). \textbf{C} Sequence conservation around nucleosomes that have an EBF1 binding site within 100bp (red) and all nucleosomes (blue).} \label{suppl_encode_peaks_ebf1_chrom} \end{center} \end{figure} +% ======================================= SPar-K figures ======================================== + + +% ======================================= SPar-K algos ======================================== + + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{void SPar-K}% +\begin{algorithm}[H] + \label{algo_spark} + \Fn{\Function{R, K, S, I}} + { + \KwData{$R$ a 2D matrix of numericals of dimension $N \times L$; $K$ the number clusters; $S$ the shifting allowed; $I$ the maximum number of iterations.} + \KwResult{5 vectors of length $N$ with the cluster labels, the data shift values, the reference shift values, the data flip values and the distances to the cluster references.} + + $CLUSTER =$ vector of 0 of size $N$ \; + $SHIFT\_DAT =$ vector of 0 of size $N$ \; + $SHIFT\_REF =$ vector of 0 of size $N$ \; + $FLIP\_DAT =$ vector of 0 of size $N$ \; + $DISTANCE =$ vector of 0 of size $N$ \; + + \If{smoothing} + { smoothOutliers($R$) \; } + + $REF = $ a matrix of $K$ rows and $L$ columns\; + select $K$ rows of $R$ and copy them in $REF$ using seedingRandom($K$, $R$) or seedingKmeans++($K$, $R$) \; + + $n\_iter = 1$\; + $converged = false$\; + + \While{$n\_iter != I$ or not $converged$} + { + \For{$i=0$ to $N-1$} + { $D =$ a vector 0 of size $K$ \; + $S\_REF =$ a vector 0 of size $K$ \; + $S\_DAT =$ a vector 0 of size $K$ \; + $F\_DAT =$ a vector 0 of size $K$ \; + \For{$k=0$ to $K-1$} + { $D_{k},S\_REF_{k},S\_DAT_{k}, F\_DAT_{k} =$ distanceFast($REF_{k,}$, $R{i,}$, $S$) \; } + $j = $ index of minimum value in $REF$\; + $CLUSTER_{i} = D_{j}$ \; + $SHIFT\_REF_{i} = S\_REF_{j}$ \; + $SHIFT\_DAT_{i} = S\_DAT_{j}$ \; + $FLIP\_DAT_{i} = F\_DAT_{j}$ \; + $DISTANCE\_{i} = D_{j}$ \; + } + + $REF =$ computeClusterReferences($R$, $CLUSTER$, $SHIFT\_REF$, $SHIFT\_DAT$, $FLIP\_DAT$) \; + + \If{$n\_iter > 1$ and at least one value of $CLUSTER$ changed since last iteration} + { $converged = false$ \; } + \Else + { $converged = true$ \; } + $n\_iter = n\_iter + 1$ \; + } + \Return{$CLUSTER, SHIFT\_REF, SHIFT\_DAT, FLIP, DISTANCE$} + } + \caption{SPar-K algorithm.} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{MATRIX smoothOutliers}% +\begin{algorithm}[H] + \label{algo_smooth_outliers} + \Fn{\Function{MATRIX}} + { + \KwData{$MATRIX$ a 2D matrix of numericals of dimensions $N \times L$.} + \KwResult{a 2D matrix of numericals of dimensions $N \times L$. with outlier smoothed.} + + \ForEach{$ROW$ in MATRIX} + { $m$ = mean of $ROW$ \; + $s$ = standard deviation of $ROW$ \; + $lower$ = $m$ - 3*$s$ \; + $upper$ = $m$ + 3*$s$ \; + \ForEach{$value$ in $ROW$} + { \If{$value < lower$ or $value > upper$} + { \If{$value$ has a left neighbor $l$ and a right neighbor $r$} + { $value$ = ($l$ + $r$) / 2 \; } + \ElseIf{$value$ has two left neighbors $l1$ and $l2$} + { $value$ = ($l1$ + $l2$) / 2 \; } + \ElseIf{$value$ has two right neighbors $r1$ and $r2$} + { $value$ = ($r1$ + $r2$) / 2 \; } + } + } + } + \Return{$MATRIX$} + } + \caption{Smooth the data matrix by removing outliers.} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{d,s\_xf,s\_y,f\_y distanceFast}% +\begin{algorithm}[H] + \label{algo_distance_fast} + \Fn{\Function{X,Y,S}} + { \KwData{$X$ and $Y$ two vectors of size $L$ and $S$ the allowed shifting} + \KwResult{the distance between $X$ and $Y$, the shift of $X$ and $Y$ and whether $Y$ was flipped in the alignment.} + \tcc{initialize all variables and data structures} + initialize() \; + + \For{$i=0$ to $n-1$} + { $SUM\_X_0 \pluseq X_i $ \; + $SUM\_X2_0 \pluseq X_i^2$ \; + $SUM\_Y_0 \pluseq Y_i $ \; + $SUM\_Y2_0 \pluseq Y_i^2$ \; + } + $i = n$ \; + \For{$s=1$ to $s=S-1$ } + { $SUM\_X_{s} = SUM\_X_{s-1} + X_{i-n} + X_{i} $ \; + $SUM\_X2_{s} = SUM\_X2_{s-1} + X_{i-n}^{2} + X_{i}^{2}$ \; + $SUM\_Y_{s} = SUM\_Y_{s-1} + Y_{i-n} + Y_{i} $ \; + $SUM\_Y2_{s} = SUM\_Y2_{s-1} + Y_{i-n}^{2} + Y_{i}^{2}$ \; + $i \pluseq 1$ \; + } + + \tcc{compute all distances with $X$ having a shift of 0, $Y$ having a shift of 0 and all the remains ones. These functions can access and modify all variables and data structures in this function.} + fillFirstRow() \; + fillFirstColl() \; + fillRemaining() \; + + \tcc{if more than one, find the minimal distance which also minimize the alignment score} + $best_d = best\_s\_x = best\_s\_y = best\_f\_y = 0$ \; + \For{$tripplet$ in $MIN\_DIST$} + { $s\_x = tripplet_{0}$ \; + $s\_y = tripplet_{1}$ \; + $f\_y = tripplet_{2}$ \; + $min\_score = \infty$ \; + \If{$SCORES_{s\_x,s\_y} < min\_score$} + { $min\_score = SCORES_{s\_x,s\_y}$ \; + $best\_s\_x = s\_x$ \; + $best\_s\_y = s\_y$ \; + $best\_f\_y = f\_y$ \; + $best\_d = DIST_{s\_x,s\_y,f\_y}$ \; + } + } + \Return{$best\_d,best\_s\_x,best\_s\_y,best\_f\_y$} + + } + \caption{Fast algorithm to compute the correlation distance with shift and flip} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{initialize}% +\begin{algorithm}[H] + \label{initialize_algo} + \Fn{\Function{}} + { + + $l\_half = L / 2$ \; + $n = L - S + 1$ \; + $n\_half = n / 2$ \; + %\tcc{1-cor for each shift of $X$ (on rows) and each shift of $Y$ (on columns)} + $DIST =$ 3D matrix of 3 of dimensions $S*S*2$ \; + %\tcc{the sums of the pairwise products of the $X$ elements for each shift and $Y$ elements for each shift} + $SUM\_XY =$ 3D matrix of 0 of dimensions $S*S*2$ \; + %\tcc{the sums of the $X$ elements for each shift} + $SUM\_X =$ a vector of 0 of size $S$ \; + %\tcc{the sums of squares of the $X$ elements for each shift} + $SUM\_X2 =$ a vector of 0 of size $S$ \; + %\tcc{same for $Y$} + $SUM\_Y =$ a vector of 0 of size $S$ \; + $SUM\_Y2 =$ a vector of 0 of size $S$ \; + %\tcc{a centrality score for each alignment, a forward and a reverse alignments have the same score} + $SCORES =$ a 2D matrix of 0 of dimensions $S*S$ \; + %\tcc{to track minimum distances in $DIST$} + $MIN\_DIST =$ an empty list of triplets \; + $min\_dist = 3$ \; + } + \caption{A routine of distanceFast() that initializes all the necessary variables. This function can access and modify variables in distanceFast().} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{void fillFirstRow}% +\begin{algorithm}[H] + \Fn{\Function{}} + { + % \tcc{fill first row of $DIST$, 1-cor with $X$ having a shift of 0} + $from\_x = 0$ \; + $to\_x = from\_x + n$ \; + + \For{$i = 0$ to $S-1$} + { \tcc{forward orientation} + $from\_y = i$ \; + $to\_y = from\_y + n$ \; + + $SUM_XY{from\_x,from\_y,0} = 0$ \; + \For{$j = 0$ to $n-1$} + { $SUM\_XY_{from\_x,from\_y,0} \pluseq X_{from\_x+j} * Y_{from\_y+j}$ \; } + + % \tcc{correlation} + $c = \frac{n* SUM\_XY_{from\_x,from\_y,0} - SUM\_X_{from\_x} * SUM\_Y_{from\_y}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^{2}} * \sqrt{n*SUM\_Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + \If{division by 0 occurred} + { $c = 0$ \; } + + % \tcc{distance} + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,0} = d$ \; + + % \tcc{alignment centrality score, this value is the same for forward and reverse alignments} + $SCORES_{from\_x,from\_y} = \abs{l\_half - (n\_half + from\_x)} + + \abs{l\_half - (n\_half + from\_y)}$ \; + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,from\_y, 0)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } + + \tcc{reverse orientation} + $SUM_XY{from\_x,from\_y,1} = 0$ \; + \For{$j = 0$ to $n-1$} + { $SUM\_XY_{from\_x,from\_y,1} \pluseq X_{from\_x+j} * Y_{to\_y-j-1}$ \; } + + % \tcc{correlation} + $c = \frac{n* SUM\_XY_{from\_x,from\_y,1} - SUM\_X_{from\_x} * SUM\_Y_{from\_y}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^{2}} * \sqrt{n*SUM\_Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + \If{division by 0 occurred} + { $c = 0$ \; } + + % \tcc{distance} + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,1} = d$ \; + + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,from\_y, 1)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,from\_y, 1)$ to $MIN\_DIST$ \; } + } + } + \caption{A routine of distanceFast() computing all distances with $X$ having a shift of 0. This function can access and modify all variables declared in distanceFast().} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{void fillFirstCol}% +\begin{algorithm}[H] + \Fn{\Function{}} + { % \tcc{fill first row of $DIST$, 1-cor with $X$ having a shift of 0} + $from\_y = 0$ ; $to\_y = from\_y + n$ \; + $from\_y\_rev = s - from\_y - 1$ \; + $to\_y\_rev = from\_y\_rev + n$ \; + + \For{$i=0$ to $S-1$} + { $from\_x = i$ \; + $to\_x = from\_x + n$ \; + + \tcc{forward orientation} + $SUM\_XY_{from\_x,from\_y,0} = 0 $ \; + \For{$j=0$ to $n-1$} + { $SUM\_XY{from\_x,from\_y,0} \pluseq X_{from\_x+j}*Y_{from\_y+j} $ \; } + + $c = \frac{n*SUM\_XY_{from\_x,from\_y,0} - SUM\_X_{from\_x}*SUM\_Y_{from\_y}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^{2}} * \sqrt{n*SUM\_Y2_{from\_y} - SUM\_Y_{from\_y}^{2}}}$ \; + \If{division by 0 occurred} + { $c = 0$ \; } + + % \tcc{distance} + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,0} = d$ \; + + % \tcc{alignment centrality score, this value is the same for forward and reverse alignments} + $SCORES_{from\_x,from\_y} = \abs{l\_half - (n\_half + from\_x)} + + \abs{l\_half - (n\_half + from\_y)}$ \; + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,from\_y, 0)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,from\_y, 0)$ to $MIN\_DIST$ \; } + + \tcc{reverse orientation} + $SUM\_XY_{from\_x,S-1,1} = 0$ \; + \For{$j=0$ to $n-1$} + { $SUM\_XY_{from\_x,S-1,1} \pluseq X_{from\_x+j} * Y_{to\_y\_rev-1-j}$ \; } + + $c = \frac{n*SUM\_XY_{from\_x,S-1,1} - SUM\_X_{from\_x}*SUM\_Y_{S-1}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^{2}} * \sqrt{n*SUM\_Y2_{S-1} - SUM\_Y_{S-1}^{2}}}$ \; + \If{division by 0 occurred} + { $c = 0$ \; } + + % \tcc{distance} + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,1} = d$ \; + + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,S-1, 1)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,S-1, 1)$ to $MIN\_DIST$ \; } + } + } + \caption{A routine of distanceFast() computing all distances with $Y$ having a shift of 0. This function is can access and modify all variables declared in distanceFast().} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{void fillRemaining}% +\begin{algorithm}[H] + \Fn{\Function{}} + { \For{$i=1$ to $S-1$} + { $from\_x = i$ ; $to\_x = from\_x + n $ \; + \For{$j=1$ to $S-1$} + { $from\_y = j$ \; + $to\_y = from\_y + n$ \; + + \tcc{forward orientation} + $SUM\_XY_{from\_x,from\_y,0} = SUM\_XY_{from\_x-1,from\_y-1,1} - X_{from\_x-1} * Y_{from\_y-1} + X_{to\_x-1}*Y{to\_y-1}$ \; + $c = \frac{n*SUM\_XY{from\_x,from\_y,0} - SUM\_X{from\_x}*SUM\_Y{from\_y}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^2} * \sqrt{n*SUM\_Y2_{from\_Y} - SUM\_Y_{from\_Y}^2}}$ \; + + \If{division by 0 occurred} + { $c = 0$ \; } + + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,0} = d$ \; + + %\tcc{alignment centrality score, this value is the same for forward and reverse alignments} + $SCORES_{from\_x,from\_y} = \abs{l\_half - (n\_half + from\_x)} + + \abs{l\_half - (n\_half + from\_y)}$ \; + + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,from\_y,0)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,from\_y,0)$ to $MIN\_DIST$ \; } + + \tcc{reverse orientation} + $j\_rev = S - j - 1$ \; + $from\_y\_rev = j\_rev$ \; + $to\_y\_rev = from\_y\_rev + n$ \; + $SUM\_XY_{from\_x,from\_y\_rev,1} = SUM\_XY_{from\_x-1,from\_y\_rev+1,1} - X_{from\_x-1}*Y_{to\_y\_rev} + X_{to\_x-1}*Y{from\_y\_rev}$ \; + + $c = \frac{n*SUM\_XY_{from\_x,from\_y\_rev,1} - SUM\_X_{from\_x}*SUM\_Y_{from\_y\_rev}} + {\sqrt{n*SUM\_X2_{from\_x} - SUM\_X_{from\_x}^2} * \sqrt{n*SUM\_Y2_{from\_y\_rev} - SUM\_Y_{from\_y_rev}^2}}$ \; + + \If{division by 0 occurred} + { $c = 0$ \; } + + $d = 1 - c$ \; + $DIST_{from\_x,from\_y,1} = d$ \; + + \If{$d < min\_dist$} + { $min\_distance = d$ \; + append a triplet $(from\_x,from\_y\_rev,1)$ to $MIN\_DIST$ \; + } + \ElseIf{$d = min\_dist$} + { append a triplet $(from\_x,from\_y\_rev,1)$ to $MIN\_DIST$ \; } + } + } + } + \caption{A routine of distanceFast() computing all remaining distances between $X$ and $Y$. This function can access and modify all variables declared in distanceFast().} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{REF seedingRandom}% +\begin{algorithm}[H] + \label{algo_seed_random} + \Fn{\Function{K, R}} + { \KwData{$K$ the number references to initialize from $R$, a 2D matrix of numericals of dimensions $N \times L$.} + \KwResult{$REF$ a 2D matrix of numericals of dimensions $K \times L$.} + + $REF = $ a 2D matrix of dimensions $K*L$ \; + + \For{$i=0$ to $K-1$} + { $j = $ sample a number from $0$ to $N-1$ with uniform probabilities \; + \While{$j$ has already been sampled before} + { $j = $ sample a number from $0$ to $N-1$ with uniform probabilities \; } + $REF_{i,} = R_{j,}$ \; + } + \Return{$REF$} + } + \caption{Random seeding algorithm} +\end{algorithm} + +\vspace{\baselineskip}% Insert a blank line + +\SetKwProg{Fn}{}{\{}{}\SetKwFunction{Function}{REF seedingKmeans++}% +\begin{algorithm}[H] + \label{algo_seed_kmeans++} + \Fn{\Function{K, R, S}} + { \KwData{$K$ the number references to initialize from $R$, a 2D matrix of numericals of dimensions $N \times L$, allowing a shifting of $S$.} + \KwResult{$REF$ a 2D matrix of numericals of dimensions $K \times L$.} + + $REF = $ a 2D matrix of dimensions $K*L$ \; + $DIST\_TO\_CLOSEST = $ a vector of size $N$\; + + \tcc{choose first reference, a standard deviation equals to 0 should be avoided otherwise computing a distance against this reference will always be equal to 1 (see how distance are computed).} + $j = $ sample a number from $0$ to $N-1$ with uniform probabilities but for which $DATA_{j,}$ has a standard deviation different from $0$ \; + $REF_{0,} = DATA_{j,}$ \; + + \tcc{choose next references} + \For{$k=1$ to $K-1$} + { \For{$i=0$ to $N-1$} + { \tcc{distance to all current references for this region} + $DIST\_TO\_CENTERS =$ a vector of size $k$ ; + \For{$j=0$ to $k-1$} + { $DIST\_TO\_CENTERS_{j,} =$ distanceFast($REF_{j,}$, $R_{i,}$, $S$) \; } + \tcc{distance to closest current reference, for this region} + $DIST\_TO\_CLOSEST{i,} =$ minimum value of $DIST\_TO\_CENTERS$\; + } + + $j =$ sample a number from 0 to $N-1$ using $DIST\_TO\_CLOSEST$ as the probability/weight distribution for each point to be sample. \; + \While{$j$ has already been sampled before} + { $j =$ sample a number from 0 to $N-1$ using $DIST\_TO\_CLOSEST$ as the probability/weight distribution for each point to be sample. \; } + $REF_{k,} = R{j,}$ \; + } + \Return{REF} + } + \caption{Kmeans++ seeding algorithm.} +\end{algorithm} + + + % ======================================= ATAC-seq figures ======================================== \begin{figure}[H] \begin{center} \includegraphics[scale=0.3]{images/ch_atac-seq/sp1_motifs_6class_noshift_flip.png} \captionof{figure}{\textbf{Open chromatin classes around SP1 motifs :} EMRead was run without shifing (+/- 10bp) but with flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.} \label{suppl_emread_sp1_noshift_flip} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.3]{images/ch_atac-seq/sp1_motifs_6class_shift_flip.png} \captionof{figure}{\textbf{Open chromatin classes around SP1 motifs :} EMRead was run with shifing (+/- 10bp) flipping to identify different classes of footprints around 15'883 SP1 motifs. The aggregation signal around the 6 different classes found are shown by decreasing class probability. The open chromatin patterns are displayed in red, the nucleosomes are displayed in blue. The aggregated DNA sequence is displayed as a logo. The y-axis ranges from the minimum to the maximum signal observed. For the DNA logo, this corresponds to 0 and 2 bits respectively.} \label{suppl_emread_sp1_shift_flip} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.4]{images/ch_atac-seq/simulated_sequences_2class_flip_best_motifs.png} \captionof{figure}{\textbf{Simulated data motifs :} motifs used for the data generation (labeled "True motif") and the best scoring - based on the AUC - partition motifs (labeled "Found motif"). The partition with EMSequence was run such that it was searching for motifs of 11bp, slightly longer than those used for the data generation. "RC" stands for reverse complement. The motifs tree and alignment was build using the motifStack R package \citep{ou_motifstack_2018}.} \label{suppl_atac_seq_emseq_best_motifs} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.35]{images/ch_atac-seq/sp1_motifs_10class.png} \captionof{figure}{\textbf{SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.} \label{suppl_emseq_sp1_10class} \end{center} \end{figure} \begin{figure}[H] \begin{center} \includegraphics[scale=0.35]{images/ch_atac-seq/sp1_motifs_10class.png} \captionof{figure}{\textbf{SP1 motifs :} partition of 15'883 801bp sequences centered on a SP1 binding site using EMSequence. These sequences were classified by EMSequence to search for 10 different 30bp long motifs ($801 - 30 = 771$ of shifting freedom). The optimization was run for 20 iterations. The different classes are ordered by decreasing overall probability. Arrows atop of the motifs indicates head-to-tail arrangements of SP1 motifs.} \label{suppl_emseq_sp1_10class} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=0.30]{images/ch_atac-seq/peaks_rmsk_sampled_sequences_23class.png} \captionof{figure}{\textbf{Extended sequence and chromatin models} found in 10'000 monocytes regulatory regions. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.} \label{suppl_atac_seq_23class} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=0.30]{images/ch_atac-seq/data_classPU1_2class.png} \captionof{figure}{\textbf{PU.1 sub-classes} obtained by extracting PU.1 class data and subjecting them to a ChIPPartitioning classification into 2 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.} \label{suppl_atac_seq_pu1_subclass} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=0.30]{images/ch_atac-seq/data_classjun_3class.png} \captionof{figure}{\textbf{AP1 sub-classes} obtained by extracting AP1 class data and subjecting them to a ChIPPartitioning classification into 3 classes. The displayed logos correspond to each class sequence aggregation. The corresponding chromatin accessibility (red) and nucleosome occupancy (blue) are displayed atop of the logos. The classes are displayed by overall decreasing probability. A zoom over the central part of each class aggregation is shown in the top right inlet.} \label{suppl_atac_seq_ap1_subclass} \end{center} -\end{figure} \ No newline at end of file +\end{figure} diff --git a/tail/biblio.aux b/tail/biblio.aux index 48ee2ef..257083c 100644 --- a/tail/biblio.aux +++ b/tail/biblio.aux @@ -1,192 +1,193 @@ \relax \providecommand\hyper@newdestlabel[2]{} \bibstyle{apalike} \bibdata{tail/bibliography} \bibcite{adey_rapid_2010}{{1}{2010}{{Adey et~al.}}{{}}} \bibcite{aerts_toucan:_2003}{{2}{2003}{{Aerts et~al.}}{{}}} \bibcite{aibar_scenic:_2017}{{3}{2017}{{Aibar et~al.}}{{}}} \bibcite{ambrosini_chip-seq_2016}{{4}{2016a}{{Ambrosini et~al.}}{{}}} \bibcite{ambrosini_chip-seq_2016-1}{{5}{2016b}{{Ambrosini et~al.}}{{}}} \bibcite{ambrosini_pwmscan:_2018}{{6}{2018}{{Ambrosini et~al.}}{{}}} \bibcite{ambrosini_signal_2003}{{7}{2003}{{Ambrosini et~al.}}{{}}} \bibcite{angerer_single_2017}{{8}{2017}{{Angerer et~al.}}{{}}} -\bibcite{athar_arrayexpress_2019}{{9}{2019}{{Athar 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