A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

Germline copy number variants (CNVs) and somatic copy number alterations (SCNAs) are of significant importance in syndromic conditions and cancer. Massively parallel sequencing is increasingly used to infer copy number information from variations in the read depth in sequencing data. However, this approach has limitations in the case of targeted re-sequencing, which leaves gaps in coverage between the regions chosen for enrichment and introduces biases related to the efficiency of target capture and library preparation. We present a method for copy number detection, implemented in the software package CNVkit, that uses both the targeted reads and the nonspecifically captured off-target reads to infer copy number evenly across the genome. This combination achieves both exon-level resolution in targeted regions and sufficient resolution in the larger intronic and intergenic regions to identify copy number changes. In particular, we successfully inferred copy number at equivalent to 100-kilobase resolution genome-wide from a platform targeting as few as 293 genes. After normalizing read counts to a pooled reference, we evaluated and corrected for three sources of bias that explain most of the extraneous variability in the sequencing read depth: GC content, target footprint size and spacing, and repetitive sequences. We compared the performance of CNVkit to copy number changes identified by array comparative genomic hybridization. We packaged the components of CNVkit so that it is straightforward to use and provides visualizations, detailed reporting of significant features, and export options for integration into existing analysis pipelines. CNVkit is freely available from https://github.com/etal/cnvkit.

/pdf/cnvkit-genome-wide-copy-number-detection-and-visualization-3vzy7geu6l.pdf

CNVkit: Genome-Wide Copy Number Detection and Visualization from Targeted DNA Sequencing

The tumour microenvironment is the non-cancerous cells present in and around a tumour, including mainly immune cells, but also fibroblasts and cells that comprise supporting blood vessels. These non-cancerous components of the tumour may play an important role in cancer biology. They also have a strong influence on the genomic analysis of tumour samples, and may alter the biological interpretation of results. Here we present a systematic analysis using different measurement modalities of tumour purity in >10,000 samples across 21 cancer types from the Cancer Genome Atlas. Patients are stratified according to clinical features in an attempt to detect clinical differences driven by purity levels. We demonstrate the confounding effect of tumour purity on correlating and clustering tumours with transcriptomics data. Finally, using a differential expression method that accounts for tumour purity, we find an immunotherapy gene signature in several cancer types that is not detected by traditional differential expression analyses.

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Systematic pan-cancer analysis of tumour purity

Clonal evolution in cancer

Allele-specific copy number analysis (ASCN) from next generation sequencing (NGS) data can greatly extend the utility of NGS beyond the identification of mutations to precisely annotate the genome for the detection of homozygous/heterozygous deletions, copy-neutral loss-of-heterozygosity (LOH), allele-specific gains/amplifications. In addition, as targeted gene panels are increasingly used in clinical sequencing studies for the detection of 'actionable' mutations and copy number alterations to guide treatment decisions, accurate, tumor purity-, ploidy- and clonal heterogeneity-adjusted integer copy number calls are greatly needed to more reliably interpret NGS-based cancer gene copy number data in the context of clinical sequencing. We developed FACETS, an ASCN tool and open-source software with a broad application to whole genome, whole-exome, as well as targeted panel sequencing platforms. It is a fully integrated stand-alone pipeline that includes sequencing BAM file post-processing, joint segmentation of total- and allele-specific read counts, and integer copy number calls corrected for tumor purity, ploidy and clonal heterogeneity, with comprehensive output and integrated visualization. We demonstrate the application of FACETS using The Cancer Genome Atlas (TCGA) whole-exome sequencing of lung adenocarcinoma samples. We also demonstrate its application to a clinical sequencing platform based on a targeted gene panel.

/pdf/facets-allele-specific-copy-number-and-clonal-heterogeneity-3xflax0l31.pdf

FACETS: allele-specific copy number and clonal heterogeneity analysis tool for high-throughput DNA sequencing.

Tumor samples are typically heterogeneous, containing admixture by normal, non-cancerous cells and one or more subpopulations of cancerous cells. Whole-genome sequencing of a tumor sample yields reads from this mixture, but does not directly reveal the cell of origin for each read. We introduce THetA (Tumor Heterogeneity Analysis), an algorithm that infers the most likely collection of genomes and their proportions in a sample, for the case where copy number aberrations distinguish subpopulations. THetA successfully estimates normal admixture and recovers clonal and subclonal copy number aberrations in real and simulated sequencing data. THetA is available at http://compbio.cs.brown.edu/software/

/pdf/theta-inferring-intra-tumor-heterogeneity-from-high-3u4zeuq9zj.pdf

THetA: inferring intra-tumor heterogeneity from high-throughput DNA sequencing data

Motivation: High-throughput sequencing of tumor samples has shown that most tumors exhibit extensive intra-tumor heterogeneity, with multiple subpopulations of tumor cells containing different somatic mutations. Recent studies have quantified this intra-tumor heterogeneity by clustering mutations into subpopulations according to the observed counts of DNA sequencing reads containing the variant allele. However, these clustering approaches do not consider that the population frequencies of different tumor subpopulations are correlated by their shared ancestry in the same population of cells. Results: We introduce the binary tree partition (BTP), a novel combinatorial formulation of the problem of constructing the subpopulations of tumor cells from the variant allele frequencies of somatic mutations. We show that finding a BTP is an NP-complete problem; derive an approximation algorithm for an optimization version of the problem; and present a recursive algorithm to find a BTP with errors in the input. We show that the resulting algorithm outperforms existing clustering approaches on simulated and real sequencing data. Availability and implementation: Python and MATLAB implementations of our method are available at http://compbio.cs.brown.edu/

/pdf/a-combinatorial-approach-for-analyzing-intra-tumor-2a3zn5ltx3.pdf

A combinatorial approach for analyzing intra-tumor heterogeneity from high-throughput sequencing data

User modeling is an essential task for online recommender systems. In the past few decades, collaborative filtering (CF) techniques have been well studied to model users' long term preferences. Recently, recurrent neural networks (RNN) have shown a great advantage in modeling users' short term preference. A natural way to improve the recommender is to combine both long-term and short-term modeling. Previous approaches neglect the importance of dynamically integrating these two user modeling paradigms. Moreover, users' behaviors are much more complex than sentences in language modeling or images in visual computing, thus the classical structures of RNN such as Long Short-Term Memory (LSTM) need to be upgraded for better user modeling. In this paper, we improve the traditional RNN structure by proposing a time-aware controller and a content-aware controller, so that contextual information can be well considered to control the state transition. We further propose an attention-based framework to combine users' long-term and short-term preferences, thus users' representation can be generated adaptively according to the specific context. We conduct extensive experiments on both public and industrial datasets. The results demonstrate that our proposed method outperforms several state-of-art methods consistently.

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Adaptive user modeling with long and short-term preferences for personalized recommendation

Betweenness centrality is a fundamental centrality measure in social network analysis. Given a large-scale network, how can we find the most central nodes? This question is of key importance to numerous important applications that rely on betweenness centrality, including community detection and understanding graph vulnerability. Despite the large amount of work on designing scalable approximation algorithms for betweenness centrality, estimating it on large-scale networks remains a computational challenge. 
In this paper, we study the Betweenness Centrality Maximization problem: given a graph $G=(V,E)$ and a positive integer $k$, find a set $S^* \subseteq V$ that maximizes betweenness centrality subject to the cardinality constraint $|S^*| \leq k$. We present an efficient randomized algorithm that provides a $(1-1/e-\epsilon)$-approximation with high probability, where $\epsilon>0$. Our results improve the current state-of-the-art result by Yoshida~\cite{yoshida2014almost}. Furthermore, we provide theoretical evidence for the validity of a crucial assumption in the literature of betweenness centrality estimation, namely that in real-world networks $O(|V|^2)$ shortest paths pass through the top-$k$ central nodes, where $k$ is a constant. On the experimental side, we perform an extensive experimental analysis of our method on real-world networks, demonstrate its accuracy and scalability, and study different properties of central nodes. Finally, we provide three graph mining applications of our method.

Ahmad Mahmoody

Papers

THetA: inferring intra-tumor heterogeneity from high-throughput DNA sequencing data

A combinatorial approach for analyzing intra-tumor heterogeneity from high-throughput sequencing data

Adaptive user modeling with long and short-term preferences for personalized recommendation

Scalable Betweenness Centrality Maximization via Sampling

On zero-sum 6-flows of graphs