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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(More)
AMS classification: 05C20 05C50 05C78 Keywords: Flow Nowhere-zero flow Zero-sum flow For a graph G, a zero-sum flow is an assignment of non-zero real numbers on the edges of G such that the total sum of all edges incident with any vertex of G is zero. A zero-sum k-flow for a graph G is a zero-sum flow with labels from the set {±1,. .. , ±(k − 1)}. In this(More)
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(More)
This peer-reviewed article can be downloaded, printed and distributed freely for any purposes (see copyright notice below). which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Tumor samples are typically heterogeneous, containing admixture by normal, non-cancerous cells and one(More)
Many cancer genome sequencing efforts are underway with the goal of identifying the somatic mutations that drive cancer progression. A major difficulty in these studies is that tumors are typically heterogeneous, with individual cells in a tumor having different complements of somatic mutations. However, nearly all DNA sequencing technologies sequence DNA(More)
We formulate and study a fundamental search and detection problem, Schedule Optimization, motivated by a variety of real-world applications, ranging from monitoring content changes on the web, social networks, and user activities to detecting failure on large systems with many individual machines. We consider a large system consists of many nodes, where(More)
Let G be a simple graph of order n and size m which is not a tree. If 3 is a natural number and the length of every cycle of G is divisible by , then m −2 (n − 2), and the equality holds if and only if the following hold: (i) is odd and G is a cycle of order or (ii) is even and G is a generalized θ-graph with paths of length 2. It is shown that for a (0(More)
Detecting new information and events in a dynamic network by probing individual nodes has many practical applications: discovering new webpages, analyzing influence properties in network, and detecting failure propagation in electronic circuits or infections in public drinkable water systems. In practice, it is infeasible for anyone but the owner of the(More)
Betweenness centrality (BWC) 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 great importance to many key applications that rely on BWC, including community detection and understanding graph vulnerability. Despite the large amount of work on scalable(More)