Related papers: A Novel Combinatorial Method for Estimating Transc…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
Background: In the Nearest-Neighbor Thermodynamic Model, a standard approach for RNA secondary structure prediction, the energy of the multiloops is modeled using a linear entropic penalty governed by three branching parameters. Although…
There are currently plenty of programs available for mapping short sequences (reads) to a genome. Most of them, however, including such popular and actively developed programs as Bowtie, BWA, TopHat and many others, are based on…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…
Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that has stimulated enormous interest in statistics, data science, and computational biology due to the high dimensionality, complexity, and large scale associated with…
Single-cell transcriptomics techniques, such as scRNA-seq, attempt to characterize gene expression profiles in each cell of a heterogeneous sample individually. Due to growing amounts of data generated and the increasing complexity of the…
The RNA-sequencing (RNA-seq) is becoming increasingly popular for quantifying gene expression levels. Since the RNA-seq measurements are relative in nature, between-sample normalization of counts is an essential step in differential…
Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…
Graph Neural Networks (GNNs) often struggle to capture the link-specific structural patterns crucial for accurate link prediction, as their node-centric message-passing schemes overlook the subgraph structures connecting a pair of nodes.…
We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has…
Subgraph isomorphism counting is an important problem on graphs, as many graph-based tasks exploit recurring subgraph patterns. Classical methods usually boil down to a backtracking framework that needs to navigate a huge search space with…
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is…
Clustering analysis is fundamental in single-cell RNA sequencing (scRNA-seq) data analysis for elucidating cellular heterogeneity and diversity. Recent graph-based scRNA-seq clustering methods, particularly graph neural networks (GNNs),…
Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
We investigate the problem of computing the top-$k$ simple shortest paths in weighted digraphs. While the single-pair variant -- finding the top-$k$ simple shortest paths between two specified vertices -- has been extensively studied over…
Motivation: RNA-seq has made feasible the analysis of a whole set of expressed mRNAs. Mapping-based assembly of RNA-seq reads sometimes is infeasible due to lack of high-quality references. However, de novo assembly is very challenging due…