Related papers: Informed and Automated k-Mer Size Selection for Ge…
Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…
Motivation: Building the histogram of occurrences of every $k$-symbol long substring of nucleotide data is a standard step in many bioinformatics applications, known under the name of $k$-mer counting. Its applications include developing de…
Genome assembly is a prominent problem studied in bioinformatics, which computes the source string using a set of its overlapping substrings. Classically, genome assembly uses assembly graphs built using this set of substrings to compute…
The problem of assembling DNA fragments starting from imperfect strings given by a sequencer, classified as NP hard when trying to get perfect answers, has a huge importance in several fields, because of its relation with the possibility of…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
K-mer counting is a requisite process for DNA assembly because it speeds up its overall process. The frequency of K-mers is used for estimating the parameters of DNA assembly, error correction, etc. The process also provides a list of…
The de novo assembly of large, complex genomes is a significant challenge with currently available DNA sequencing technology. While many de novo assembly software packages are available, comparatively little attention has been paid to…
G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the…
We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that…
De novo genome assembly is the process of stitching short DNA sequences to generate longer DNA sequences, without using any reference sequence for alignment. It enables high-throughput genome sequencing and thus accelerates the discovery of…
Generative models for graphs are increasingly becoming a popular tool for researchers to generate realistic approximations of graphs. While in the past, focus was on generating graphs which follow general laws, such as the power law for…
Genome sequencing is essential to decode genetic information, identify organisms, understand diseases and advance personalized medicine. A critical step in any genome sequencing technique is genome assembly. However, de novo genome…
DNA technologies have evolved significantly in the past years enabling the sequencing of a large number of genomes in a short time. Nevertheless, the underlying computational problem is hard, and many technical factors and limitations…
De novo genome assembly is challenging in highly repetitive regions; however, reference-guided assemblers often suffer from bias. We propose a framework for pangenome-guided sequence assembly, which can resolve short-read data in complex…
Metagenome assembly is the process of transforming a set of short, overlapping, and potentially erroneous DNA segments from environmental samples into the accurate representation of the underlying microbiomes's genomes. State-of-the-art…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
Fast coverage of k-space is a major concern to speed up data acquisition in Magnetic Resonance Imaging (MRI) and limit image distortions due to long echo train durations. The hardware gradient constraints (magnitude, slew rate) must be…
Advances in data collecting technologies in genomics have significantly increased the need for tools designed to study the genetic basis of many diseases. Effective statistical methods should excel in both prediction accuracy and biomarker…
In computational genomics, many analyses rely on efficient storage and traversal of $k$-mers, motivating compact representations such as spectrum-preserving string sets (SPSS), which store strings whose $k$-mer spectrum matches that of the…