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Reconstructing components of a genomic mixture from data obtained by means of DNA sequencing is a challenging problem encountered in a variety of applications including single individual haplotyping and studies of viral communities.…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce…
Gene expression datasets offer insights into gene regulation mechanisms, biochemical pathways, and cellular functions. Additionally, comparing gene expression profiles between disease and control patients can deepen the understanding of…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
Molecular biology explains function of molecules by their geometrical and electronical structures that are mainly determined by utilization of quantum effects in chemistry. However, further quantum effects are not thought to play any…
Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions,…
Gene function prediction from microarray data is a first step toward better understanding the machinery of the cell from relatively cheap and easy-to-produce data. In this paper we investigate whether the knowledge of many metabolic…
Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell…
We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we…
Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the…
How to represent the genetic code? Despite the fact that it is extensively known, the DNA mapping into proteins remains as one of the relevant discoveries of genetics. However, modern genomic signal processing usually requires converting…
The techniques of data-driven backmapping from coarse-grained (CG) to fine-grained (FG) representation often struggle with accuracy, unstable training, and physical realism, especially when applied to complex systems such as proteins. In…
Bioinformatics, which is now a well known field of study, originated in the context of biological sequence analysis. Recently graphical representation takes place for the research on DNA sequence. Research in biological sequence is mainly…
Molecular transitions -- such as protein folding, allostery, and membrane transport -- are central to biology yet remain notoriously difficult to simulate. Their intrinsic rarity pushes them beyond reach of standard molecular dynamics,…
An interpretable generative model for handwritten digits synthesis is proposed in this work. Modern image generative models, such as Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), are trained by backpropagation…
Short blunt-ended DNA duplexes comprising 6 to 20 base pairs self-assemble into polydisperse semi-flexible chains due to hydrophobic stacking interactions between terminal base pairs. Above a critical concentration, which depends on…
The recent advances in sequencing technologies enables the assembly of individual genomes to the reference quality. How to integrate multiple genomes from the same species and to make the integrated representation accessible to biologists…
Much of the natural variation for a complex trait can be explained by variation in DNA sequence levels. As part of sequence variation, gene-gene interaction has been ubiquitously observed in nature, where its role in shaping the development…
The analysis of sequences (e.g., protein, DNA, and SMILES string) is essential for disease diagnosis, biomaterial engineering, genetic engineering, and drug discovery domains. Conventional analytical methods focus on transforming sequences…