Related papers: Quantifying Genetic Innovation: Mathematical Found…

We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…

Persistent homology tracks topological features across geometric scales, encoding birth and death of cycles as barcodes. We develop a complementary theory where the filtration parameter is algebraic precision rather than geometric scale.…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Reconciling a gene tree with a species tree is an important task that reveals much about the evolution of genes, genomes, and species, as well as about the molecular function of genes. A wide array of computational tools have been devised…

Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…

Multiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms. We describe a…

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there…

Gene finding is the task of identifying the locations of coding sequences within the vast amount of genetic code contained in the genome. With an ever increasing quantity of raw genome sequences, gene finding is an important avenue towards…

Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes, which can complicate the reconstruction problem due to the fact that…

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different…

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…

We present TreeClone, a latent feature allocation model to reconstruct tumor subclones subject to phylogenetic evolution that mimics tumor evolution. Similar to most current methods, we consider data from next-generation sequencing of tumor…

Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…

Mixed communities of organisms are found in many environments (from the human gut to marine ecosystems) and can have profound impact on human health and the environment. Metagenomics studies the genomic material of such communities through…

Using software UDEC to simulate the instability failure process of slope under seismic load, studing the dynamic response of slope failure, obtaining the deformation characteristics and displacement cloud map of slope, then analyzing the…

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…

Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive…

Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…