Related papers: Splitting pairs and the number of clusters generat…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
Natural genomes sometimes encode two different proteins in staggered reading frames of the same DNA sequence. Despite the prevalence of these 'overlapping genes' across the tree of life, it remains unknown whether arbitrary protein pairs…
The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic…
In the well-studied Stable Roommates problem, we seek a stable matching of agents into pairs, where no two agents prefer each other over their assigned partners. However, some instances of this problem are unsolvable, lacking any stable…
With the help of a simple 20 letters, lattice model of heteropolymers, we investigate the energy landscape in the space of designed good-folder sequences. Low-energy sequences form clusters, interconnected via neutral networks, in the space…
Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered.…
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we…
We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…
We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as…
We have simulated the evolution of sexually reproducing populations composed of individuals represented by diploid genomes. A series of eight bits formed an allele occupying one of 128 loci of one haploid genome (chromosome). The…
Replicability requires that algorithmic conclusions remain consistent when rerun on independently drawn data. A central structural question is composition: given $k$ problems each admitting a $\rho$-replicable algorithm with sample…
Haplotyping is the bioinformatics problem of predicting likely haplotypes based on given genotypes. It can be approached using Gusfield's perfect phylogeny haplotyping (PPH) method for which polynomial and linear time algorithms exist.…
In cancer research, clustering techniques are widely used for exploratory analyses and dimensionality reduction, playing a critical role in the identification of novel cancer subtypes, often with direct implications for patient management.…
Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…
The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci.…
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. In [Neukirch, Bovier, 2016] it is proved that…
We propose a new approach for clustering DNA features using array CGH data from multiple tumor samples. We distinguish data-collapsing: joining contiguous DNA clones or probes with extremely similar data into regions, from clustering:…