Related papers: Mutation model for oligonucleotides fitting a Yule…
A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution…
A quantum spin chain is identified by the labels of a vector state of a Kashiwara crystal basis. The intensity of the one-spin flip is assumed to depend from the variation of the labels. The rank ordered plot of the numerically computed,…
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…
The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -- also called "histories" -- with a finite number $n$ of leaves. We study the…
We study a model of a population with individuals sampled from different species. The Yule-$\Lambda$ nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a constant rate…
We consider a model of a population in which individuals are sampled from different species. The Yule-Kingman nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a…
In this short note the QED extension of the nucleon spin sum rule is considered. To this end, the leading-order (LO) QED evolution kernels for the quark/gluon helicity and orbital-angular-momentum (OAM) distributions are calculated, as well…
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
Given a gene-tree labeled topology $G$ and a species tree $S$, the "ancestral configurations" at an internal node $k$ of $S$ represent the combinatorially different sets of gene lineages that can be present at $k$ when all possible…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states…
The Yule process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Omega-trees,…
Circular double stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo…
Using the XXZ model for the description of one-dimensional magnetic materials we show that an energy flux, j_E, produces a shift, dk (j_E)^0.5, in the characteristic wavenumber of the spin-spin correlations. We estimate dk for a realistic…
For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool…
We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise…
We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
The main statistical distributions applicable to the analysis of genome architecture and genome tracks are briefly discussed and critically assessed. Although the observed features in distributions of element lengths can be equally well…
Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the…