Related papers: Repeat distributions from unequal crossovers
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental…
Chromosomal crossovers play a crucial role in meiotic cell division, as they ensure proper chromosome segregation and increase genetic variability. Experiments have consistently revealed two key observations across species: (i) the number…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…
In the present paper we propose to describe gene networks in biological systems using probabilistic algorithms. We describe gene duplication in the process of biological evolution using introduction of the replica procedure for…
We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size…
Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…
Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are…
A model of genomic sequence evolution on a species tree should include not only a sequence substitution process, but also a coalescent process, since different sites may evolve on different gene trees due to incomplete lineage sorting.…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of…
We show that evolutionary computation can be implemented as standard Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms' can be constructed that are reversible Markov chains that satisfy detailed balance; it…
Some genes can change their relative locations in a genome. Thus for different individuals of the same species, the orders of genes might be different. Such jumping genes are called transposons. A practical problem is to determine…
We study derangements of $\{1,2,\ldots,n\}$ under the Ewens distribution with parameter $\theta$. We give the moments and marginal distributions of the cycle counts, the number of cycles, and asymptotic distributions for large $n$. We…
Due to its ability to summarise 'real-time' epidemic behaviour, the time-dependent reproduction number, Rt, is a useful metric for tracking pathogen transmission and quantifying the effects of interventions during infectious disease…