Related papers: Thinned COE random matrix models for DNA replicati…
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
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…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…
In this paper, a new natural discrete version of the one parameter polynomial exponential family of distributions have been proposed and studied. The distribution is named as Natural Discrete One Parameter Polynomial Exponential (NDOPPE)…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…
Genome wide comparisons between enteric bacteria yield large sets of conserved putative regulatory sites on a gene by gene basis that need to be clustered into regulons. Using the assumption that regulatory sites can be represented as…
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…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study…
The origin of life can be understood mathematically to be the origin of information that can replicate. The likelihood that entropy spontaneously becomes information can be calculated from first principles, and depends exponentially on the…
Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…
We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation, and that follow the same distribution as the original observation, up to a (known) scaling of a…