Related papers: Distributions of Triplets in Genetic Sequences
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The…
Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…
Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…
We obtain new results concerning the Sato-Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having prescribed arithmetic…
We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained…
In this article we propose a novel method to estimate the frequency distribution of linguistic variables while controlling for statistical non-independence due to shared ancestry. Unlike previous approaches, our technique uses all available…
We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…
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…
In this paper we consider Markov chains with transition rates that depend on a small parameter $\varepsilon$. Under a mild assumption on the asymptotics of these transition rates, we describe the behavior of the chain at various…