Related papers: Distributions of Triplets in Genetic Sequences
We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity of recombining segments, several studies examined whether this could lead to the…
In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN)…
The multiple parameter logistic equation has previously been utilized to determine the global stability of ternary codes, based on the arrangement of different symbols within the code. This approach has been extended to DNA and RNA…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…
We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…
We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms,…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…