Related papers: A basic model of mutations
This study focuses on the problem of testing for normality of innovations in stationary time series models.To achieve this, we introduce an information matrix (IM) based test. While the IM test was originally developed to test for model…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…
The number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of…
Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be…
With recent advances in sequencing technologies, large amounts of epigenomic data have become available and computational methods are contributing significantly to the progress of epigenetic research. As an orthogonal approach to methods…
Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The simplest model of evolution, whose equilibrium state is…
We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
I develop a theoretical framework for inferring nonequilibrium equations of motion from incomplete experimental data. I focus on genuinely irreversible, Markovian processes, for which the incomplete data are given in the form of snapshots…
The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical…
This paper presents and derives the interrelations between survival analysis and master equation. Survival analysis deals with modeling the transitions between succeeding states of a system in terms of hazard rates. Questions related with…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation - that is, on the one hand, the formation of a…
For each element of certain families of integer sequences, we study the term-wise ratios of the Hankel transforms of three sequences related to that element by series reversion. In each case, the ratios define well-known sequences, and in…
Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.
Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings…
We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings…
The link between a particular class of growth processes and random matrices was established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. During the…