Related papers: Extended error threshold mechanism in {\it quasisp…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given…
The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA search is…
Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost…
We study the dynamics of genetic code evolution. The model of Vetsigian et al. [1] and Vetsigian [2] uses the mechanism of horizontal gene transfer to demonstrate convergence of the genetic code to a near universal solution. We reproduce…
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
Quantitative methods for studying biodiversity have been traditionally rooted in the classical theory of finite frequency tables analysis. However, with the help of modern experimental tools, like high throughput sequencing, we now begin to…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
We present a theoretical as well as experimental investigation of a population of self-replicating segments of code subject to random mutation and survival of the fittest. Under the assumption that such a system constitutes a minimal system…
A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible…
How mutations accumulate in genomes is the central question of molecular evolution theories, however our understanding of this process is far from complete. Drake's rule is a notoriously universal property of genomes from microbes to…
We study entropy and optimal transport theory in the free probabilistic setting motivated by the large-$n$ theory of random tuples of matrices. We define a new version of free entropy $\chi_{\operatorname{chron}}^{\mathcal{U}}$, which is…
A self-replicating system where the elements belonging to a solution category can replicate themselves by copying their own informations, is considered. The information carried by each element is defined by an element of all the n multiple…
Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The…
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds…