Related papers: Constrained evolution algebras and dynamical syste…
We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution,…
Consider the maximal nilpotent subalgebra $n_+(A_1^{(1)})$ of the simplest affine algebra $A_1^{(1)}$ which is one of the $\mathbb{N}$-graded Lie algebras with minimal number of generators. We show truncated versions of this algebra in…
We explore a Boltzmann scheme for studying the evolution of compact binary populations of globular clusters. We include processes of compact-binary formation by tidal capture and exchange encounters, binary destruction by dissociation and…
The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits…
Context: Field stars are not always single stars, but can often be found in bound double systems. Since binary frequencies in the birth places of stars, young embedded clusters, are sometimes even higher than on average the question arises…
We investigate the dynamical formation and evolution of binaries containing neutron stars in dense globular clusters. Our numerical simulations combine a simple Monte Carlo prescription for stellar dynamics, a sophisticated binary…
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing…
Close white dwarf binaries play an important role across a range of astrophysics, including thermonuclear supernovae, the Galactic low-frequency gravitational wave signal, and the chemical evolution of the Galaxy. Progress in developing a…
Based on a simple object, an i.i.d. sequence of positive integer-valued random variables, $\{a_n\}_{n\in \mathbb{Z}}$, we introduce and study two random structures and their connections. First, a population dynamics, in which each…
We study evolutionary equations in exponentially weighted $\mathrm{L}^{2}$-spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the $\nu$-adjoint system, which turns out to describe a…
Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be two simple algebras with involution over $K$. In this note we study the embedding problem for algebras with involution. More specifically, if the…
Developmental constraints have been postulated to limit the space of feasible phenotypes and thus shape animal evolution. These constraints have been suggested to be the strongest during either early or mid-embryogenesis, which corresponds…
We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
Bicubic maps are in bijection with \beta(0,1)-trees. We introduce two new ways of decomposing \beta(0,1)-trees. Using this we define an endofunction on \beta(0,1)-trees, and thus also on bicubic maps. We show that this endofunction is in…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present the first known examples of undirected structures acting as suppressors of selection for any fitness…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…