Related papers: Dynamical systems generated by a gonosomal evoluti…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of {\it Drosophila melanogaster} can exhibit significant topological changes to facilitate dynamic regulatory…
We introduce the gonosomal algebra. Gonosomal algebra extend the evolution algebra of the bisexual population (EABP) defined by Ladra and Rozikov. We show that gonosomal algebras can represent algebraically a wide variety of sex…
The geometric phase is a fundamental quantity characterizing the holonomic feature of quantum systems. It is well known that the evolution operator of a quantum system undergoing a cyclic evolution can be simply written as the product of…
We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Using the example of a nonlinear driven damped oscillator, we show that this phase is resilient to…
We study a genetic regulatory network model developed to demonstrate that genetic robustness can evolve through stabilizing selection for optimal phenotypes. We report preliminary results on whether such selection could result in a…
This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or…
In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…
We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…
The significant role of epigenetic mechanisms within natural systems has become increasingly clear. This paper uses a recently presented abstract, tunable Boolean genetic regulatory network model to explore aspects of epigenetics. It is…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate…
In this paper, we study a discrete-time dynamical system generated by the evolution operator of a wild mosquito population with specific rates of birth and emergence from larvae to adults. The death rates of larvae and adults are assumed to…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
Handedness in humans - better performance using either the left or right hand - is personally familiar, moderately heritable, and regulated by many genes, including those involved in general body symmetry. But behavioral handedness, i.e.…