相关论文: Non-Markovian gene expression
We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial…
This study introduces a comparative modeling framework using stationary and non-stationary transition probabilities within a Markov Decision Process (MDP) to assess COVID-19 disease dynamics. Stationary transition probabilities assume…
We investigate simple models for strictly non-ergodic stochastic processes $x_t$ ($t$ being the discrete time step) focusing on the expectation value $v$ and the standard deviation $\delta v$ of the empirical variance $v[x]$ of finite time…
We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
One of the fundamental questions in population dynamics is how biological populations respond to environmental perturbations. In population dynamics, the mean fitness and the fraction of a trait in the steady state are important because…
At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…
We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$…
The inherent probabilistic nature of the biochemical reactions, and low copy number of species can lead to stochasticity in gene expression across identical cells. As a result, after induction of gene expression, the time at which a…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
At present, the problem to steer a non-Markovian process with minimum energy between specified end-point marginal distributions remains unsolved. Herein, we consider the special case for a non-Markovian process y(t) which, however, assumes…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
By examining the deterministic limit of a general $\epsilon$-dependent generator for Markovian dynamics, which includes the continuous Fokker-Planck equations and discrete chemical master equations as two special cases, the intrinsic…
We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition path theory we…