Related papers: Stochastic models of the chemostat
Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Small systems in a thermodynamic medium --- like colloids in a suspension or the molecular machinery in living cells --- are strongly affected by the thermal fluctuations of their environment. Physicists model such systems by means of…
The purpose of this paper is to show that it is possible to replace Monod's type model of a chemostat by a constraint based model of bacteria at the genome scale. This new model is an extension of the RBA model of bacteria developed in a…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Estimating the parameters governing the dynamics of a system is a prerequisite for its optimal control. We present a simple but powerful method that we call STEADY, for STochastic Estimation algorithm for DYnamical variables, to estimate…
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…