Related papers: Incorporating age and delay into models for biophy…

Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…

For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…

We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in…

We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

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…

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation…

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…

Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed…

In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment…

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…