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Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Cellular reactions have multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary in a wide range. This diversity leads to hybrid models that combine deterministic and stochastic…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space…
Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of…
Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction…
Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred…
This paper is a short summary of the main results in the thesis [1]. Based on the P2P paradigm we construct a stochastic model for a live media streaming content delivery network. Starting from the behavior of the out degree process of each…
In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically…
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…