Related papers: Generalizing Gillespie's direct method to enable n…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…
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 propose a faster algorithm for individual based simulations for adaptive dynamics based on a simple modification to the standard Gillespie Algorithm for simulating stochastic birth-death processes. We provide an analytical explanation…
Higher-order dynamics refer to mechanisms where collective mutual or synchronous interactions differ fundamentally from their pairwise counterparts through the concept of many-body interactions. Phenomena absent in pairwise models, such as…
Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's Stochastic Simulation Algorithm (SSA) for chemical…
With recent and rapid advancements in artificial intelligence (AI), understanding the foundation of purposeful behaviour in autonomous agents is crucial for developing safe and efficient systems. While artificial neural networks have…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological…
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always…
A detailed algorithmic explanation is required for how a network of chemical reactions can generate the sophisticated behavior displayed by living cells. Though several previous works have shown that reaction networks are computationally…
Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…
Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we…
In the present paper we propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some…
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. We…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
The jump unravelling of a quantum master equation decomposes the dynamics of an open quantum system into abrupt jumps, interspersed by periods of coherent dynamics when no jumps occur. Such open quantum systems are ubiquitous in quantum…