Related papers: Fast approximate simulation of finite long-range s…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…
Tau-leaping is a popular discretization method for generating approximate paths of continuous time, discrete space, Markov chains, notably for biochemical reaction systems. To compute expected values in this context, an appropriate…
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via…
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 propose the $S$-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the $\tau$-leaping and $R$-leaping algorithms. These algorithms are…
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational…
We propose a $\tau$-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional $\tau$-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
Background: Species abundance distributions in chemical reaction network models cannot usually be computed analytically. Instead, stochas- tic simulation algorithms allow sample from the the system configuration. Although many algorithms…
We consider the important problem of estimating parameter sensitivities for stochastic models of reaction networks that describe the dynamics as a continuous-time Markov process over a discrete lattice. These sensitivity values are useful…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes, we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy…
Tau leap schemes were originally designed for the efficient time stepping of discrete state and continuous in time Markov processes arising in stochastic chemical kinetics. Previous convergence results on tau leaping schemes have been…
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…