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"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
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 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…
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…
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…
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…
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…
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…
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…
Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…
Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
A new algorithm, "HiER-leap", is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies…
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…
Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy…