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We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the…

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…

Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

We present a novel approach aimed at high-performance uncertainty quantification for time-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loeeve expansion…

A discrete model for computer simulations of the clustering dynamics of Social Amoebae is presented. This model incorporates the wavelike propagation of extracellular signaling cAMP, the sporadic firing of cells at early stage of…

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…

Most of our understanding of bacterial chemotaxis comes from studies of Escherichia coli. However, recent evidence suggests significant departures from the E. coli paradigm in other bacterial species. This variation may stem from different…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…

The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as…

Many practical techniques for probabilistic inference require a sequence of distributions that interpolate between a tractable distribution and an intractable distribution of interest. Usually, the sequences used are simple, e.g., based on…

A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting…

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…

Much of our mechanistic understanding of the functions of biological macromolecules is based on static structural experiments, which can be modelled either as single structures or conformational ensembles. While these provide us with…

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…

Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing…