Related papers: Stochastic filtering for multiscale stochastic rea…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses,…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical…
New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme…
Event-based sampling has been proposed as a general technique for lowering the average communication rate in remote state estimation, which can be important in scenarios with constraints on resources such as network bandwidth or sensor…
Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…
We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…
We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…
2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that filtering textures after…
"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…