Related papers: Exact propagation without analytical solutions
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…
Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…
Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a…
Time course measurement of single molecules on a cell surface provides detailed information on the dynamics of the molecules, which is otherwise inaccessible. To extract the quantitative information, single particle tracking (SPT) is…
We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable…
We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one…
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…
Stochastic models of reaction-diffusion systems are important for the study of biochemical reaction networks where species are present in low copy numbers or if reactions are highly diffusion limited. In living cells many such systems…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so…