Related papers: A stochastic differential equation based algorithm…

An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for…

Speckled illumination enhances widefield fluorescence microscopy by enabling optical sectioning and super resolution. In random illumination microscopy, sequences of speckled illumination patterns are used to excite fluorescent samples and…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…

A procedure is developed to rigorously decompose experimental loss spectra of medium-energy electrons reflected from solid surfaces into contributions due to surface and volume electronic excitations. This can be achieved by analysis of two…

Accurate mesh-free simulation of fluid flows involving complex boundaries requires that the boundaries be captured accurately in terms of particles. In the context of incompressible/weakly-compressible fluid flow, the SPH method is more…

Branched flow is an interesting phenomenon that can occur in diverse systems. It is usually linear in the sense that the flow does not alter the medium properties. Branched flow of light on thin films was recently discovered. A question of…

This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…

In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…

Autonomous synthesis and characterization of inorganic materials requires the automatic and accurate analysis of X-ray diffraction spectra. For this task, we designed a probabilistic deep learning algorithm to identify complex multi-phase…

In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…

Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…

We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random…

Diffusion models have shown impressive performance for generative modelling of images. In this paper, we present a novel semantic segmentation method based on diffusion models. By modifying the training and sampling scheme, we show that…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

Coherent imaging systems, such as medical ultrasound and synthetic aperture radar (SAR), are subject to corruption from speckle due to sub-resolution scatterers. Since speckle is multiplicative in nature, the constituent image regions…

The plasma edge flow, situated at the intricate boundary between plasma and neutral particles, plays a pivotal role in the design of nuclear fusion devices such as divertors and pumps. Traditional numerical simulation methods, such as the…