Related papers: Reflected diffusions defined via the extended Skor…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Electron back-scatter diffraction (EBSD) has traditionally relied upon methods such as the Hough transform and dictionary Indexing to interpret diffraction patterns and extract crystallographic orientation. However, these methods encounter…

In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction…

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we…

Non-Hermitian optics has revealed a series of counterintuitive phenomena with profound implications for sensing, lasing, and light manipulation. While the non-Hermiticity of Hamitonians is well-recognized, recent advancements in…

In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a…

In spite of the utility of 3-D electron back-scattered diffraction (EBSD) microscopy, the data collection process can be time-consuming with serial-sectioning. Hence, it is natural to look at other modalities, such as polarized light (PL)…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…

We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…

Equivariant diffusion policies (EDPs) combine the generative expressivity of diffusion models with the strong generalization and sample efficiency afforded by geometric symmetries. While steering these policies with reinforcement learning…

Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…

This paper investigates random walks and diffusion limits on a broad class of fractal graphs generated by Edge Iterated Graph Systems (EIGS). We prove that the rescaled simple random walks converge in the…

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…

This paper is devoted to the study of reflected Stochastic Differential Equations with jumps when the constraint is not on the paths of the solution but acts on the law of the solution. This type of reflected equations have been introduced…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but…