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In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon…
In this paper we study the class of optimal entropy-transport problems introduced by Liero, Mielke and Savar\'e in Inventiones Mathematicae 211 in 2018. This class of unbalanced transport metrics allows for transport between measures of…
In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the standard output least-squares formulation where the…
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex…
In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic PDE from measurements. The convex energy functional method with Tikhonov regularization is applied to tackle this problem. For the discretization…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…
Poor performance of quantitative analysis in histopathological Whole Slide Images (WSI) has been a significant obstacle in clinical practice. Annotating large-scale WSIs manually is a demanding and time-consuming task, unlikely to yield the…
Different theoretical methods used for the description of diffractive processes in small-x deep inelastic scattering are reviewed. The semiclassical approach, where a partonic fluctuation of the incoming virtual photon scatters off a…
A neutron optical transport system is proposed which comprises nested short elliptical mirrors located halfway between two common focal points M and M'. It images cold neutrons from a diverging beam or a source with finite size at M by…
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing…
One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while…
This paper addresses the challenging problem of category-level pose estimation. Current state-of-the-art methods for this task face challenges when dealing with symmetric objects and when attempting to generalize to new environments solely…
Inverting real images into the noise space is essential for editing tasks using diffusion models, yet existing methods produce non-Gaussian noise with poor editability due to the inaccuracy in early noising steps. We identify the root…
We introduce light diffusion, a novel method to improve lighting in portraits, softening harsh shadows and specular highlights while preserving overall scene illumination. Inspired by professional photographers' diffusers and scrims, our…
The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use is made of…
We consider a diffusion equation with highly oscillatory coefficients that admits a homogenized limit. As an alternative to standard corrector problems, we introduce here an embedded corrector problem, written as a diffusion equation in the…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…