Related papers: Nonlinear diffusion processes: geometric ideas and…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to…
The paper is an overview of the main contributions of a Bulgarian team of researchers to the problem of finding the possible structures and waves in the open nonlinear heat conducting medium, described by a reaction-diffusion equation.…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a…
In the realm of image generation, the quest for realism and customization has never been more pressing. While existing methods like concept sliders have made strides, they often falter when it comes to no-AIGC images, particularly images…
Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension $d=1$) or hypersurface (in dimension $d\geq2$).…
Some issues in inclusive and exclusive diffractive processes are discussed.
Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In…
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
The paper shows how the diffusive movement of ions through a channel protein can be described as a chemical reaction over an arbitrary shaped potential barrier. The result is simple and intuitive but without approximation beyond the…
Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…
Generative AI models have revolutionized various fields by enabling the creation of realistic and diverse data samples. Among these models, diffusion models have emerged as a powerful approach for generating high-quality images, text, and…
This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya,…