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We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. Here, we describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov…
Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…
We analyze response of a macromolecule near to a substrate; the substrate is tiled in the sequential and specific manner so that repeat units of the macromolecule may have different response on its adsorption in different directions onto…
We introduce a mathematical framework for retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules and their interaction using string diagrams in layered props - a recently introduced…
We introduce an original model of quantum phenomena, a model that provides a picture of a "deep structure", an "underlying pattern" of quantum dynamics. We propose that the source of a particle and all of that particle's possible detectors…
It has been recently shown that collisional models can be used to derive a general form for the master equations which describe the reduced time evolution of a composite multipartite quantum system, whose components "propagate" in an…
We introduce a new class of Fokker-Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can…
We use the decoherent histories approach to quantum theory to derive the form of an effective theory describing the coupling of classical and quantum variables. The derivation is carried out for a system consisting of a large particle…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It…
We use density functional theory to describe the phase behaviors of rigid molecules. The construction of kernel function G(x, P, x, P) is discussed. Excluded-volume potential is calculated for two types of molecules with C_{2v} symmetry.…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
The striped patterns in rocks, characterized by thin dark bands and thick light bands, are a result of the natural processes that have shaped the rocks through in situ metamorphism. Notably, the dark and light bands are composed of similar…
Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only…
It has been speculated that gravity could be an emergent phenomenon, with classical general relativity as an effective, macroscopic theory, valid only for classical systems at large temporal and spatial scales. As in classical continuum…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…