Related papers: Quasi-steady-state approximation and numerical sim…

In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…

In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail…

In Molecular Communications via Diffusion (MCvD), messenger molecules are emitted by a transmitter and propagate randomly through the fluidic environment. In biological systems, the environment can be considered a bounded space, surrounded…

With the emergence of diffusion models as a frontline generative model, many researchers have proposed molecule generation techniques with conditional diffusion models. However, the unavoidable discreteness of a molecule makes it difficult…

A stochastic model for the dynamics of enzymatic catalysis in explicit, effective solvents under physiological conditions is presented. Analytically-computed first passage time densities of a diffusing particle in a spherical shell with…

The Patlak-Keller-Segel system of equations (PKS) is a classical example of aggregation-diffusion equation in which the repulsive effect of diffusion is in competition with the attractive chemotaxis term. Recent work on the…

Large Language Models (LLMs) generalize across tasks via reusable representations and flexible reasoning, yet remain brittle in real deployment under evolving tasks and continual distribution shift. A common approach is Test-Time Adaptation…

Despite the growing success of diffusion models in continuous-valued domains (e.g., images), similar efforts for discrete domains such as text have yet to match the performance of autoregressive language models. In this work, we present…

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…

We study the reaction-diffusion Lotka-Volterra predator-prey model with Dirichlet boundary condition. In the case of equal diffusion rates and equal growth rates, the synchronized steady state solution is proved to be locally asymptotically…

We investigate how to couple a learnable brain-like'' controller to a cell-like'' Gray--Scott substrate to steer pattern formation with minimal effort. A compact convolutional policy is embedded in a differentiable PyTorch…

This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend…

We have calculated the strength distributions of the dipole response in spherical nuclei, ranging all over the periodic table. The calculations were performed within two microscopic models: the discretized quasiparticle random phase…

Cytoplasmic streaming, the coherent flow of cytoplasm, plays a critical role in transport and mixing over large scales in eukaryotic cells. In many large cells, this process is driven by active forces at the cell boundary, such as cortical…

Low-density lipoproteins (LDLs) serve as nutrient reservoirs in egg yolk for embryonic development and as promising drug carriers. Both roles critically depend on their mobility in densely crowded biological environments. Under these…

Comprehending the long-timescale dynamics of protein-ligand complexes is very important for drug discovery and structural biology, but it continues to be computationally challenging for large biomolecular systems. We introduce…

We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose of this work is to identify when solutions decay to…

Diffusion models have shown promise in text generation, but often struggle with generating long, coherent, and contextually accurate text. Token-level diffusion doesn't model word-order dependencies explicitly and operates on short, fixed…

Predicting spatial gene expression from routine H\&E enables large-scale molecular profiling, yet current models treat this as isolated pointwise tasks, thereby overlooking essential biological structures like gene coordination and spatial…

We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…