Related papers: Renewal reward perspective on linear switching dif…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of…
Masked diffusion models (MDMs) offer a promising non-autoregressive alternative for large language modeling. Standard decoding methods for MDMs, such as confidence-based sampling, select tokens independently based on individual token…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…
Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
A variety of biomolecular systems rely on exploratory dynamics to reach target locations or states within a cell. Without a mechanism to remotely sense and move directly towards a target, the system must sample over many paths, often…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences across domains from natural language to biological sequence generation. For example, in the protein inverse folding task,…
Intercellular signaling has an important role in organism development, but not all communication occurs using the same mechanism. Here, we analyze the energy efficiency of intercellular signaling by two canonical mechanisms: diffusion of…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
Local drug delivery has received much recognition in recent years, yet it is still unpredictable how drug efficacy depends on physicochemical properties and delivery kinetics. The purpose of the current study is to provide a useful…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…
Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion…