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We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially-varying diffusivity $D(r)$, mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
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…
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
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…
Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different…
Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target…
Cellular traffic prediction is of great importance for operators to manage network resources and make decisions. Traffic is highly dynamic and influenced by many exogenous factors, which would lead to the degradation of traffic prediction…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
Long DNA molecules can be mapped by cutting them with restriction enzymes inside a narrow channel. Once cut, the individual fragments thus produced move away from each other due to diffusion and entropic effects. We investigate how long it…
We seek to characterize the motility of mouse fibroblasts on 2D substrates. Utilizing automated tracking techniques, we find that cell trajectories are super-diffusive, where displacements scale faster than t^(1/2) in all directions. Two…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…