Related papers: Diffusion in sparse networks: linear to semi-linea…
Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…
Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a…
We analyze diffusion of particles on a two dimensional square lattice. Each lattice site contains an arbitrary number of particles. Interactions affect particles only in the same site, and are macroscopically represented by the excess…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
Diffusion models represent a powerful family of generative models widely used for image and video generation. However, the time-consuming deployment, long inference time, and requirements on large memory hinder their applications on…
Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and…
We consider the time dependent dispersion properties of overdamped tracer particles diffusing in a one dimensional periodic potential under the influence of an additional constant tilting force $F$. The system is studied in the region where…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
We investigate diffusion in supersonic, turbulent, compressible flows. Supersonic turbulence can be characterized as network of interacting shocks. We consider flows with different rms Mach numbers and where energy necessary to maintain…
A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in…
The prediction of diffusion in solids is necessary to understand the microstructure evolution in materials out of equilibrium. Although one can reasonably predict diffusive transport coefficients using atomistic methods, these approaches…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
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…
The Diffusion Map is a nonlinear dimensionality reduction technique used to analyze high-dimensional data, with recent applications extending to datasets from the social sciences. Previous research has given little attention to how the…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
We consider a sequence of idealized measurements of time-separation $\Delta t$ onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and…