Related papers: Computing Diffusion State Distance using Green's F…
Diffusion distillation provides an effective approach for learning lightweight and few-steps diffusion models with efficient generation. However, evaluating their generalization remains challenging: theoretical metrics are often impractical…
This paper investigates random walks and diffusion limits on a broad class of fractal graphs generated by Edge Iterated Graph Systems (EIGS). We prove that the rescaled simple random walks converge in the…
Over the last few years, network science has proved to be useful in modeling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex…
This work is an attempt to transfer to biology the methods developed in physics for formulating and solving the kinetic equations in which the kernel of the integral operator in spatial coordinates is slowly decreasing with increasing…
Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high…
Distributed diffusion is a powerful algorithm for multi-task state estimation which enables networked agents to interact with neighbors to process input data and diffuse information across the network. Compared to a centralized approach,…
This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering…
The $L^k$-Wasserstein distance $\mathbb{W}_k (k\ge 1)$ and the probability distance $\mathbb{W}_\psi$ induced by a concave function $\psi$, are estimated between different diffusion processes with singular coefficients. As applications, the…
Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
Information, ideas, and diseases, or more generally, contagions, spread over space and time through individual transmissions via social networks, as well as through external sources. A detailed picture of any diffusion process can be…
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint…
Diffusion-based trajectory optimization has emerged as a powerful planning paradigm, but existing methods require either learned score networks trained on large datasets or analytical dynamics models for score computation. We introduce…
Modelling diffusion processes on dynamic contact networks is an important research area for epidemiology, marketing, cybersecurity, and ecology. However, current diffusion models cannot capture transmissions occurring for indirect…
The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node…