Related papers: Message-Passing Algorithms and Homology
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…
This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert…
Holographic MIMO communications, enabled by large-scale antenna arrays with quasi-continuous apertures, is a potential technology for spectrum efficiency improvement. However, the increased antenna aperture size extends the range of the…
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,…
Persistent homology (PH) characterizes the shape of brain networks through persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…
A statistical system is classically defined on a set of microstates $E$ by a global energy function $H : E \to \mathbb{R}$, yielding Gibbs probability measures (softmins) $\rho^\beta(H)$ for every inverse temperature $\beta = T^{-1}$. Gibbs…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
Distributed computing is a standard way to scale up machine learning and data science algorithms to process large amounts of data. In such settings, avoiding communication amongst machines is paramount for achieving high performance. Rather…
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…
The purpose of this paper is to introduce a new condition \[ \hbox{(C)$\hspace{1cm} \alpha \int_{0}^{u}f(s)ds \leq uf(u)+\beta u^{2}+\gamma,\,\,u>0$} \] for some $\alpha, \beta, \gamma>0$ with…
The operator-theoretic dichotomy underlying diffusion on directed networks is \emph{symmetry versus non-self-adjointness} of the Markov transition operator. In the reversible (detailed-balance) regime, a directed random walk $P$ is…
Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a…
Reactio-nonlocal diffusion equations model nonlocal transport and anomalous diffusion by replacing the Laplacian with a fractional power, capturing diffusion mechanisms beyond Brownian motion. We primarily study the semilinear problem \[…
Using the theory of $L^p$-graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value…
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…
We establish conditions for which graph Laplacians $\Delta_{\lambda,\epsilon}$ on compact, boundaryless, smooth submanifolds $\mathcal{M}$ of Euclidean space are semiclassical pseudodifferential operators ($\Psi$DOs): essentially, that the…
This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian…
In diffusion-based algorithms for adaptive distributed estimation, each node of an adaptive network estimates a target parameter vector by creating an intermediate estimate and then combining the intermediate estimates available within its…