Related papers: Spectral Independence Beyond Uniqueness using the …
In this article, we derive a sharp mixing time estimate of the Glauber dynamics for the Curie-Weiss-Potts model in the low-temperature regime. In contrast to the high-temperature regime studied by Cuff et al. (J. Stat. Phys. 149: 432-477,…
This work develops scientific computing techniques to further the exploration of using boundary control alone to optimize mixing in Stokes flows. The theoretical foundation including mathematical model and the optimality conditions for…
The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…
Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…
Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…
We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for…
Graph self-supervised learning (GSSL) has emerged as a compelling framework for extracting informative representations from graph-structured data without extensive reliance on labeled inputs. In this study, we introduce Graph Interplay…
Given a reaction-diffusion system interacting via a complex network, we propose two different techniques to modify the network topology while preserving its dynamical behaviour. In the region of parameters where the homogeneous solution…
We study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of…
We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties of the stationary measure from within a…
This work introduces the IB-score, a family of independence-based score functions for robust learning of Markov networks independence structures. Markov networks are a widely used graphical representation of probability distributions, with…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
With great theoretical and practical significance, identifying the node spreading influence of complex network is one of the most promising domains. So far, various topology-based centrality measures have been proposed to identify the node…
We extend results of R. Holley beyond the integer lattice to a large class of groups which includes free groups. In particular we show that a shift-invariant measure is Gibbs if and only if it is Glauber-invariant. Moreover, any…
This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks…
We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete…