Related papers: Spectral Independence Beyond Uniqueness with. the …
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random graph with fixed connectivity) is investigated by an approximate theory which provides exact results for equilibrium properties. The time-dependent solutions of the…
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…
We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…
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…
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbol{\beta} > 1$ and external fields $\boldsymbol{\lambda}<1$ (or symmetrically, $\boldsymbol{\lambda}>1$) on…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs,…
We propose a new model and estimation framework for spatiotemporal streamflow exceedances above a threshold that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture…
A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
In this paper, we prove a general result concerning finite-range, attractive interacting particle systems on $\{-1, 1\}^{\mathbb{Z}^d}$. If the particle system has a unique stationary measure and, in a precise sense, relaxes to this…
An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…
The direct detection of exoplanets with high-contrast instruments can be boosted with high spectral resolution. For integral field spectrographs yielding hyperspectral data, this means that the field of view consists of diffracted starlight…
We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing…
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,…
We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\beta$ and random boundary conditions $\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the…
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…
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…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…