Related papers: Strong spatial mixing for colorings on trees and i…

We analyse uniformly random proper $k$-colourings of sparse graphs with maximum degree $\Delta$ in the regime $\Delta < k\ln k $. This regime corresponds to the lower side of the shattering threshold for random graph colouring, a…

We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla…

We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…

We establish rapid mixing of the random-cluster Glauber dynamics on random $\Delta$-regular graphs for all $q\ge 1$ and $p<p_u(q,\Delta)$, where the threshold $p_u(q,\Delta)$ corresponds to a uniqueness/non-uniqueness phase transition for…

We present a perfect marginal sampler of the unique Gibbs measure of a spin system on $\mathbb Z^2$. The algorithm is an adaptation of a previous `lazy depth-first' approach by the authors, but relaxes the requirement of strong spatial…

We study Gibbsian models of unbounded integer-valued spins on trees which possess a symmetry under height-shift. We develop a theory relating boundary laws to gradient Gibbs measures, which applies also in cases where the corresponding…

We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. This covariate…

In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct colors. Since finding such a tree is NP-hard in general,…

We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the…

We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…

The mode of a collection of values (i.e., the most frequent value in the collection) is a key summary statistic. Finding the mode in a given range of an array of values is thus of great importance, and constructing a data structure to solve…

The problem of sampling proper $q$-colorings from uniform distribution has been extensively studied. Most of existing samplers require $q\ge \alpha \Delta+\beta$ for some constants $\alpha$ and $\beta$, where $\Delta$ is the maximum degree…

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ALO20]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations, and implies that…

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is…

Spatial modulation (SM) is a promising multiple-input multiple-output system used to increase spectral efficiency. The maximum likelihood (ML) decoder jointly detects the transmitted SM symbol, which is of high complexity. In this paper, a…

We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…

We study Markov chains for randomly sampling $k$-colorings of a graph with maximum degree $\Delta$. Our main result is a polynomial upper bound on the mixing time of the single-site update chain known as the Glauber dynamics for planar…

Quantitative susceptibility mapping (QSM) utilizes MRI signal phase to estimate local tissue susceptibility, which has been shown useful to provide novel image contrast and as biomarkers of abnormal tissue. QSM requires addressing a…

On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…

Exploring MSSM parameter space after the discovery of Higgs Boson with mass 125 GeV naturally demands large top-squark mixing or large trilinear coupling parameter $A_t$ in particular, so as to avoid excessively heavy squark, specially for…