Related papers: Bounding the partition function of spin-systems

Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…

We propose a notion of contraction function for a family of graphs and establish its connection to the strong spatial mixing for spin systems. More specifically, we show that for anti-ferromagnetic Potts model on families of graphs…

We solve a 4-(bond)-vertex model on an ensemble of 3-regular Phi3 planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The method of solution, by mapping onto an Ising model in field, is inspired by…

One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal…

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…

Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…

Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for…

$ \def\vecc#1{\boldsymbol{#1}} $We design a polynomial time algorithm that for any weighted undirected graph $G = (V, E,\vecc w)$ and sufficiently large $\delta > 1$, partitions $V$ into subsets $V_1, \ldots, V_h$ for some $h\geq 1$, such…

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…

This paper lies in the context of the studies of eigenfunctions of graphs having minimum cardinality of support. One of the tools is the weight-distribution bound, a lower bound on the cardinality of support of an eigenfunction of a…

Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that…

Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…

The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key…

Let $Y_v, v\in V,$ be $[0,1]$-valued random variables having a dependency graph $G=(V,E)$. We show that \[ \mathbb{E}\left[\prod_{v\in V} Y_{v} \right] \leq \prod_{v\in V} \left\{ \mathbb{E}\left[Y_v^{\frac{\chi_b}{b}}\right]…

We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…

Let $E$ be a bounded open subset of $\mathbb{R}^n$. We study the following questions: For i.i.d. samples $X_1, \dots, X_N$ drawn uniformly from $E$, what is the probability that $\cup_i \mathbf{B}(X_i, \delta)$, the union of $\delta$-balls…

Given a simple connected non-directed graph $G=(V(G),E(G))$, we consider two families of graph invariants: $RX_\Sigma(G) = \sum_{uv \in E(G)} F(r_u,r_v)$ (which has gained interest recently) and $RX_\Pi(G) = \prod_{uv \in E(G)} F(r_u,r_v)$…