Related papers: The Cavity Approach to Parallel Dynamics of Ising …
Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions…
A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm cite{BKL75}, which is efficient but is hard to parallelize using conservative methods. Our parallel algorithm is…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
We develop lagged Metropolis-Hastings walk for sampling from simple undirected graphs according to given stationary sampling probabilities. We explain how to apply the technique together with designed graphs for sampling of units-in-space.…
The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like and undirected random graphs, this observable is…
Nonequilibrium behavior and dynamic phase transition properties of a kinetic Ising model under the influence of periodically oscillating random-fields have been analyzed within the framework of effective field theory (EFT) based on a…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the…
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…
We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellular automaton inspired by the cavity…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$ penalization methods. However, current methods assume that the data are independent and…
Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we introduce…
Graph pattern matching is a fundamental operation for the analysis and exploration ofdata graphs. In thispaper, we presenta novel approachfor efficiently finding homomorphic matches for hybrid graph patterns, where each pattern edge may be…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…