Related papers: Random clusters in the Villain and XY models
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
Correlations among the independently measured physical properties of globular clusters (GCs) can provide powerful tests for theoretical models and new insights into their dynamics, formation, and evolution. We review briefly some of the…
In this work we obtain wrapping probabilities for Ising spin clusters on a torus. We use the analogy with the tricritical point of a Potts model with dilution. The formula obtained are tested against numerical simulation. We also provide…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed…
A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…
We investigate the distributions of the link overlap, P(Q), in 3-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states, and calculate its contribution to P(Q). We find…
Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network…
Boxplots and related visualization methods are widely used exploratory tools for taking a first look at collections of univariate variables. In this note an extension is provided that is specifically designed to detect and display…
In this paper, we first review some basic concepts associated with a model for social interaction previously proposed by us. Each agent is seen as an array of variables that can be found in different states. The agents are then allowed to…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In…
The paper presents a new numerical approach for studying the thermodynamical and dynamical properties of finite spin-$\frac{1}{2}$ $XY$ chains. Special attention is given to examining the influence of disorder on the average transverse…
Latent features learned by deep learning approaches have proven to be a powerful tool for machine learning. They serve as a data abstraction that makes learning easier by capturing regularities in data explicitly. Their benefits motivated…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…
The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly…