相关论文: Random clusters in the Villain and XY models

In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind…

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground…

There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper…

Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…

Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of…

Tree-level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted…

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…

In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models…

We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their…

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed…

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is…

We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…

In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…

In addressing the challenge of exponential scaling with the number of agents we adopt a cluster-based representation to approximately solve asymmetric games of very many players. A cluster groups together agents with a similar "strategic…

The Widom-Rowlinson model of a fluid mixture is studied using a new cluster algorithm that is a generalization of the invaded cluster algorithm previously applied to Potts models. Our estimate of the critical exponents for the two-component…

We show how clustering standard errors in one or more dimensions can be justified in M-estimation when there is sampling or assignment uncertainty. Since existing procedures for variance estimation are either conservative or invalid, we…

In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal…

We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the…