Related papers: Cluster mechanisms in the fully frustrated Ising m…
We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We…
Simulations of frustrated quantum antiferromagnets suffer from a severe sign problem. We solve the ergodicity problem of the loop-cluster algorithm in a natural way and apply a powerful strategy to address the sign problem. For the spin 1/2…
We investigate a frustrated Ising spin system on the garnet lattice composed of a specific network of corner-sharing triangles. By means of Monte Carlo simulations with the heat bath algorithm, we discuss the magnetic properties at finite…
We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…
Though biological and artificial complex systems having inhibitory connections exhibit high degree of clustering in their interaction pattern, the evolutionary origin of clustering in such systems remains a challenging problem. Using…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Simulation results of Ising systems for several update rules, observables, and dimensions are analyzed. The lattice-size dependence is discussed for the autocorrelation times and for the weights of eigenvalues, giving fit results in the…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the…
The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
We present the loop algorithm, a new type of cluster algorithm that we recently introduced for the F model. Using the framework of Kandel and Domany, we show how to GENERALIZE the algorithm to the arrow flip symmetric 6 vertex model. We…
Data analysis plays an indispensable role for value creation in industry. Cluster analysis in this context is able to explore given datasets with little or no prior knowledge and to identify unknown patterns. As (big) data complexity…
This study focuses on exploring the use of local interpretability methods for explaining time series clustering models. Many of the state-of-the-art clustering models are not directly explainable. To provide explanations for these…
Clustering is one of the most common tasks of Machine Learning. In this paper we examine how ideas from topology can be used to improve clustering techniques.
Within a general cluster framework, we discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For…
We consider a zero-field Ising model defined on a quasiperiodic graph, the so-called Labyrinth tiling. Exact information about the critical behaviour is obtained from duality arguments and the subclass of models which yield commuting…