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Given their widespread usage in the real world, the fairness of clustering methods has become of major interest. Theoretical results on fair clustering show that fairness enjoys transitivity: given a set of small and fair clusters, a…
There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…
We apply the microscopic coupled-cluster method (CCM) to the spin-$1\over2$ $XXZ$ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us…
The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem…
This paper presents a novel clustering algorithm from the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) algorithmic family. The newly proposed clustering variant leverages the concept of similarity and…
The ground state of an antiferromagnetic Heisenberg model on L X L clusters joined by a single bond and balanced Bethe clusters are investigated with quantum Monte Carlo and modified spin-wave theory. The improved Monte Carlo method of…
Local constraint is closely related to the gauge field, so constrained models are usually effective low energy descriptions and important in condensed matter physics. On the other hand, local restriction hinders the application of numerical…
Clustering is an important research topic for wireless sensor networks (WSNs). A large variety of approaches has been presented focusing on different performance metrics. Even though all of them have many practical applications, an…
Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, like Wolff, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear…
Network dismantling aims at breaking a network into disconnected components, and attacking vertices that intersect with many loops has proven to be a most efficient strategy. But the existing loop-focusing methods treat the short loops…
In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…
Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to…
Many real-world systems can be studied in terms of pattern recognition tasks, so that proper use (and understanding) of machine learning methods in practical applications becomes essential. While a myriad of classification methods have been…
We implement a cluster-update Monte Carlo algorithm to simulate magnetic dipoles of the XY-spin type confined in a two-dimensional plane. The long-range character and anisotropy in the dipole interaction are handled by using the…
An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel…