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In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

Machine Learning · Computer Science 2020-05-20 Shijie Xu , Jiayan Fang , Xiang-Yang Li

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

Data Structures and Algorithms · Computer Science 2023-07-27 Antares Chen , Lorenzo Orecchia , Erasmo Tani

We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising…

Probability · Mathematics 2016-07-20 Andrea Collevecchio , Timothy M. Garoni , Timothy Hyndman , Daniel Tokarev

We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer…

Disordered Systems and Neural Networks · Physics 2008-08-04 Yoshiki Matsuda , Hidetoshi Nishimori , Koji Hukushima

The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…

Quantum Physics · Physics 2022-11-16 Yusen Wu , Jingbo Wang

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

Combinatorics · Mathematics 2015-08-04 Alexander Barvinok , Pablo Soberón

We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical…

Machine Learning · Computer Science 2022-06-07 S. Yagiz Olmez , Amirhossein Taghvaei , Prashant G. Mehta

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

Optimization and Control · Mathematics 2015-01-20 Giorgos Stathopoulos , Milan Korda , Colin N. Jones

In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…

Mathematical Physics · Physics 2024-03-11 João Maia

This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…

Combinatorics · Mathematics 2016-09-06 Jonathan Berry , Mark Goldberg

We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…

Statistical Mechanics · Physics 2011-09-28 Daniel G. Barci , Daniel A. Stariolo

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Data Structures and Algorithms · Computer Science 2013-09-25 Vincent Blondel , Kyomin Jung , Pushmeet Kohli , Devavrat Shah

This paper introduces a technique to enhance the efficiency of quadratic machine learning models, particularly Field-Aware Factorization Machines (FFMs) handling binary data. Our approach strategically reduces model size through optimized…

Materials Science · Physics 2025-03-27 Yasuharu Okamoto

We investigate the application of graph-cut methods for the study of the critical behaviour of the two-dimensional random-field Ising model. We focus on exact ground-state calculations, crossing the phase boundary of the model at zero…

Disordered Systems and Neural Networks · Physics 2022-04-04 Argyro Mainou , Nikolaos G. Fytas , Martin Weigel

Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute…

Machine Learning · Computer Science 2024-11-14 Hamidreza Behjoo , Michael Chertkov

The density of states for the three-dimensional Ising model is calculated with high-precision from multicanonical simulations. This allows us to estimate the leading partition function zeros for lattice sizes up to L=32. Combining previous…

Statistical Mechanics · Physics 2008-11-26 Nelson A. Alves , J. R. Drugowich de Felicio , Ulrich H. E. Hansmann

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort recently toward developing novel,…

We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…

Statistical Mechanics · Physics 2007-05-23 V. N. Plechko

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…

Mathematical Physics · Physics 2016-11-23 Valentin Bonzom , Francesco Costantino , Etera R. Livine