Related papers: Linked Cluster Expansions via Hypergraph Decomposi…
We propose a computational methodology based on a hierarchical cluster growth process to solve spin-3/2 Ising models efficiently. The method circumvents the exponential complexity (\(4^{N}\)) of the canonical ensemble partition function by…
We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad clustering coefficient. We determine the average quad clustering coefficient and its distribution in real-world hypergraphs and compare…
We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians $\mathcal{H}=\mathcal{H}_0 +V$. Its cluster additivity is an essential ingredient to set up perturbative or…
In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…
The variety and complexity of relations in multimedia data lead to Heterogeneous Information Networks (HINs). Capturing the semantics from such networks requires approaches capable of utilizing the full richness of the HINs. Existing…
In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the…
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Deep clustering has recently emerged as a promising technique for complex data clustering. Despite the considerable progress, previous deep clustering works mostly build or learn the final clustering by only utilizing a single layer of…
This paper presents a concise tutorial on spectral clustering for broad spectrum graphs which include unipartite (undirected) graph, bipartite graph, and directed graph. We show how to transform bipartite graph and directed graph into…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
The simulation of strongly correlated electron systems remains a formidable challenge. Certain experimentally relevant dynamical response functions are especially difficult to calculate, due to issues of finite-size effects and the ill…
Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…
A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a…
Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the…
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems.…
Machine learning is becoming widely used in condensed matter physics. Inspired by the concept of image super-resolution, we propose a method to increase the size of lattice spin configurations using deep convolutional neural networks.…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish…