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Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…
We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We…
Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here we provide a…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. Hence, every injective colouring is a star colouring and every star colouring…
Entanglement has evolved from an enigmatic concept of quantum physics to a key ingredient of quantum technology. It explains correlations between measurement outcomes that contradict classical physics, and has been widely explored with…
Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic…
Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based…
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a…
We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the…
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
One of the greatest challenges facing our society is the discovery of new innovative crystal materials with specific properties. Recently, the problem of generating crystal materials has received increasing attention, however, it remains…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. A considerable body of works has been devoted to exploring their properties and applications. In this…