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Suppose an experiment is conducted on pairs of objects with outcome responses a continuous variable measuring the interactions among the pairs. Furthermore, assume the response variable is hard to measure numerically but easy to be coded…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…
The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions $\Gamma^{(i)}$ and the third-order aperture…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Federated causal discovery aims to uncover the causal relationships between entities while protecting data privacy, which has significant importance and numerous applications in real-world scenarios. Existing federated causal structure…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are…
We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
The human brain is a complex system defined by multi-way, higher-order interactions invisible to traditional pairwise network models. Although a diverse array of analytical methods has been developed to address this shortcoming, the field…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…
Recently, graphs have been widely used to represent many different kinds of real world data or observations such as social networks, protein-protein networks, road networks, and so on. In many cases, each node in a graph is associated with…