Related papers: Network-theoretic approach to sparsified discrete …
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
We make several advances broadly related to the maintenance of electrical flows in weighted graphs undergoing dynamic resistance updates, including: 1. More efficient dynamic spectral vertex sparsification, achieved by faster length…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We introduce a new method of statistical analysis to characterise the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
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…
We consider a soluble model of large $\phi^{4}$-graphs randomly embedded in one compactified dimension; namely the large-order behaviour of finite-temperature perturbation theory for the partition function of the anharmonic oscillator. We…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riemannian manifolds. Building upon the Navier-Stokes equations,…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Sparsification aims at extracting a reduced core of associations that best preserves both the dynamics and topology of networks while reducing the computational cost of simulations. We show that the semi-metric topology of complex networks…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense…
We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…