Related papers: Spectral partitions on infinite graphs
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
For thermal systems, standard perturbation theory breaks down because of the absence of stable, observable asymptotic states. We show, how the introduction of {\it statistical} quasi-particles (stable, but not observable) gives rise to a…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…
Several graphical representations of the mass and width spectrum of unstable subatomic particles are presented. Such plots are useful tools for introducing students to the particle zoo and provide students an alternate way to organize…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan square root separation result for planar…
The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
Hierarchies are of fundamental interest in both stochastic optimal control and biological control due to their facilitation of a range of desirable computational traits in a control algorithm and the possibility that they may form a core…
Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be…
Heat can flow from cold to hot at any phase separation. Therefore Lynden-Bell's gravo-thermal catastrophe must be reconsidered. The original objects of Thermodynamics, the separation of phases at first order phase transitions, like boiling…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…