Related papers: Geometric structures in pseudo-random graphs
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
We confirm recently proposed theorems for the structure of next-to-soft corrections in gauge and gravity theories using diagrammatic techniques, first developed for use in QCD phenomenology. Our aim is to provide a useful alternative…
Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…
In this note, we study non-transitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasi-isometric regular…
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
In this paper, we develop the groundwork for a graph theoretic toy model of supersymmetric quantum mechanics. Using discrete Witten-Morse theory, we demonstrate that finite graphs have a natural supersymmetric structure and use this…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…