Related papers: Graph kinematics of discrete physical objects: bey…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten…
Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a…
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry…
We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
We develop two approaches to Quantum (or Non-commutative) Graphs based on arbitrary von Neumann algebras $M\subseteq\mathcal B(H)$: one looking at operator bimodules of Hilbert--Schmidt (instead of bounded) operators, and the second looking…
The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in 2D materials, where even a line defect can…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various categorical structures in a systematic and…
We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more…
Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…
The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…
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…