Related papers: Graphical C(3)-T(6) implies CAT(0)

We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical $C'(1/6)$--small cancellation condition is cubulable. This yields a new large class of…

This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various `nonpositive…

We study complex surfaces with locally CAT(0) polyhedral Kahler metrics and construct such metrics on CP^2 with various orbifold structures. In particular, in relation to questions of Gromov and Davis-Moussong we construct such metrics on a…

Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…

This note presents some numerical examples worked out in order to show the reader how to implement, within a widely accessible computational setting, the methodology for achieving zero cancellation in linear multivariable systems discussed…

We embed a countably categorical group G into a locally compact group c(G) with a non-trivial topology and study how topological properties of c(G) are connected with the structure of definable subgroups of G.

In this paper we study CAT(0) groups and their splittings as graphs of groups. For one-ended CAT(0) groups with isolated flats we prove a theorem characterizing exactly when the visual boundary is locally connected. This characterization…

This is the second in a series of papers on the relation between algebraic set theory and predicative formal systems. In part I, we introduced the notion of a predicative category of small maps and obtained the result that such categories…

We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also…

We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural embedding in the torus or in the Klein bottle. We also show that locally grid graphs are minors of hexagonal tilings…

We give a new construction of a C*-algebra from a cancellative semigroup $P$ via partial isometric representations, generalising the construction from the second named author's thesis. We then study our construction in detail for the…

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…

Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…

We introduce the notion of k-lower divergence for geodesic rays in CAT(0) spaces. Building on the work of Charney and Sultan we give various characterizations of k-contracting geodesic rays using k-lower divergence and k-slim triangles. We…

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in…

Current deep learning models for classification tasks in computer vision are trained using mini-batches. In the present article, we take advantage of the relationships between samples in a mini-batch, using graph neural networks to…

We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473

The notions of nonpositive curved spaces and biautomatic groups are generalizations of the geometric properties of hyperbolic spaces and computational properties of their fundamental groups. Given the mutual origins of these conditions, one…

We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…