Related papers: Hyperbolic tilings and formal language theory
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
Supergroups of some hyperbolic space groups are classified as a continuation of our former works. Fundamental domains will be integer parts of truncated tetrahedra belonging to families F1 - F4, for a while, by the notation of E. Moln\'{a}r…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
How can we represent hierarchical information present in large type inventories for entity typing? We study the ability of hyperbolic embeddings to capture hierarchical relations between mentions in context and their target types in a…
In this paper, we remind previous results about the tilings $\{p,q\}$ of the hyperbolic plane. We introduce two new ways to split the hyperbolic plane in order to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.
We survey the known results regarding the boundaries of word-hyperbolic groups.
In recent years several novel models were developed to process natural language, development of accurate language translation systems have helped us overcome geographical barriers and communicate ideas effectively. These models are…
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) of cyclic zonotopes. The combinatorial theory of these objects is of interest in its own right and also has a…
We introduce a family of trivalent expanders which tessellate compact hyperbolic surfaces with large isometry groups. We compare this family with Platonic graphs and modifications of them and prove topological and spectral properties of…
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…
We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…
We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well known methods available for uniformly hyperbolic systems.
The aim of this paper is to explain a link between symplectic isotopies of open objects such as balls and flexibility properties of symplectic hypersurfaces. We get connectedness results for spaces of symplectic ellipsoids or maximal…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
In this paper we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules.…
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.