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Torsion-weighted spanning acycle entropy in cubical lattices and Mahler measures
We compute the eigenvalues of up-Laplacians on cubical lattices and derive the torsion-weighted count of spanning acycles in cubical lattices by...
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Large deviation principle for persistence diagrams of random cubical filtrations
The objective of this article is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size...
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Face numbers of barycentric subdivisions of cubical complexes
The h -polynomial of the barycentric subdivision of any n -dimensional cubical complex with nonnegative cubical h -vector is shown to have only real...
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Homology Groups of Cubical Sets with Connections
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of “connection” as a new kind of degeneracy. In this...
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Improved approximate rips filtrations with shifted integer lattices and cubical complexes
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive...
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On a Convex Geometric Connection to Threshold Logic
A convex geometric connection to Threshold Logic will be reviewed. We have presented necessary and sufficient conditions to recognize cut-complexes...
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Property Testing and Expansion in Cubical Complexes
We consider expansion and property testing in the language of incidence geometry, covering both simplicial and cubical complexes in any dimension. We...
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Special cubulation of strict hyperbolization
We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence...
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Right-Angled Spaces and Groups
The notion of a “polyhedral product” of a collection of spaces (or pairs of spaces) indexed by the vertex set I of a simplicial complex L is used to...
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A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes
This paper presents the first polynomial time algorithm to compute geodesics in a CAT(0) cubical complex in general dimension. The algorithm is a...
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Fundamental Groups of Real Toric Spaces over Simple Polytopes
In this paper we study the cubical stuctures and fundamental groups of real toric spaces. We give an explicit presentation of the fundamental group...
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On Alan Schoen’s I-WP minimal surface
We discuss in detail Alan Schoen’s I-WP surface, an embedded triply periodic minimal surface of genus 4 with cubical symmetries. We exhibit various...
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Homotopy, homology, and persistent homology using closure spaces
We develop persistent homology in the setting of filtrations of (Čech) closure spaces. Examples of filtrations of closure spaces include metric...
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Homology and Euler characteristic of generalized anchored configuration spaces of graphs
In this paper we consider the generalized anchored configuration spaces on n labeled points on a graph. These are the spaces of all configurations of n ...
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The Persistent Homology of Dual Digital Image Constructions
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes,...
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Hierarchically hyperbolic groups and uniform exponential growth
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For...
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On hierarchical hyperbolicity of cubical groups
Let χ be a proper CAT(0) cube complex admitting a proper cocompact action by a group G . We give three conditions on the action, any one of which...
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Stirling complexes
In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number of resources to labeled nodes of a...
