Using graphs to model pairwise relationships between entities is a ubiquitous framework for
studying complex systems and data. Simplicial complexes extend this dyadic model of …

In this paper, we present three distributed algorithms for coverage verification in sensor
networks with no location information. We demonstrate how, in the absence of localization …

Algebraic topology is one of the most important creations in mathematics which uses
algebraic tools to study topological spaces. The basic goal is to find algebraic invariants that …

Fix a finite set of points in Euclidean n-space E^n, thought of as a point-cloud sampling of a
certain domain D⊂E^n. The Vietoris–Rips complex is a combinatorial simplicial complex …

Persistent Homology is a computational method of data mining in the field of Topological
Data Analysis. Large-scale data analysis with persistent homology is computationally …

With the aim to generalize the theory of Lp and L π de Rham cohomology to metric measure
spaces, we define the scaled Alexander-Spanier cohomology and Lp and L π Alexander …

A cut locus of a point p in a compact Riemannian manifold M is defined as the set of points
where minimizing geodesics issued from p stop being minimizing. It is known that a cut locus …

A coverage problem of sensor networks is studied. Following recent works by Ghrist et al., in
which computational topological methods are applied for the coverage problem, We present …

We describe a data structure, a rectangular complex, that can be used to represent
hyperconvex metric spaces that have the same topology (although not necessarily the same …

In this paper we generalize work using topological methods for testing wireless/sensor
network coverage to the problem of covering a geographically-distributed wireless network …