We study the homology of a filtered d-dimensional simplicial complex K as a single
algebraic entity and establish a correspondence that provides a simple description over …

Since a real univariate polynomial does not always have real roots, a very natural
algorithmic problem, is to design a method to count the number of real roots of a given …

Extracting useful information from large data sets can be a daunting task. Topological
methods for analysing data sets provide a powerful technique for extracting such …

Euler calculus with applications to signals and sensing Page 86 Proceedings of Symposia in
Applied Mathematics Proceedings of Symposia in Applied Mathematics Volume 70 , 2012 Euler …

H=-A+ V,(1.1) where A is the discrete Laplacian on Z d and V a potential, plays a central role
in quanturn mechanics. Starting with the seminal paper by P. Anderson [2], many works …

This paper presents a new reduction algorithm for the efficient computation of the homology
of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets …

This paper is a survey of the upper bounds on the complexity of basic algebraic and
geometric operations with Pfaffian and Noetherian functions, and with sets definable by …

∂ tu=(ϵ+ V) u+ δ| u| 2pu(p> 0)(1.1) on Zd×[0,∞), where 0< ϵ, δ≪ 1, is the discrete
Laplacian: ij={1,| i− j| l1= 1, 0, otherwise,(1.2) and V={vj} j∈ Zd, the potential, is a family of …

Topological data analysis offers a robust way to extract useful information from noisy,
unstructured data by identifying its underlying structure. Recently, an efficient quantum …

We prove that the 1-d quantum harmonic oscillator is stable under spatially localized, time
quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This …