5 papers
Solving polynomial inequalities over spaces of convex sets and applications
Saugata Basu, Hamidreza Amini Khorasgani, Hemanta K. Maji +1
We develop a symbolic elimination theory for finite systems of recursive containment inequalities whose unknowns are convex subsets of a finite-dimensional real vector space. The r…
Essential Simplices Dominate in Harmonic Representatives of One-Dimensional Persistent Classes
Saugata Basu, Aldo Guzmán-Sáenz, Laxmi Parida
Persistent homology summarizes the birth and death of topological features, but it does not by itself specify where a feature is located in the underlying complex. Harmonic persist…
On the convergence of critical points on real algebraic sets and applications to optimization
Saugata Basu, Ali Mohammad-Nezhad
Let and the zero set $V=\zero(\mathcal{P},\R^n)$, where is a finite set of polynomials. We i…
Bounds on the realizations of zero-nonzero patterns and sign conditions of polynomials restricted to varieties and applications
Saugata Basu, Laxmi Parida
We obtain upper bounds, independent of the ambient dimension, for the number of realizable zero-nonzero patterns and (over ordered fields) sign conditions of a finite family of pol…
Probing omics data via harmonic persistent homology
Davide Gurnari, Aldo Guzmán-Sáenz, Filippo Utro +3
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics d…