3 papers
math.AT2020
Homological Scaffold via Minimal Homology Bases
Marco Guerra, Alessandro De Gregorio, Ulderico Fugacci +2
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representa…
math.PR2020
Alternative probabilistic representations of Barenblatt-type solutions
Alessandro De Gregorio, Roberto Garra
A general class of probability density functions \[u(x,t)=Ct^{-αd}\left (1-\left (\frac{\|x\|}{ct^α}\right )^β\right )_+^γ,\quad x\in \mathbb{R}^d,t>0,\] is considered, containing…
math.AT2020
Landscapes of data sets and functoriality of persistent homology
Wojciech Chacholski, Alessandro De Gregorio, Nicola Quercioli +1
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a…