146 citations · 193 across the 10 of their papers we have counts for
12 papers
Testing the variety hypothesis
A. Lerario, P. Roos Hoefgeest, M. Scolamiero +1
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of g…
Certifying Robustness via Topological Representations
Jens Agerberg, Andrea Guidolin, Andrea Martinelli +3
We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis.…
Relative Representations: Topological and Geometric Perspectives
Alejandro García-Castellanos, Giovanni Luca Marchetti, Danica Kragic +1
Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based…
Algebraic Wasserstein distances and stable homological invariants of data
Jens Agerberg, Andrea Guidolin, Isaac Ren +1
Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this…
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…
Homotopical decompositions of simplicial and Vietoris Rips complexes
Wojciech Chacholski, Alvin Jin, Martina Scolamiero +1
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of suc…
Quantifying topological invariants of neuronal morphologies
Lida Kanari, Paweł Dłotko, Martina Scolamiero +4
Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspe…
Topological analysis of the connectome of digital reconstructions of neural microcircuits
Pawe Dotko, Kathryn Hess, Ran Levi +6
A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simul…
Multidimensional Persistence and Noise
Martina Scolamiero, Wojciech Chachólski, Anders Lundman +2
In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the categor…
Combinatorial presentation of multidimensional persistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
A multifiltration is a functor indexed by that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the na…
A presentation of general multipersistence modules computable in polynomial time?
Antonio Patriarca, Martina Scolamiero, Francesco Vaccarino
Multipersistence homology modules were introduced by G.Carlsson and A.Zomorodian which gave, together with G.Singh, an algorithm to compute their Groebner bases. Although their alg…
Combinatorial resolutions of multigraded modules and multipersistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
Let and a multigraded module. In this work we interpret as a multipersistent homology module and give a multigraded resolution of it. The construction…