15 citations · 24 across the 9 of their papers we have counts for
10 papers
The fiber of persistent homology for trees
David Beers, Jacob Leygonie
Consider the space of continuous functions on a geometric tree whose persistent homology gives rise to a finite generic barcode . We show that there are exactly as many path…
Algorithmic Reconstruction of the Fiber of Persistent Homology on Cell Complexes
Jacob Leygonie, Gregory Henselman-Petrusek
Let be a finite simplicial, cubical, delta or CW complex. The persistence map takes a filter as input and returns the barcodes $\math…
A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis
Jacob Leygonie, Mathieu Carrière, Théo Lacombe +1
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as…
Fiber of Persistent Homology on Morse functions
Jacob Leygonie, David Beers
Let be a Morse function on a smooth compact manifold with boundary. The path component containing of the space of Morse functions giving rise to…
The Fiber of Persistent Homology for simplicial complexes
Jacob Leygonie, Ulrike Tillmann
We study the inverse problem for persistent homology: For a fixed simplicial complex , we analyse the fiber of the continuous map on the space of filters that assi…
Optimisation of Spectral Wavelets for Persistence-based Graph Classification
Ka Man Yim, Jacob Leygonie
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice…
A Framework for Differential Calculus on Persistence Barcodes
Jacob Leygonie, Steve Oudot, Ulrike Tillmann
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to…
Adversarial Computation of Optimal Transport Maps
Jacob Leygonie, Jennifer She, Amjad Almahairi +2
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) ar…
Combining neural networks and signed particles to simulate quantum systems more efficiently, Part III
Jean Michel Sellier, Gaetan Marceau Caron, Jacob Leygonie
This work belongs to a series of articles which have been dedicated to the combination of signed particles and neural networks to speed up the time-dependent simulation of quantum…
Combining neural networks and signed particles to simulate quantum systems more efficiently, Part II
Jean Michel Sellier, Jacob Leygonie, Gaetan Marceau Caron
Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of…