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Concept

Persistence module

Publications associées (11)

Persistence and the Sheaf-Function Correspondence

Nicolas Michel Berkouk

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a finite dimensional real vector space, Kashiwara-Schapira have recently in ...

Cambridge Univ Press2023

The Impact of Data Persistence Bias on Social Media Studies

Tugrulcan Elmas

Social media studies often collect data retrospectively to analyze public opinion. Social media data may decay over time and such decay may prevent the collection of the complete dataset. As a result, the collected dataset may differ from the complete data ...

Assoc Computing Machinery2023

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Algebraic Homotopy Interleaving Distance

Nicolas Michel Berkouk

The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

2020

Optimization of a Py-GC/MS method for silicone -based lubricants analysis

Christophe Roussel

Condom evidence can be analysed using several analytical techniques, such as FTIR, MALDI-MS or DART-TOF-MS, but the only one that was used on real samples for transfer and persistence studies in the context of sexual assault or rape cases was Py-GC/MS. How ...

2020

A system for planning and/or providing neuromodulation

Grégoire Courtine, Marco Capogrosso, Fabien Bertrand Paul Wagner, Vincent Delattre, Karen Minassian

The present invention relates to a system for planning and/or providing neuromodulation (10), especially neurostimulation, comprising - a stimulation related basic data storage module (28) for storing the stimulation related basic data, - a stimulation rel ...

2019

A system for planning and/or providing neurostimulation for a patient

Grégoire Courtine, Marco Capogrosso, Fabien Bertrand Paul Wagner, Vincent Delattre, Tomislav Milekovic, Flavio Raschella

The present invention relates to a system (10) for planning and/or providing neurostimulation for a patient, comprising: - a pathological spinal cord map storage module (48) for storing at least one pathological spinal cord map (49) describing the activati ...

2019

Practical Deep Stereo (PDS): Toward applications-friendly deep stereo matching

François Fleuret, Anton Ivanov, Stepan Tulyakov

End-to-end deep-learning networks recently demonstrated extremely good performance for stereo matching. However, existing networks are difficult to use for practical applications since (1) they are memory-hungry and unable to process even modest-size image ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Multidimensional Persistence and Noise

Martina Scolamiero

In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71-93, 2009; Lesnick in Found Comput Math 15(3):613-650, 2015) via what we call tame functors and noise systems. A noise system leads to a p ...

Springer2017

Combinatorial presentation of multidimensional persistent homology

Martina Scolamiero

A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x(1),...x(r)]-module structure on the homology of a multifiltration of ...

Elsevier2017