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Concept

Topological data analysis

Publications associées (26)

Cochains are all you need

Kelly Spry Maggs

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

Topological photonic transport in disordered scattering networks

Zhe Zhang, Zhechen Zhang

This Ph.D. thesis unveils the unique topological phenomena occurring in such networks, focusing on the intricate interplay between their Floquet topology, the presence of disorder, and their unitary scattering at microscopic and macroscopic scales. Using t ...

EPFL2024

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

Topologically Better Delineation of Curvilinear Structures

Doruk Oner

Curvilinear structures are frequently observed in a variety of domains and are essential for comprehending neural circuits, detecting fractures in materials, and determining road and irrigation canal networks. It can be costly and time-consuming to manuall ...

EPFL2023

Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet

Klaus Kern, Marko Burghard, Lukas Powalla

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, mor ...

Wiley-V C H Verlag Gmbh2023

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

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

A Shadow Perspective on Equivariant Hochschild Homologies

Kathryn Hess Bellwald

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

OXFORD UNIV PRESS2022

Landau levels of the Euler class topology

Oleg Yazyev, Yifei Guan

Two-dimensional systems with C2T (PT) symmetry exhibit the Euler class topology E is an element of Z in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating pha ...

AMER PHYSICAL SOC2022

Quasi-symmetry-protected topology in a semi-metal

Philip Johannes Walter Moll, Matthias Carsten Putzke, Yi-Chiang Sun, Chunyu Guo, Xiangwei Huang, Jonas De Jesus Diaz Gomez

The concept of quasi-symmetry-a perturbatively small deviation from exact symmetry-is introduced and leads to topological materials with strong resilience to perturbations. ...

NATURE PORTFOLIO2022

The Impact of Changes in Resolution on the Persistent Homology of Images

Adélie Eliane Garin

Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requiremen ...

IEEE2021

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

Geometric landscapes for material discovery within energy–structure–function maps

Berend Smit, Seyedmohamad Moosavi, Henglu Xu

Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal–organic frameworks (MOFs). To aid disco ...

2020

Experimental observation of the acoustic Z2 Weyl semimetallic phase in synthetic dimensions

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Scalar waves such as airborne sound lack an intrinsic spin degree of freedom, making the realization of sonic Z2 topological phases based on spin degeneracy challenging. Here, we demonstrate the relevance of synthetic dimensions and higher-dimensional topo ...

2020

Topological wave insulators: a review

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other in ...

2020

Topological exploration of artificial neuronal network dynamics

Kathryn Hess Bellwald, Gard Spreemann

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and statistical mechani ...

2019

Two-Tier Mapper, an unbiased topology-based clustering method for enhanced global gene expression analysis

Kathryn Hess Bellwald, Cathrin Brisken, Jacques Rougemont, Rachel Marcone

Motivation: Unbiased clustering methods are needed to analyze growing numbers of complex data sets. Currently available clustering methods often depend on parameters that are set by the user, they lack stability, and are not applicable to small data sets. ...

Oxford University Press2019

Topological states on the breathing kagome lattice

Adrien Bolens

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without se ...

2019