Concept
Size theory
Related publications (13)
Topologically Better Delineation of Curvilinear Structures
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 ...
EPFL2023From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem
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 involve ...
EPFL2022The Impact of Changes in Resolution on the Persistent Homology of Images
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 ...
IEEE2021Geometric 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 ...
2020Topological 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 ...
MIT PRESS2019A higher homotopic extension of persistent (co)homology
Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in induces a multiplicative filtration on the dg algebra of simplicial cochains, w ...
2018Principal component component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functi ...
Elsevier2016Shape-Persistent, Thermoresponsive Polypeptide Brushes Prepared by Vapor Deposition Surface-Initiated Ring-Opening Polymerization of alpha-Amino Acid N-Carboxyanhydrides
Harm-Anton Klok, Solenne Desseaux
Surface-grafting thermoresponsive polymers allows the preparation of thin polymer brush coatings with surface properties that can be manipulated by variation of temperature. In most instances, thermoresponsive polymer brushes are produced using polymers th ...
Amer Chemical Soc2015Enactive robot vision
The complexity of today's autonomous robots poses a major challenge for Artificial Intelligence. These robots are equipped with sophisticated sensors and mechanical abilities that allow them to enter our homes and interact with humans. For example, today's ...
EPFL2007Polyphenylene dendrimers as scaffolds for shape-persistent multiple peptide conjugates
The present work describes synthetic concepts for the coupling of peptides to polyphenylene dendrimers (PPDs). Novel functionalized cyclopentadienones have been synthesized whose Diels-Alder cycloaddition with various core molecules leads to polyphenylene ...
2005