UMedia

start over

Person aiming a gun at a tree outside of the cabin at the maple sugar camp in Trout Lake

Description:: The person in the photograph may be Cavour Hartley.
Contributed By:: Archives and Special Collections, Kathryn A. Martin Library, University of Minnesota Duluth
Last Updated:: 2024-02-08

Persistent Homology to Protein Structural Analysis

Description:: Persistent homology and persistent diagrams have been developed as tools of topological data analysis. They provide a robust topological characterization of a given (discrete) geometrical data. In this talk, I will present our recent researches on applying persistent diagrams to protein structural analysis. Topological characterizations of prote...
Creator:: Hiraoka, Yasu (Kyushu University)
Created:: 2013-06-04
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent Homology of Time-Delay Embeddings

Description:: We present in this talk a theoretical framework for studying the persistent homology of point clouds from time-delay (or sliding window) embeddings. We will show that maximum 1-d persistence yields a suitable measure of periodicity at the signal level, and present theorems which relate the resulting diagrams to the choices of window size, embedd...
Creator:: Perea, Jose A (Duke University)
Created:: 2013-10-10
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent Homology of Self-maps

Description:: When a topological space is known only from sampling,persistence provides a useful tool to study its homologicalproperties. In many applications one can sample not only the space,but also a map acting on the space. The understanding of thetopological features of the map is often of interest, in particularin the analysis of time series dynamics b...
Creator:: Mrozek, Marian (Jagiellonian University)
Created:: 2013-10-09
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent homology and microlocal sheaf theory

Description:: After a brief review on sheaves in the derived setting and the notion of gamma-sheaves, I will expose the main results of arXiv:1705.00955 and arXiv:1805.00349, a joint work with Masaki Kashiwara. The aim is to better understand persistent homology in higher dimension. For that purpose, one first proves that constructible sheaves on a real finit...
Creator:: Schapira, Pierre (UniversitĂ© de Paris VI
Created:: 2018-05-22
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2019-02-04

Persistent homology and its fibre (Remotely)

Description:: Persistent homology is a main tool in topological data analysis. So it is natural to ask how strong this quantifier is and how much information is lost. There are many ways to ask this question. Here we will concentrate on the case of level set filtrations on simplicial sets. Already the example of a triangle yields a rich structure with the Möb...
Creator:: Tillmann, Ulrike (University of Oxford)
Created:: 2022-08-03
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2022-09-06

Persistent Homology and Applications

Creator:: Carlsson, Gunnar (Stanford University)
Created:: 2013-09-24
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent Homology Analysis of Biomolecules

Description:: Proteins are the most important biomolecules for livingorganisms. The understanding of protein structure, function, dynamics, andtransport is one of the most challenging tasks in biological science. Wehave introduced persistent homology for extracting molecular topologicalfingerprints (MTFs) based on the persistence of molecular topologicalinvar...
Creator:: Xia, Kelin (Michigan State University)
Created:: 2015-07-20
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent Holes in the Universe

Description:: I will present a new topological formalism that, for the first time,describes topology as a multi-scale concept. This has a direct and strongrelevance to the topological analysis of structure formation process inthe cosmos, given that this proceeds in a hierarchical fashion. Rooted inalgebraic topology, the concepts I will describe stem from (pe...
Creator:: Pranav, Pratyush (Rijksuniversiteit te Groningen)
Created:: 2013-10-14
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistent cup-length

Description:: Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by softwares, such as Ripser. The cup product operation which is available at cohomology level gives rise to a graded ring structure that extends the usual vector space structure and is ...
Creator:: Zhou, Ling (The Ohio State University)
Created:: 2022-08-02
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2022-09-06

Persistent Cohomology for Dynamical Systems

Description:: I will describe a recently-developed approach to studying experimental data obtained from a periodic or quasiperiodic dynamical system. The idea is to use persistent cohomology to construct robust new coordinate functions on the data. These coordinates take values in the circle, so they may correspond to phase variables or angular variables impl...
Creator:: de Silva, Vin (Pomona College)
Created:: 2013-11-19
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistence Probabilities

Description:: Persistence probabilities concern how likely it is that a stochasticprocess has a long excursion above fixed level and of what are therelevant scenarios for this behavior. Power law decay is expectedin many cases of physical significance and the issue is to determineits power exponent parameter. I will describe recent progress in thisdirection (...
Creator:: Dembo, Amir (Stanford University)
Created:: 2014-11-01
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistence of Common Topological Structures by a Commutative Triple Ladder Quiver

Description:: In this talk, I present a new method to detect robust common topological structures of two geometric objects. The idea is to extend the notion of persistent homology to representations on a commutative triple ladder quiver. (i) I show that representations on the commutative triple ladder quiver are finite type. (ii) The Auslander-Reiten quiver o...
Creator:: Hiraoka, Yasu (Kyushu University)
Created:: 2014-03-06
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistence and point clouds' Functoriality, diagrams, difficulties in classifying diagrams, multidimensional persistence, Gröbner bases

Creator:: Carlsson, Gunnar (Stanford University)
Created:: 2009-06-23
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persistence and Category Theory

Description:: I find it convenient to think about persistence in terms of category theory. I will explain why this is natural, and how it simplifies my thinking. Sometimes it gives access to deeper theorems, and more often it is a tidy language that expresses just what I need. Examples will include: sublevelset and interlevelset homology; merge trees and Reeb...
Creator:: de Silva, Vin
Created:: 2013-10-09
Contributed By:: University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:: 2018-06-19

Persion Furniture store and office building

Creator:: Breitwish, A. J. (Photographer)
Created:: 1924
Contributed By:: University of Minnesota Libraries, Northwest Architectural Archives.
Last Updated:: 2017-11-27