Suppose ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. Vin de Silva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity d...
Creator:
Adams, Henry (University of Minnesota, Twin Cities)
Created:
2014-03-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been Vietoris-Rips and witness complexes. While the Vietoris-Rips complexis simple to compute and is a good vehicle fo...
Creator:
Dey, Tamal K. (The Ohio State University)
Created:
2013-10-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk will summarize the basics of persistent homology, including Rips and Cech complexes, filtrations, homology, the structure theorem for persistence modules, and barcodes.This introductory talk is designed to reinforce the mathematical foundations of persistent homology, preparing participants for the subsequent talks in this workshop.
Creator:
Wright, Matthew (St. Olaf College)
Created:
2018-08-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk will introduce the central ideas of discrete Morse theory in high-performance (persistent) homology computation. Historically rooted in deep and beautiful structures from smooth geometry, this theory may be viewed, from a computational standpoint, as a very direct means of organizing cellular data to improve efficiency. Time permitting...
Creator:
Henselman, Gregory (University of Pennsylvania)
Created:
2018-08-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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.
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.
Homology has long been accepted as an important computational tool forquantifying complex structures. In many applications these structures arise asnodal domains or excursion sets of real-valued functions, and are thereforeamenable to a numerical study based on suitable discretizations. Such anapproach immediately raises the question of how accu...
Creator:
Wanner, Thomas (George Mason University)
Created:
2014-02-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We describe a topos of sheaves with the property that classical persistent homology of a filtered complex (should) be the internal simplicial homology functor of the logic specified by the base space of the sheaves. All relevant background to understand definitions and their ramifications will be provided in the talk.
Creator:
Vejdemo-Johansson, Mikael (Royal Institute of Technology (KTH))
Created:
2013-10-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.