Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data
The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …
Topology and data
G Carlsson - Bulletin of the American Mathematical Society, 2009 - ams.org
AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …
Computing persistent homology
A Zomorodian, G Carlsson - … of the twentieth annual symposium on …, 2004 - dl.acm.org
We study the homology of a filtered d-dimensional simplicial complex K as a single
algebraic entity and establish a correspondence that provides a simple description over …
algebraic entity and establish a correspondence that provides a simple description over …
Morse theory for filtrations and efficient computation of persistent homology
K Mischaikow, V Nanda - Discrete & Computational Geometry, 2013 - Springer
Morse Theory for Filtrations and Efficient Computation of Persistent Homology |
SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a journal …
SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a journal …
[图书][B] Algorithms and theory of computation handbook, volume 2: special topics and techniques
MJ Atallah, M Blanton - 2009 - books.google.com
This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …
topics, techniques, and applications. Along with updating and revising many of the existing …
Poset topology: tools and applications
ML Wachs - arXiv preprint math/0602226, 2006 - arxiv.org
These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes include …
Combinatorics (July 2004) provide an overview of poset topology. These notes include …
A topological measurement of protein compressibility
In this paper we partially clarify the relation between the compressibility of a protein and its
molecular geometric structure. To identify and understand the relevant topological features …
molecular geometric structure. To identify and understand the relevant topological features …
Topological data analysis
A Zomorodian - Advances in applied and computational topology, 2012 - books.google.com
Scientific data is often in the form of a finite set of noisy points, sampled from an unknown
space, and embedded in a high-dimensional space. Topological data analysis focuses on …
space, and embedded in a high-dimensional space. Topological data analysis focuses on …
Discrete Morse theoretic algorithms for computing homology of complexes and maps
We provide explicit and efficient reduction algorithms based on discrete Morse theory to
simplify homology computation for a very general class of complexes. A set-valued map of …
simplify homology computation for a very general class of complexes. A set-valued map of …
Coreduction homology algorithm
This paper presents a new reduction algorithm for the efficient computation of the homology
of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets …
of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets …