Suggested Readings, Videos, etc.
Readings:
Topology and Data by Gunnar Carlsson
Barcodes: The Persistent Topology of Data by Robert Ghrist
Simplicial Models and Topological Inference in Biological Systems by Vidit Nanda and Radmila Sazdanovic
Videos:
Matthew Wright’s Introduction to Persistent Homology
Gunnar Carlsson’s Introduction to Topological Data Analysis
Michael Lesnick’s Topological Data Analysis and Persistent Homology
Vidit Nanda’s Topological Data Analysis
TDA applied to neuroscience
Chad Giusti’s list of TDA and neuroscience paper’s bibliography: http://www.chadgiusti.com/bib.html
For directed simplicial complexes and its usage in neuroscience:
https://arxiv.org/abs/1601.01580
and the Phat based software package here:
http://neurotop.gforge.inria.fr/
For an application of topological invariant to understand shape of neurons have a look here:
https://arxiv.org/abs/1603.08432
Papers and links about TDA software
A roadmap for the computation of persistent homology, Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington https://arxiv.org/abs/1506.08903
Peter Bubenik’s Intro to TDA page (includes worksheet and files for R workshop including Perseus and Persistence Landscape Toolbox http://people.clas.ufl.edu/peterbubenik/intro-to-tda/
Software Guides:
For Gudhi, JavaPlex, and PHAT (scroll down to the “Computational Topology” section)
Software
http://www.math.upenn.edu/~ghrist/preprints/Eirene.pdf
Nebneuron https://github.com/nebneuron
Perseus http://people.maths.ox.ac.uk/nanda/perseus/index.html
Here are executable for osx and windows:
OSX:
Gudhi: https://gforge.inria.fr/frs/download.php/file/36770/GUDHI_2.0.0_OSX_UTILS.beta.tar.gz
Statistical package for Gudhi: https://gforge.inria.fr/frs/download.php/file/36772/GUDHI_PERSISTENCE_REPRESENTATIONS_OSX_10.7+_UTILS.beta.tar.gz
Windows:
Gudhi: https://gforge.inria.fr/frs/download.php/file/36771/GUDHI_2.0.0_WIN64_UTILS.beta.zip
Statistical package for Gudhi: https://gforge.inria.fr/frs/download.php/file/36776/GUDHI_PERSISTENCE_REPRESENTATIONS_WIN64_UTILS.beta.zip