Book Chapter10.1090/HMATH/037/01
On Analysis Situs
Henri Poincaré,John Stillwell +1 more
- 16 Sep 2010
- pp 1-3
150
About: The article was published on 16 Sep 2010. The article focuses on the topics: Situs.
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Citations
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References
Topological pattern recognition for point cloud data
TL;DR: The definition and computation of homology in the standard setting of simplicial complexes and topological spaces are discussed, then it is shown how one can obtain useful signatures, called barcodes, from finite metric spaces, thought of as sampled from a continuous object.
Reconceiving the hippocampal map as a topological template
TL;DR: It is tested that the hippocampal place cells may ultimately be interested in a space's topological qualities more than its geometry; such higher-order functioning would be more consistent with other known hippocampal functions.
Topological analysis of data
TL;DR: The TDA paradigm is presented and some applications are presented, in order to highlight its relevance to the data science community.
•Book
Basic Complex Analysis
Barry Simon
- 09 Dec 2015
TL;DR: The Cauchy integral theorem and its consequences are discussed in this paper, with a focus on spaces of analytic functions, fractional linear transformations, conformal maps, and elliptic functions.
113
The early days of geometric nonlinear control
TL;DR: This paper discusses an initial phase of the development of geometric nonlinear control, including material on the broader context from which it emerged, and limits the scope of the project to something manageable.
81