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Simplicial Complexes of Graphs

2007-11-15 Mathematics
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Release : 2007-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 585/5 ( reviews)

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Book Synopsis Simplicial Complexes of Graphs by : Jakob Jonsson

Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson. This book was released on 2007-11-15. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.

Topological Signal Processing

2014-01-07 Technology & Engineering
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Release : 2014-01-07
Genre : Technology & Engineering
Kind : eBook
Book Rating : 048/5 ( reviews)

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Book Synopsis Topological Signal Processing by : Michael Robinson

Download or read book Topological Signal Processing written by Michael Robinson. This book was released on 2014-01-07. Available in PDF, EPUB and Kindle. Book excerpt: Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.

Algebraic L-theory and Topological Manifolds

1992-12-10 Mathematics
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Release : 1992-12-10
Genre : Mathematics
Kind : eBook
Book Rating : 242/5 ( reviews)

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Book Synopsis Algebraic L-theory and Topological Manifolds by : Andrew Ranicki

Download or read book Algebraic L-theory and Topological Manifolds written by Andrew Ranicki. This book was released on 1992-12-10. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Combinatorial Algebraic Topology

2008-01-08 Mathematics
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Release : 2008-01-08
Genre : Mathematics
Kind : eBook
Book Rating : 514/5 ( reviews)

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Book Synopsis Combinatorial Algebraic Topology by : Dimitry Kozlov

Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov. This book was released on 2008-01-08. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Random Simplicial Complexes

2013 Random graphs
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Release : 2013
Genre : Random graphs
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Random Simplicial Complexes by : Lior Aronshtam

Download or read book Random Simplicial Complexes written by Lior Aronshtam. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: Random graphs are vastly researched and are of great importance in modern discrete mathematics. A graph may be viewed as a one-dimensional simplicial complex.

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