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Author : Nathan Simon Wallach
Release : 2007
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Topological and Combinatorial Properties of Random Simplicial Complexes by : Nathan Simon Wallach
Download or read book Topological and Combinatorial Properties of Random Simplicial Complexes written by Nathan Simon Wallach. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ginestra Bianconi
Release : 2021-12-23
Genre : Science
Kind : eBook
Book Rating : 426/5 ( reviews)
Book Synopsis Higher-Order Networks by : Ginestra Bianconi
Download or read book Higher-Order Networks written by Ginestra Bianconi. This book was released on 2021-12-23. Available in PDF, EPUB and Kindle. Book excerpt: Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.
Author : Caroline Jane Klivans
Release : 2003
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Combinatorial Properties of Shifted Complexes by : Caroline Jane Klivans
Download or read book Combinatorial Properties of Shifted Complexes written by Caroline Jane Klivans. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face with a node of smaller label results in a collection which is also a face. A primary motivation for considering shifted complexes is a procedure called shifting. Shifting associates a shifted complex to any simplicial complex in a way which preserves meaningful information, while simplifying the structure of the complex. For example, shifting preserves the f-vector of a complex but always reduces the topology to a wedge of spheres. Shifting has proved to be a successful tool for answering questions regarding f-vectors. While most of the previous results on shifted complexes are algebraic or topological in nature, we explore the combinatorics of shifted complexes. We give intrinsic characterization theorems for shifted complexes and shifted matroid complexes. In addition, we show results on the enumeration of shifted complexes and connections to various combinatorial structures.
Author : Yi Zhao
Release : 2021-05-25
Genre : Mathematics
Kind : eBook
Book Rating : 334/5 ( reviews)
Book Synopsis Simplicial Complexes In Complex Systems: In Search For Alternatives by : Yi Zhao
Download or read book Simplicial Complexes In Complex Systems: In Search For Alternatives written by Yi Zhao. This book was released on 2021-05-25. Available in PDF, EPUB and Kindle. Book excerpt: For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.
Author : Mark de Longueville
Release : 2013
Genre : Mathematics
Kind : eBook
Book Rating : 093/5 ( reviews)
Book Synopsis A Course in Topological Combinatorics by : Mark de Longueville
Download or read book A Course in Topological Combinatorics written by Mark de Longueville. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.
