Simplicial Complexes In Complex Systems

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Simplicial Complexes In Complex Systems: In Search For Alternatives

Author : Yi Zhao
Publisher : World Scientific
ISBN 13 : 9811226334
Total Pages : 149 pages
Book Rating : 4.8/5 (112 download)

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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 and published by World Scientific. This book was released on 2021-05-25 with total page 149 pages. 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.

Simplicial Complexes in Complex Systems

Author : Slobodan Maletić
Publisher :
ISBN 13 : 9787560363073
Total Pages : 162 pages
Book Rating : 4.3/5 (63 download)

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Book Synopsis Simplicial Complexes in Complex Systems by : Slobodan Maletić

Download or read book Simplicial Complexes in Complex Systems written by Slobodan Maletić and published by . This book was released on 2017 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simplicial Complexes in Complex Systems

Author : Yi Zhao
Publisher :
ISBN 13 : 9789811226328
Total Pages : 149 pages
Book Rating : 4.2/5 (263 download)

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Book Synopsis Simplicial Complexes in Complex Systems by : Yi Zhao

Download or read book Simplicial Complexes in Complex Systems written by Yi Zhao and published by . This book was released on 2021 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simplicial Complexes

Author : Sheena
Publisher : Tredition Gmbh
ISBN 13 : 9783384278166
Total Pages : 0 pages
Book Rating : 4.2/5 (781 download)

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Book Synopsis Simplicial Complexes by : Sheena

Download or read book Simplicial Complexes written by Sheena and published by Tredition Gmbh. This book was released on 2024-07-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title improves upon the original by: Intrigue: "Beyond Faces" sparks curiosity about what lies beyond a basic feature of simplicial complexes. Power: "Power" emphasizes the wider significance of these structures. The piece could delve into face numbers as a foundational concept: Counting Faces: Explain how the number of faces (points, edges, triangles, etc.) provides initial insights into a simplicial complex's structure. Simplex Homology: Briefly introduce this concept, highlighting how it uses face numbers to reveal hidden properties of the shape. The focus would then shift on the broader applications of simplicial complexes: Modeling Complex Systems: Discuss how these structures can represent complex networks, from social connections to the human brain. Topological Analysis: Highlight how simplicial complexes allow us to analyze the fundamental properties of shapes independent of size or deformation. Applications in Science and Engineering: Explore their use in fields like computer graphics, 3D printing, and even physical simulations. "Beyond Faces" suggests a few content directions: Higher Dimensions: Briefly touch upon how simplicial complexes can represent shapes beyond our usual 3D world. Visualizations: Emphasize the importance of using visualizations or interactive tools to help readers grasp these concepts. Historical Context: Briefly discuss the development of simplicial complexes and their role in the history of mathematics.

Higher-Order Networks

Author : Ginestra Bianconi
Publisher : Cambridge University Press
ISBN 13 : 1108805426
Total Pages : 150 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Higher-Order Networks by : Ginestra Bianconi

Download or read book Higher-Order Networks written by Ginestra Bianconi and published by Cambridge University Press. This book was released on 2021-12-23 with total page 150 pages. 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.

Simplicial Complexes of Graphs

Author : Jakob Jonsson
Publisher : Springer Science & Business Media
ISBN 13 : 3540758585
Total Pages : 376 pages
Book Rating : 4.5/5 (47 download)

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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 and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 376 pages. 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.

Computational Models of Complex Systems

Author : Vijay Kumar Mago
Publisher : Springer Science & Business Media
ISBN 13 : 3319012851
Total Pages : 199 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Computational Models of Complex Systems by : Vijay Kumar Mago

Download or read book Computational Models of Complex Systems written by Vijay Kumar Mago and published by Springer Science & Business Media. This book was released on 2013-10-31 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the readers will have stimulating experiences to pursue research in these directions.

Hypernetworks In The Science Of Complex Systems

Author : Jeffrey Johnson
Publisher : World Scientific
ISBN 13 : 1783264438
Total Pages : 349 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Hypernetworks In The Science Of Complex Systems by : Jeffrey Johnson

Download or read book Hypernetworks In The Science Of Complex Systems written by Jeffrey Johnson and published by World Scientific. This book was released on 2013-11-29 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams.This volume makes an important contribution to the science of complex systems by: (i) extending network theory to include dynamic relationships between many elements; (ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii) providing a new methodological approach to analyze complex systems; and (iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application.

Higher-Order Systems

Author : Federico Battiston
Publisher : Springer Nature
ISBN 13 : 3030913740
Total Pages : 436 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Higher-Order Systems by : Federico Battiston

Download or read book Higher-Order Systems written by Federico Battiston and published by Springer Nature. This book was released on 2022-04-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.

Topological Tools for Understanding Complex Systems

Author : Michelle H Feng
Publisher :
ISBN 13 :
Total Pages : 139 pages
Book Rating : 4.:/5 (116 download)

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Book Synopsis Topological Tools for Understanding Complex Systems by : Michelle H Feng

Download or read book Topological Tools for Understanding Complex Systems written by Michelle H Feng and published by . This book was released on 2020 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: The behavior of complex systems is often influenced by their structure. In mathematics, the field of algebraic topology has been especially useful for characterizing mathematical structures. Topological data analysis (TDA) is a growing field in which methods from algebraic topology are applied to studying the structure of data. TDA has been used in a variety of applications, including biological data, granular materials, and demography. Social interactions are heavily informed by space and have complex structure due to patterns in the way humans arrange themselves geographically. Consequently, social applications can benefit from the application of TDA. In this dissertation, I develop topological methods for studying spatial networks and apply them to a wide variety of data sets. In particular, I study methods for building topological spaces (specifically, simplicial complexes) based on data. I present two novel simplicial-complex constructions, the adjacency complex and the level-set complex, for spatial data. I apply both constructions to random networks, cities, voting, and scientific images, gaining insights into the structure of these systems. I also propose a novel simplicial complex construction for studying patterns of neighborhood formation based on combining demographic and spatial data. I present case studies in neighborhood segregation for two U.S. cities. In addition to my topological research, I discuss two projects in the study of social systems using methods from network analysis. I present an extension to multilayer networks of the Hegselmann--Krause model for opinion dynamics and discuss preliminary findings on its convergence properties. I also present a framework for estimating homelessness underreporting in California Local Education agencies (LEAs).

Distributed Computing Through Combinatorial Topology

Author : Maurice Herlihy
Publisher : Newnes
ISBN 13 : 0124047289
Total Pages : 335 pages
Book Rating : 4.1/5 (24 download)

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Book Synopsis Distributed Computing Through Combinatorial Topology by : Maurice Herlihy

Download or read book Distributed Computing Through Combinatorial Topology written by Maurice Herlihy and published by Newnes. This book was released on 2013-11-30 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. - Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews - Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding - Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols - Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises

Higher Order Networks: An Introduction to Simplicial Complexes

Author : Ginestra Bianconi
Publisher : Cambridge University Press
ISBN 13 : 1108726739
Total Pages : 149 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Higher Order Networks: An Introduction to Simplicial Complexes by : Ginestra Bianconi

Download or read book Higher Order Networks: An Introduction to Simplicial Complexes written by Ginestra Bianconi and published by Cambridge University Press. This book was released on 2021-12-23 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.

Combinatorial Connectivities in Social Systems

Author : ATKIN
Publisher : Birkhäuser
ISBN 13 : 3034857500
Total Pages : 253 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Combinatorial Connectivities in Social Systems by : ATKIN

Download or read book Combinatorial Connectivities in Social Systems written by ATKIN and published by Birkhäuser. This book was released on 2013-11-27 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a presentation of my recent research work into the theory and applications of mathematical relations between finite sets. The consequent results and concepts are expressed in 'conjunction' with the idea of a union of simplicial complexes and the algorithms and overall methodology have become known as Q-Analysis. The mathematical ideas are essentially comhinatorial and are developed in Section-A of the book, whilst Section-R contains an application to a community study (that of the IJniversity of Rssex). All of the work has been published elsewhere, in the usual form of papers, and a comprehensive introduction to the whole approach will be found in my earlier book, Mathematical Structure in Human Affairs (Heinemann, London 1974). Much of the research work referred to in this present hook would not have been possible without the co-operation of my research team, of whom I would particularly like to thank J.II. Johnson, and its puhlication owes a lot to the secretarial help provided by ~Iary Low. R.H. Atkin IJniversity of Rssex U.K.

Topological Signal Processing

Author : Michael Robinson
Publisher : Springer Science & Business Media
ISBN 13 : 3642361048
Total Pages : 245 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Topological Signal Processing by : Michael Robinson

Download or read book Topological Signal Processing written by Michael Robinson and published by Springer Science & Business Media. This book was released on 2014-01-07 with total page 245 pages. 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.

Geometric and Topological Inference

Author : Jean-Daniel Boissonnat
Publisher : Cambridge University Press
ISBN 13 : 1108419399
Total Pages : 247 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Geometric and Topological Inference by : Jean-Daniel Boissonnat

Download or read book Geometric and Topological Inference written by Jean-Daniel Boissonnat and published by Cambridge University Press. This book was released on 2018-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Computational Science – ICCS 2008

Author : Marian Bubak
Publisher : Springer Science & Business Media
ISBN 13 : 3540693866
Total Pages : 771 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Computational Science – ICCS 2008 by : Marian Bubak

Download or read book Computational Science – ICCS 2008 written by Marian Bubak and published by Springer Science & Business Media. This book was released on 2008-06-11 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set LNCS 5101-5103 constitutes the refereed proceedings of the 8th International Conference on Computational Science, ICCS 2008, held in Krakow, Poland in June 2008. The 167 revised papers of the main conference track presented together with the abstracts of 7 keynote talks and the 100 revised papers from 14 workshops were carefully reviewed and selected for inclusion in the three volumes. The main conference track was divided into approximately 20 parallel sessions addressing topics such as e-science applications and systems, scheduling and load balancing, software services and tools, new hardware and its applications, computer networks, simulation of complex systems, image processing and visualization, optimization techniques, numerical linear algebra, and numerical algorithms. The second volume contains workshop papers related to various computational research areas, e.g.: computer graphics and geometric modeling, simulation of multiphysics multiscale systems, computational chemistry and its applications, computational finance and business intelligence, physical, biological and social networks, geocomputation, and teaching computational science. The third volume is mostly related to computer science topics such as bioinformatics' challenges to computer science, tools for program development and analysis in computational science, software engineering for large-scale computing, collaborative and cooperative environments, applications of workflows in computational science, as well as intelligent agents and evolvable systems.

Modern Graph Theory Algorithms with Python

Author : Colleen M. Farrelly
Publisher : Packt Publishing Ltd
ISBN 13 : 1805120174
Total Pages : 290 pages
Book Rating : 4.8/5 (51 download)

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Book Synopsis Modern Graph Theory Algorithms with Python by : Colleen M. Farrelly

Download or read book Modern Graph Theory Algorithms with Python written by Colleen M. Farrelly and published by Packt Publishing Ltd. This book was released on 2024-06-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solve challenging and computationally intensive analytics problems by leveraging network science and graph algorithms Key Features Learn how to wrangle different types of datasets and analytics problems into networks Leverage graph theoretic algorithms to analyze data efficiently Apply the skills you gain to solve a variety of problems through case studies in Python Purchase of the print or Kindle book includes a free PDF eBook Book DescriptionWe are living in the age of big data, and scalable solutions are a necessity. Network science leverages the power of graph theory and flexible data structures to analyze big data at scale. This book guides you through the basics of network science, showing you how to wrangle different types of data (such as spatial and time series data) into network structures. You’ll be introduced to core tools from network science to analyze real-world case studies in Python. As you progress, you’ll find out how to predict fake news spread, track pricing patterns in local markets, forecast stock market crashes, and stop an epidemic spread. Later, you’ll learn about advanced techniques in network science, such as creating and querying graph databases, classifying datasets with graph neural networks (GNNs), and mining educational pathways for insights into student success. Case studies in the book will provide you with end-to-end examples of implementing what you learn in each chapter. By the end of this book, you’ll be well-equipped to wrangle your own datasets into network science problems and scale solutions with Python.What you will learn Transform different data types, such as spatial data, into network formats Explore common network science tools in Python Discover how geometry impacts spreading processes on networks Implement machine learning algorithms on network data features Build and query graph databases Explore new frontiers in network science such as quantum algorithms Who this book is for If you’re a researcher or industry professional analyzing data and are curious about network science approaches to data, this book is for you. To get the most out of the book, basic knowledge of Python, including pandas and NumPy, as well as some experience working with datasets is required. This book is also ideal for anyone interested in network science and learning how graph algorithms are used to solve science and engineering problems. R programmers may also find this book helpful as many algorithms also have R implementations.