Advances in Disordered Systems, Random Processes and Some Applications

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This book offers a unified perspective on the study of complex systems, with contributions written by leading scientists from various disciplines.

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Title Statements

Full title :Advances in Disordered Systems, Random Processes and Some Applications.

Summary

This book offers a unified perspective on the study of complex systems, with contributions written by leading scientists from various disciplines.

Edition Statements

Publication Date:2016.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2016.

The Physical Object

Description:1 online resource (384 pages)

Edition Identifiers

ISBN:9781316868508, 1316868508, 9781316866887, 1316866882, 9781107124103, 1107124107
oclc:ocn969637057
LC Classification:QA402.A2975 2017
Dewey Decimal:003/.857

Cover -- Half-title -- Title page -- Copyright information -- Table of contents -- List of Contributors -- Preface -- 1 Topological Field Theory of Data: Mining Data Beyond Complex Networks -- 1.1 A Philosophical Introduction -- 1.2 The Reference Landscape -- 1.3 The Challenge -- 1.4 Step One: Topological Data Analysis -- 1.5 Step Two: from Data Topology to Data Field -- 1.6 The Topological Field Theory of Data -- 1.7 The Formal Language Theory Facet -- 1.8 Language, Structure and Behavior, Automata -- 1.9 Emergence of Patterns -- 1.10 Conclusions -- 1.11 Acknowledgments -- References -- 2 A Random Walk in Diffusion Phenomena and Statistical Mechanics -- 2.1 Introduction -- 2.2 Different Approaches to Diffusion -- 2.2.1 Macroscopic Perspective (Fick's Law) -- 2.2.2 Physical Perspective (Einstein's Theory) -- 2.2.3 Mathematical Perspective (Wiener Process) -- 2.2.4 Microscopic Perspective (Random Walks) -- 2.2.4.1 The Continuum Limit of Random Walks -- 2.2.5 Continuous-time Random Walks -- 2.2.6 Mathematical Tools: Characteristic Functions -- 2.2.7 Mathematical Tools: Generating Functions and Tauberian Theorems -- 2.2.8 Anomalous Diffusion -- 2.2.9 Mathematical Tools: an Algebraic …