A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

(Volume V)

Author: Leon O Chua

Publisher: World Scientific

ISBN: 9814397563

Category: Mathematics

Page: 352

View: 1771


This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence. Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss. Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules. But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine. Contents:Period-2 Rules:Recap of Period-2 RulesBasin Tree DiagramsRobust ω-Limit Orbits of Local Rules Belonging to Group 2Quasi Global-EquivalenceSuper String S and Super Decimal xSConcluding RemarksPeriod-3, Period-6, and Permutive Rules:List of the 88 Minimal Equivalence RulesBasin Tree Diagrams, Omega-Limit Orbits and Time-τ Characteristic Function of Rules from Group 3Robust ω-Limit Orbits of Rules from Group 3Permutive RulesConcluding Remarks Readership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory. Keywords:Cellular Automata;CNN;Chua;Wolfram;Wolfram's New Kind of Science;Computer Science;Complexity;Nonlinear Dynamics

A New Kind of Science

Author: United States Congress,United States Senate,Committee On Commerce

Publisher: N.A

ISBN: 9781981755455


Page: 32

View: 8298


A new kind of science : hearing before the Subcommittee on Science, Technology, and Space of the Committee on Commerce, Science, and Transportation, United States Senate, One Hundred Eighth Congress, first session, September 4, 2003.

A New Kind of Computational Biology

Cellular Automata Based Models for Genomics and Proteomics

Author: Parimal Pal Chaudhuri,Soumyabrata Ghosh,Adip Dutta,Somshubhro Pal Choudhury

Publisher: Springer

ISBN: 9811316392

Category: Computers

Page: 335

View: 4605


This book reflects more than three decades of research on Cellular Automata (CA), and nearly a decade of work on the application of CA to model biological strings, which forms the foundation of 'A New Kind of Computational Biology' pioneered by the start-up, CARLBio. After a brief introduction on Cellular Automata (CA) theory and functional biology, it reports on the modeling of basic biological strings with CA, starting with the basic nucleotides leading to codon and anti-codon CA models. It derives a more involved CA model of DNA, RNA, the entire translation process for amino acid formation and the evolution of protein to its unique structure and function. In subsequent chapters the interaction of Proteins with other bio-molecules is also modeled. The only prior knowledge assumed necessary is an undergraduate knowledge of computer programming and biology. The book adopts a hands-on, “do-it-yourself” approach to enable readers to apply the method provided to derive the CA rules and comprehend how these are related to the physical ‘rules’ observed in biology. In a single framework, the authors have presented two branches of science – Computation and Biology. Instead of rigorous molecular dynamics modeling, which the authors describe as a Bottoms-Up model, or relying on the Top-Down new age Artificial Intelligence (AI) and Machine Language (ML) that depends on extensive availability of quality data, this book takes the best from both the Top-Down and Bottoms-up approaches and establishes how the behavior of complex molecules is represented in CA. The CA rules are derived from the basic knowledge of molecular interaction and construction observed in biological world but mapped to a few subset of known results to derive and predict results. This book is useful for students, researchers and industry practitioners who want to explore modeling and simulation of the physical world complex systems from a different perspective. It raises the inevitable the question – ‘Are life and the universe nothing but a collection of continuous systems processing information’.

A New Kind of Social Science

Study of Self-organization of Human Dynamics

Author: Vlad Dimitrov

Publisher: Lulu.com

ISBN: 1411601424

Category: Psychology

Page: 184

View: 2614


This book introduces a new kind of social inquiry centered in exploration of the self-organizing nature of human dynamics. The author links the study of social complexity with his original research into uncertainty inherent in human knowing and learning.

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

Author: Leon O. Chua

Publisher: World Scientific Publishing Company Incorporated


Category: Computers

Page: 340

View: 8183


Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli ??-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the “Isle of Eden” found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.

A New Kind of Conversation

Blogging Toward a Postmodern Faith

Author: Myron Bradley Penner

Publisher: InterVarsity Press

ISBN: 0830857133

Category: Religion

Page: 208

View: 5361


Using a blog format, A New Kind of Conversation is an experimental book that enters into a conversational theological exploration with five evangelical leaders and academics (Brian McLaren, Bruce Ellis Benson, Ellen Haroutunian, Mabiala Kenzon and Myron Bradley Penner), who are the primary bloggers.Originally posted on anewkindofconversation.com, people all over the world were invited to blog on the following topics:What is "Postmodernity"?What is a Postmodern Evangelical?Theology and (Non)(Post) FoundationalismThe Bible, Theology and PostmodernismEvangelical Faith and (Postmodern) OthersPostmodern ApologeticsPostmodern MinistrySpiritual Formation in a Postmodern Context.This book is a condensed version of that conversation.

'It is a New Kind of Diaspora'

Explorations in the Sociopolitical and Cultural Context of Psychoanalysis

Author: Riccardo Steiner

Publisher: Karnac Books

ISBN: 1780497652

Category: Psychology

Page: 212

View: 6531


Riccardo Steiner, one of the most well known historians of psychoanalysis has in the numerous papers in this volume traced the relationship between psychoanalysis and the larger cultural sphere with clarity and erudition. This, the first book he has written, examines the effects of the "new diaspora" in the field - the emigration of German and Austrian analysts during the Nazi persecution, especially to London. In particular he draws upon the correspondence between Ernest Jones and Anna Freud to illuminate the attitudes of those two central figures to "the politics of emigration".Together with other sources, including the correspondence between Jones and Brill, Sigmund Freud and others, as well as further archival documents, Steiner brilliantly describes the tensions and ambiguities that persisted in London and elsewhere during the pre-war period - and which sowed the seeds of wartime "Controversial Discussions". "It is a New Kind of Diaspora": Explorations in the Sociopolitical and Cultural Context of Psychoanalysis is sure to become a classic text in the history of psychoanalysis.

Mathematics and Computation in Music

First International Conference, MCM 2007, Berlin, Germany, May 18-20, 2007. Revised Selected Papers

Author: Timour Klouche,Thomas Noll

Publisher: Springer Science & Business Media

ISBN: 3642045782

Category: Computers

Page: 530

View: 3524


This volume comprises a selection of papers presented at the first International C- ference on Mathematics and Computation in Music – mcm2007. The conference took place at the Staatliches Institut für Musikforschung PK – National Institute for Music Research in Berlin during May 18–20, 2007 and was jointly organized by the National Institute for Music Research Berlin and the Society of Mathematics and Computation in Music. The papers were selected for the conference by the program committee and classfied into talks and posters. All papers underwent further selection, revision and elaboration for this book publication. The articles cover a research field which is heterogeneous with respect to content, scientific language and methodology. On one hand, this reflects the heterogeneity and richness of the musical subject domain itself. On the other hand, it exemplifies a t- sion which has been explicitly intended by both the organizers and the founders of the society, namely to support the integration of mathematical and computational - proaches to music theory, composition, analysis and performance. The subdivision into three parts reflects the original structure of the program. These parts are opened by invited papers and followed by talks and posters.