A Nonlinear Dynamics Perspective of Wolfram s New Kind of Science

Author: Leon O Chua
Publisher: World Scientific
ISBN: 9789814397568
Release Date: 2012-03-13
Genre: Mathematics

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

Symmetrien der Natur

Author: Klaus Mainzer
Publisher: Walter de Gruyter
ISBN: 9783110853650
Release Date: 1988-01-01
Genre: Philosophy


Deterministisches Chaos

Author: Heinz Georg Schuster
Publisher: Wiley-VCH
ISBN: 3527290893
Release Date: 1994-08-25
Genre: Science

Die vorliegende deutsche Übersetzung parallel zur 3.Auflage von "Deterministic Chaos" ist gründlich überarbeitet worden. Dabei wurde ein neues Kapitel über die Kontrolle von Chaos aufgenommen. Übersetzungen ins Japanische, Chinesische, Russische und Polnische zeigen das internationale Interesse an diesem Buch. Aus den Rezensionen der ersten Auflage: 'Schusters Buch gibt eine sehr gute Übersicht über den heutigen Stand auf diesem Gebiet...der Aufbau seines Werkes entspricht der Logik der verwendeten Mathematik, welche auf dem Konzept des dynamischen Systems beruht. Studenten am Beginn wissenschaftlicher Arbeit an chaotischen Systemen und Wissenschaftler, die sich neu einarbeiten wollen, werden dieses Buch sehr lesenswert finden.' Nature 'Dieser Text setzt Maßstäbe, die für andere Autoren und Herausgeber eine Herausforderung sein sollten.' Physics Bulletin

Gruppenanalyse

Author: Dieter Sandner
Publisher: Springer-Verlag
ISBN: 9783642712470
Release Date: 2013-03-12
Genre: Psychology


Advances in Cognitive Neurodynamics

Author: Rubin Wang
Publisher: Springer Science & Business Media
ISBN: 9781402083877
Release Date: 2008-09-15
Genre: Medical

Fifty years ago, enthused by successes in creating digital computers and the DNA model of heredity, scientists were con?dent that solutions to the problems of und- standing biological intelligence and creating machine intelligence were within their grasp. Progress at ?rst seemed rapid. Giant ‘brains’ that ?lled air-conditioned rooms were shrunk into briefcases. The speed of computation doubled every two years. What these advances revealed is not the solutions but the dif?culties of the pr- lems. We are like the geographers who ‘discovered’ America, not as a collection of islands but as continents seen only at shores and demanding exploration. We are astounded less by the magnitude of our discoveries about how brains cogitate than by the enormity of the tasks we have undertaken, to explain and replicate the higher functions of brains. Five decades of brain research have led to the emergence of a new ?eld, which spans the entire range of brain cognition from quantum ?elds to social interactions, and which is combined by the conceptions of nonlinear neurodynamics operating simultaneously at and across all levels. A new breed of scientists has emerged, schooled in multiple academic disciplines, comfortable in working with data from different levels, and conversant with the mathematical tools that are essential to cross boundaries.

Scientific medical

Author: National Research Council (U.S.). Committee on American Scientific and Technical Bibliography
Publisher:
ISBN: UCSC:32106002832621
Release Date: 1954
Genre: Medicine


Quantenrealit t

Author: HERBERT
Publisher: Springer-Verlag
ISBN: 9783034866811
Release Date: 2013-11-11
Genre: Juvenile Nonfiction


World Congress of Medical Physics and Biomedical Engineering 2006

Author: Sun I. Kim
Publisher: Springer Science & Business Media
ISBN: 9783540368410
Release Date: 2007-07-05
Genre: Technology & Engineering

These proceedings of the World Congress 2006, the fourteenth conference in this series, offer a strong scientific program covering a wide range of issues and challenges which are currently present in Medical physics and Biomedical Engineering. About 2,500 peer reviewed contributions are presented in a six volume book, comprising 25 tracks, joint conferences and symposia, and including invited contributions from well known researchers in this field.

Big Data

Author: Heinrich Geiselberger
Publisher: Suhrkamp Verlag
ISBN: 9783518733639
Release Date: 2013-10-21
Genre: Political Science

Die Ausspähprogramme Prism und Tempora, die durch den Whistleblower Edward Snowden bekannt wurden, sind nur die Spitze des Datenbergs. Auskunfteien, Internetunternehmen und Einzelhandelsketten sammeln schon seit Jahren Informationen über die Bürger. Möglich wird all das durch Big Data, also die Möglichkeit, ungeahnte Mengen an Daten zu erheben, zu speichern und zu analysieren. Big Data, darin sind sich Analysten und Wissenschaftler einig, könnte die Art und Weise, wie wir Entscheidungen treffen, konsumieren, forschen und leben dramatisch verändern. Manche fühlen sich dabei an George Orwells 1984 erinnert, anderen sehen darin eine digitale Glaskugel, die gigantische Wachstumschancen bietet und neue Forschungswelten eröffnet. Der Band bietet einen Überblick über die vielfältigen Anwendungsbereiche und Akteure, renommierte Praktiker, Soziologen und Technikexperten beleuchten das Thema Big Data aus unterschiedlichen Perspektiven. Mit Beiträgen von Chris Anderson (The Long Tail), Dirk Baecker, Peter Glaser, Michael Hagner und Dirk Helbing, Bruno Latour, Frank Schirrmacher und vielen anderen.