Selected Problems In The Theory Of Classical Cellular Automata

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Selected Problems in the Theory of Classical Cellular Automata

Author : V. Aladjev
Publisher :
ISBN 13 : 9781729673508
Total Pages : 410 pages
Book Rating : 4.6/5 (735 download)

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Book Synopsis Selected Problems in the Theory of Classical Cellular Automata by : V. Aladjev

Download or read book Selected Problems in the Theory of Classical Cellular Automata written by V. Aladjev and published by . This book was released on 2018-11-05 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the book we present certain results of the work we have done in the theory of Classical Cellular Automata (CA). At present, these results form an essential constituent of the CA problematics. In particular, we have studied such problems as the nonconstructability problem in the CA, the decomposition problem of global transition functions in the CA, the extremal constructive possibilities, the parallel formal grammars and languages defined by the CA, the complexity of finite configurations and global transition functions in the CA, the modelling problem in classical CA, etc. At present, the CA problematics is a rather well developed independent field of the mathematical cybernetics that has a rather considerable field of various appendices. In addition, with the equal right the CA problematics can be considered as a component of such fields as discrete parallel dynamical systems, discrete mathematics, cybernetics, complex systems and some others. In our viewpoint, the book will represent an indubitable interest for students, post-graduates and persons working for doctor's degree of the appropriate faculties of universities, above all, of naturally scientific level along with teachers in subjects such as mathematical and physical modelling, discrete mathematics, automata theory, computer science, cybernetics, theoretical biology, computer technique, and a lot of others. In recent years, the classical CA models are one of the most promising simulating environments for various highly parallel discrete processes, objects and phenomena admitting reversible dynamics, that is enough important from a physical point of view, in the first place.

Selected Problems in the Theory of Classical Cellular Automata

Author : Michael Leonid Shishakov
Publisher :
ISBN 13 : 9781730950377
Total Pages : 412 pages
Book Rating : 4.9/5 (53 download)

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Book Synopsis Selected Problems in the Theory of Classical Cellular Automata by : Michael Leonid Shishakov

Download or read book Selected Problems in the Theory of Classical Cellular Automata written by Michael Leonid Shishakov and published by . This book was released on 2018-11-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the book we present certain results of the work we have done in the theory of Classical Cellular Automata (CA). At present, these results form an essential constituent of the CA problematics. In particular, we have studied such problems as the nonconstructability problem in the CA, the decomposition problem of global transition functions in the CA, the extremal constructive possibilities, the parallel formal grammars and languages defined by the CA, the complexity of finite configurations and global transition functions in the CA, the modelling problem in classical CA, etc. At present, the CA problematics is a rather well developed independent field of the mathematical cybernetics that has a rather considerable field of various appendices. In addition, with the equal right the CA problematics can be considered as a component of such fields as discrete parallel dynamical systems, discrete mathematics, cybernetics, complex systems and some others. In our viewpoint, the book will represent an indubitable interest for students, post-graduates and persons working for doctor's degree of the appropriate faculties of universities, above all, of naturally scientific level along with teachers in subjects such as mathematical and physical modelling, discrete mathematics, automata theory, computer science, cybernetics, theoretical biology, computer technique, and a lot of others. In recent years, the classical CA models are one of the most promising simulating environments for various highly parallel discrete processes, objects and phenomena admitting reversible dynamics, that is enough important from a physical point of view, in the first place.

Solvable Cellular Automata

Author : Henryk Fukś
Publisher : Springer Nature
ISBN 13 : 3031387007
Total Pages : 304 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Solvable Cellular Automata by : Henryk Fukś

Download or read book Solvable Cellular Automata written by Henryk Fukś and published by Springer Nature. This book was released on 2023-10-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of the book is solvability of cellular automata, that is, expressing the state of a given cell after a given number of steps by an explicit formula. The author considers solutions of two types of initial value problems for cellular automata, the deterministic one and the probabilistic one. In the first chapter the basic concepts of cellular automata theory are introduced. Deterministic initial value problem is introduced next and solutions for selected simple rules are also presented. In the following chapters various techniques for solving the deterministic problem are introduced, using elementary CA rules of increasing complexity as examples. The second part of the book introduces the concept of probability measure in the context of cellular automata and the probabilistic initial value problem for both deterministic and probabilistic rules. The book is amply illustrated with examples and applications such as the density classification problem, phase transitions in traffic models or the diffusion of innovations model. In the appendix, solution formulae (both deterministic and probabilistic) for over 60 elementary cellular automata rules are listed. Ruelle-Frobenius-Perron equations for all 88 minimal elementary cellular automata are also provided.

Theory and Applications of Cellular Automata

Author : Stephen Wolfram
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789971501235
Total Pages : 560 pages
Book Rating : 4.5/5 (12 download)

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Book Synopsis Theory and Applications of Cellular Automata by : Stephen Wolfram

Download or read book Theory and Applications of Cellular Automata written by Stephen Wolfram and published by World Scientific Publishing Company Incorporated. This book was released on 1986-01-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Science & Business Media
ISBN 13 : 3642140343
Total Pages : 446 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Science & Business Media. This book was released on 2010-08-24 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Cellular Automata And Complexity

Author : Stephen Wolfram
Publisher : CRC Press
ISBN 13 : 0429973721
Total Pages : 615 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Cellular Automata And Complexity by : Stephen Wolfram

Download or read book Cellular Automata And Complexity written by Stephen Wolfram and published by CRC Press. This book was released on 2018-03-08 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram made the radical proposal that one should instead build models that are based directly on simple computer programs. Wolfram made a detailed study of a class of such models known as cellular automata, and discovered a remarkable fact: that even when the underlying rules are very simple, the behaviour they produce can be highly complex, and can mimic many features of what we see in nature. And based on this result, Wolfram began a program of research to develop what he called A Science of Complexity."The results of Wolfram's work found many applications, from the so-called Wolfram Classification central to fields such as artificial life, to new ideas about cryptography and fluid dynamics. This book is a collection of Wolfram's original papers on cellular automata and complexity. Some of these papers are widely known in the scientific community others have never been published before. Together, the papers provide a highly readable account of what has become a major new field of science, with important implications for physics, biology, economics, computer science and many other areas.

Quantum Cellular Automata

Author : Massimo Macucci
Publisher : Imperial College Press
ISBN 13 : 1860949061
Total Pages : 299 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Quantum Cellular Automata by : Massimo Macucci

Download or read book Quantum Cellular Automata written by Massimo Macucci and published by Imperial College Press. This book was released on 2006 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quantum Cellular Automaton (QCA) concept represents an attempt to break away from the traditional three-terminal device paradigm that has dominated digital computation. Since its early formulation in 1993 at Notre Dame University, the QCA idea has received significant attention and several physical implementations have been proposed. This book provides a comprehensive discussion of the simulation approaches and the experimental work that have been undertaken on the fabrication of devices capable of demonstrating the fundamentals of QCA action. Complementary views of future perspectives for QCA technology are presented, highlighting a process of realistic simulation and of targeted experiments that can be assumed as a model for the evaluation of future device proposals. Contents: The Concept of Quantum-Dot Cellular Automata (C S Lent); QCA Simulation with the Occupation-Number Hamiltonian (M Macucci & M Governale); Realistic Time-Independent Models of a QCA Cell (J Martorell et al.); Time-Independent Simulation of QCA Circuits (L Bonci et al.); Simulation of the Time-Dependent Behavior of QCA Circuits with the Occupation-Number Hamiltonian (I Yakimenko & K-F Berggren); Time-Dependent Analysis of QCA Circuits with the Monte Carlo Method (L Bonci et al.); Implementation of QCA Cells with SOI Technology (F E Prins et al.); Implementation of QCA Cells in GaAs Technology (Y Jin et al.); Non-Invasive Charge Detectors (G Iannaccone et al.); Metal Dot QCA (G L Snider et al.); Molecular QCA (C S Lent); Magnetic Quantum-Dot Cellular Automata (MQCA) (A Imre et al.). Readership: Physicists, electronic engineers and academics.

Game of Life Cellular Automata

Author : Andrew Adamatzky
Publisher : Springer Science & Business Media
ISBN 13 : 1849962170
Total Pages : 576 pages
Book Rating : 4.8/5 (499 download)

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Book Synopsis Game of Life Cellular Automata by : Andrew Adamatzky

Download or read book Game of Life Cellular Automata written by Andrew Adamatzky and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway’s Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

Cellular Automata: Analysis and Applications

Author : Karl-Peter Hadeler
Publisher : Springer
ISBN 13 : 3319530437
Total Pages : 467 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Cellular Automata: Analysis and Applications by : Karl-Peter Hadeler

Download or read book Cellular Automata: Analysis and Applications written by Karl-Peter Hadeler and published by Springer. This book was released on 2017-05-27 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification)? These classifications suggest that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question of whether the properties of cellular automata are decidable. Surjectivity and injectivity are examined, and the seminal Garden of Eden theorems are discussed. In turn, the third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows us to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media. In addition, models for sand piles, the dynamics of infectious d

The Cellular Automaton Interpretation of Quantum Mechanics

Author : Gerard 't Hooft
Publisher : Springer
ISBN 13 : 331941285X
Total Pages : 296 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Cellular Automaton Interpretation of Quantum Mechanics by : Gerard 't Hooft

Download or read book The Cellular Automaton Interpretation of Quantum Mechanics written by Gerard 't Hooft and published by Springer. This book was released on 2016-09-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.

Cellular Automata

Author : Howard Gutowitz
Publisher : MIT Press
ISBN 13 : 9780262570862
Total Pages : 510 pages
Book Rating : 4.5/5 (78 download)

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Book Synopsis Cellular Automata by : Howard Gutowitz

Download or read book Cellular Automata written by Howard Gutowitz and published by MIT Press. This book was released on 1991 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices.Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole.Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.

Classical Cellular Automata. Homogeneous Structures

Author : V. Z. Aladjev
Publisher : Fultus Corporation
ISBN 13 : 1596822228
Total Pages : 480 pages
Book Rating : 4.5/5 (968 download)

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Book Synopsis Classical Cellular Automata. Homogeneous Structures by : V. Z. Aladjev

Download or read book Classical Cellular Automata. Homogeneous Structures written by V. Z. Aladjev and published by Fultus Corporation. This book was released on 2010-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book on cellular automata (CA) considers such questions as nonconstructible configurations, extremal possibilities of CA, complexity of finite configurations and global transition functions, modeling in CA, decomposition of global transition functions, appendices of CA, etc.

Exercises in Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3031103912
Total Pages : 638 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Exercises in Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Exercises in Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2023-11-01 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk

Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3031433289
Total Pages : 562 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Cellular Automata and Groups by : Tullio Ceccherini-Silberstein

Download or read book Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2024-02-16 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.

Cellular Automata Machines

Author : Tommaso Toffoli
Publisher : MIT Press
ISBN 13 : 9780262200608
Total Pages : 284 pages
Book Rating : 4.2/5 (6 download)

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Book Synopsis Cellular Automata Machines by : Tommaso Toffoli

Download or read book Cellular Automata Machines written by Tommaso Toffoli and published by MIT Press. This book was released on 1987 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Computation -- Computation by Abstracts Devices.

Cellular Automata Representation of Submicroscopic Physics

Author : Victor Christianto
Publisher : Infinite Study
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4./5 ( download)

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Book Synopsis Cellular Automata Representation of Submicroscopic Physics by : Victor Christianto

Download or read book Cellular Automata Representation of Submicroscopic Physics written by Victor Christianto and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Krasnoholovets theorized that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properties of matter.

Select Topics in the PHYSICS OF THE ORIGIN OF LIFE

Author : V. Alexander Stefan
Publisher : Stefan University Press
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4./5 ( download)

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Book Synopsis Select Topics in the PHYSICS OF THE ORIGIN OF LIFE by : V. Alexander Stefan

Download or read book Select Topics in the PHYSICS OF THE ORIGIN OF LIFE written by V. Alexander Stefan and published by Stefan University Press. This book was released on 2002-12-05 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: the origin-of-life problem and the proteinoid theory molecular biology and the reconstruction of microbial phylogenies: des liaisons dangereuses? prebiotic chirality and life concentration and organization of precursors at inorganic interplayers and interfaces THE CHEMICAL ORIGINS OF LIFE AND MIND symmetry breaking and the origin of life THE WEAK FORCE AND SETH: THE SEARCH FOR EXTRA-TERRESTRIAL HOMOCHIRALITY COMMUNICATION BETWEEN ACTION AND REACTION UNDERLYING THE PHYSICAL ORIGIN OF LIFE randomness, determinism, and evolution