**Auteur :**

**la langue :** en

**Éditeur:** Academic Press

**Date de sortie :** 1980-04-29

The Mathematical Theory of L Systems

**Auteur :** John L. Rhodes

**la langue :** en

**Éditeur:** World Scientific

**Date de sortie :** 2010

This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now. This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics. The material and references have been brought up to date bythe editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of "punctuated equilibrium" (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.

**Auteur :** Przemyslaw Prusinkiewicz

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2012-12-06

Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.

**Auteur :** G. Rozenberg

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2012-12-06

This book is dedicated to Aristid Lindenmayer on the occasion of his 60th birthday on November 17, 1985. Contributions range from mathematics and theoretical computer science to biology. Aristid Lindenmayer introduced language-theoretic models for developmental biology in 1968. Since then the models have been cus tomarily referred to as L systems. Lindenmayer's invention turned out to be one of the most beautiful examples of interdisciplinary science: work in one area (developmental biology) induces most fruitful ideas in other areas (theory of formal languages and automata, and formal power series). As evident from the articles and references in this book, the in terest in L systems is continuously growing. For newcomers the first contact with L systems usually happens via the most basic class of L systems, namely, DOL systems. Here "0" stands for zero context between developing cells. It has been a major typographical problem that printers are unable to distinguish between 0 (zero) and 0 (oh). Thus, DOL was almost always printed with "oh" rather than "zero", and also pronounced that way. However, this misunderstanding turned out to be very fortunate. The wrong spelling "DOL" of "DOL" could be read in the suggestive way: DO L Indeed, hundreds of researchers have followed this suggestion. Some of them appear as contributors to this book. Of the many who could not contribute, we in particular regret the absence of A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the theory of L systems has been most significant.

**Auteur :** Jan Haluska

**la langue :** en

**Éditeur:** CRC Press

**Date de sortie :** 2003-12-19

The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems. Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.

**Auteur :** Julius T. Tou

**la langue :** en

**Éditeur:** Springer Science & Business Media

**Date de sortie :** 2012-12-06

Information systems science is rapidly advancing in many directions. Di versified ideas, methodologies, and techniques as well as applications have been conceived and developed. This series intends to discuss some of the recent advances in this field. In this volume, we cover four timely topics which are of great current interest. In each chapter, an attempt is made to familiarize the reader with some basic background information on the ad vances discussed. The emphasis of this volume is placed upon parallel pro gramming, data structure models in information system design, and the principles of L systems. One of the effective means to enhance computation performance is parallel information processing on multiprocessor systems. In Chapter I, V. E. Kotov discusses the practical aspects of parallel programming. He is concerned with the languages and methods of parallel programming, per formance an~lysis, and automatic synthesis of parallel programs. In Chapter 2, A. S. Narin'yani presents the formal theory of parallel computations. These two chapters attempt to correlate and classify various methods in parallel programming, thus providing the reader with a unified approach to this important subject matter. Data structures play an important role in information system design.