1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop ment. The notion promptly attracted the attention of computer scientist...
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ISBN:
(数字)9781475714289
1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop ment. The notion promptly attracted the attention of computer scientists, who investigated 1-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed 1-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between 1-systems and the concept of fractals introduced by Benoit Mandel brot. The work by Smith inspired our studies of the application of 1-systems to computer graphics. Originally, we were interested in two problems: • Can 1-systems be used as a realistic model of plant species found in nature? • Can 1-systems be applied to generate images of a wide class of fractals? It turned out that both questions had affirmative answers. Subsequently we found that 1-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of- systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals.
This volume is the record and product of the Summer School on the Physics and Mathematics of the Nervous System, held at the International Centre for Theoretical Physics in Trieste from August 21-31, 1973, and jointly...
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ISBN:
(数字)9783642808852
ISBN:
(纸本)9783540070146
This volume is the record and product of the Summer School on the Physics and Mathematics of the Nervous System, held at the International Centre for Theoretical Physics in Trieste from August 21-31, 1973, and jointly organized by the Institute for Information Sciences, University of Tlibingen and by the Centre. The school served to bring biologists, physicists and mathemati cians together to exchange ideas about the nervous system and brain, and also to introduce young scientists to the field. The program, attended by more than a hundred scientists, was interdisciplinary both in character and participation. The primary support for the school was provided by the Volkswagen Foundation of West Germany. We are particularly indebted to Drs. G. Gambke, M. -L Zarnitz, and H. Penschuck of the Foundation for their in terest in and help with the project. The school also received major support from the International Centre for Theoretical Physics in Trieste and its sponsoring agencies, including the use of its excellent facili ties. We are deeply indebted to Professor A. Salam for his kind co operation and also to Professor P. Budini, Dr. A. M. Hamende, and to the many members of the Centre staff whose hospitality and efficiency con tributed so much to the success of the school. We are pleased to acknow ledge the generous ~id and cooperation of the University of Tlibingen and would like to thank its President, A.
The human brain, wi th its hundred billion or more neurons, is both one of the most complex systems known to man and one of the most important. The last decade has seen an explosion of experimental research on the bra...
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ISBN:
(数字)9783642464669
ISBN:
(纸本)9783540115748
The human brain, wi th its hundred billion or more neurons, is both one of the most complex systems known to man and one of the most important. The last decade has seen an explosion of experimental research on the brain, but little theory of neural networks beyond the study of electrical properties of membranes and small neural circuits. Nonetheless, a number of workers in Japan, the United States and elsewhere have begun to contribute to a theory which provides techniques of mathematical analysis and computer simulation to explore properties of neural systems containing immense numbers of neurons. Recently, it has been gradually recognized that rather independent studies of the dynamics of pattern recognition, pattern format::ion, motor control, self-organization, etc. , in neural systems do in fact make use of common methods. We find that a "competition and cooperation" type of interaction plays a fundamental role in parallel information processing in the brain. The present volume brings together 23 papers presented at a U. S. -Japan Joint Seminar on "Competition and Cooperation in Neural Nets" which was designed to catalyze better integration of theory and experiment in these areas. It was held in Kyoto, Japan, February 15-19, 1982, under the joint sponsorship of the U. S. National Science Foundation and the Japan Society for the Promotion of Science. Participants included brain theorists, neurophysiologists, mathematicians, computer scientists, and physicists. There are seven papers from the U. S.
From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A cho...
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ISBN:
(数字)9783642501241
ISBN:
(纸本)9783642501265
From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an attractive alternative. (ii) The ability of physiologically structured population models to increase our un derstanding of the relation between mechanisms at the i-level and phenomena at the p-level will depend strongly on the development of dynamical systems lab facilities which are applicable to this class of models. (iii) Physiologically structured population models are ideally suited for the for mulation of evolutionary questions. Apart from the special case of age (see Charlesworth 1980, Yodzis 1989, Caswell 1989, and the references given there) hardly any theory exists at the moment. This will, hopefully, change rapidly in the coming years. Again the development of appropriate software may turn out to be crucial.
As society becomes stressed by economic and population pressures, in turn, nature's renewable resources become stressed by harvesting pressures. For our own survival and euphoria, it is paramount that such resourc...
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ISBN:
(数字)9783642464362
ISBN:
(纸本)9783540105664
As society becomes stressed by economic and population pressures, in turn, nature's renewable resources become stressed by harvesting pressures. For our own survival and euphoria, it is paramount that such resources remain as their name implies and not be driven to extinction through short term programs of over exploitation. Consideration of the harvesting of renewable resources leads to a simple question that was the theme of the workshop and is the focus of these proceedings: SUPPoRe you are assigned the role of manager for a specific renewable resource eco system. How would you decide on harvesting policies so that the system can be exploited economically yet at the same time maintain the integrity of the system? This, of course, is a loaded question. First of all, it is not clear that there is ever anyone single decision maker who is able to set the rules for all of the harvesters in an exploited ecosystem. The political process is complicated and to some extent unpredictable. This aspect of the question is recognized to be important, but could not be addressed here. Assuming then that someone really is in charge, what would be involved in the * decision making process? As Clark points out, "there is no alternative but first to model the system. " We agree. However, if the original question was loaded, modeling is the adulterate.
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, ...
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ISBN:
(数字)9783662100677
ISBN:
(纸本)9783540525714
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
" . . . behavior is not, what an organism does itself, but to what we point. Therefore, whether a type of behavior of an organism is adequate as a certain configuration of movements, will depend on the environmen...
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ISBN:
(数字)9783642516641
ISBN:
(纸本)9783540535201
" . . . behavior is not, what an organism does itself, but to what we point. Therefore, whether a type of behavior of an organism is adequate as a certain configuration of movements, will depend on the environment in which we de scribe it. " (Humberto Maturana, Francisco Varela: El arbol del conocimiento, 1984) "A thorough analysis of behavior must result in a scheme, that shows all regularities that are to be found between the sensorical input and the motorical output of an animal. This scheme is an abstract representation of the brain. " (Valentin Braitenberg: Gehirngespinste, 1973) During the 70ies, when biomathematics (beyond Biomedical Statistics and Com puting) became more popular at universities and research institutes, the problems dealt with came mainly from the general fields of 'Population Biology' and 'Complex Systems Analysis' such as epidemics, ecosystems analysis, morphogenesis, genetics, immunology and neurology (see the first series of Springer lecture notes in biomathematics). Since then, the picture has not considerably changed, and it seems that "a thorough analysis of behavior" of single organisms and, moreover, of their mutual interactions, is far from being understood. On the contrary, mathematical modellers and analysts have been well advised to restrict their investigations to specific aspects of 'biological behavior', one of which is 'biological motion'. Until now, only a few Conference Proceedings or lecturenotes have paid attention to this important aspect, some of the earlier examples being Vol. 24: 'The measurement of biological shape and shape changes' (1978) or Vol.
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