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Frontiers In Mathematical Biology

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 From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems.
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Mathematical Structures Of Epidemic Systems

de Vincenzo Capasso

66,24€ + 10% EM CARTÃO

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 Mathematical modelling of communicable diseases has been the subject of research activity. This monograph suggests a possible classification of a large amount of models (bilinear, nonlinear, with or without structure), based on the Lyapunov stability theory and the theory of order preserving dynamical systems.
INGLÊS

Mathematical Problems In Biology - Victoria Conference

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 A conference on "Some Mathematical Problems in Biology" was held at the University of Victoria, Victoria, B. C. , Canada, from May 7 - 10, 1973. The participants and invited speakers were mathematicians interested in problems of a biological nature, and scientists actively engaged in developing mathematical models in biological fields. One aim of the conference was to attempt to assess what the recent rapid growth of mathematical interaction with the biosciences has accomplished and may accomplish in the near future. The conference also aimed to expose the problems of communication bet~",een mathematicians and biological scientists, and in doing so to stimulate the interchange of ideas. It was recognised that the topic spans an enormous breadth, and little attempt was made to balance the very diverse areas. Widespread active interest was shown in the conference, and just over one hundred people registered. The varied departments and institutions across North America from which the participants came made it both academically and geographically mixed. The chief activity of the conference was the presentation of papers. Nine invited guest speakers (see table of contents) each gave a one hour talk. These covered a wide range of topics. There were twenty-five shorter (twenty minute) contributed papers, and almost all papers l,rere followed by a five minute question and discussion period. Duplicated abstracts of presented papers were available at the meeting. An evening informal discussion meeting of participants, chaired by Dr. A. B. Tayler, and led by Drs. E. M. Hagmeier, E. C.
INGLÊS

Questions Of Uniqueness And Resolution In Reconstruction From Projections

de M. B. Katz

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 Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith''s result is discussed and clarified.
INGLÊS

Analysis Of Neural Networks

de U. An Der Heiden

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 The purpose of this work is a unified and general treatment of activity in neural networks from a mathematical pOint of view. Possible applications of the theory presented are indica ted throughout the text. However, they are not explored in de tail for two reasons : first, the universal character of n- ral activity in nearly all animals requires some type of a general approach~ secondly, the mathematical perspicuity would suffer if too many experimental details and empirical peculiarities were interspersed among the mathematical investigation. A guide to many applications is supplied by the references concerning a variety of specific issues. Of course the theory does not aim at covering all individual problems. Moreover there are other approaches to neural network theory (see e.g. Poggio-Torre, 1978) based on the different lev els at which the nervous system may be viewed. The theory is a deterministic one reflecting the average be havior of neurons or neuron pools. In this respect the essay is written in the spirit of the work of Cowan, Feldman, and Wilson (see sect. 2.2). The networks are described by systems of nonlinear integral equations. Therefore the paper can also be read as a course in nonlinear system theory. The interpretation of the elements as neurons is not a necessary one. However, for vividness the mathematical results are often expressed in neurophysiological terms, such as excitation, inhibition, membrane potentials, and impulse frequencies. The nonlinearities are essential constituents of the theory.
INGLÊS

Modelling Of Patterns In Space And Time - Proceedings Of A Workshop Held By The Sonderforschungsbereich 123 At Heidelberg July 4-8, 1983

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 This volume contains a selection of papers presented at the work shop "Modelling of Patterns in Space and Time", organized by the 80nderforschungsbereich 123, "8tochastische Mathematische Modelle", in Heidelberg, July 4-8, 1983. The main aim of this workshop was to bring together physicists, chemists, biologists and mathematicians for an exchange of ideas and results in modelling patterns. Since the mathe matical problems arising depend only partially on the particular field of applications the interdisciplinary cooperation proved very useful. The workshop mainly treated phenomena showing spatial structures. The special areas covered were morphogenesis, growth in cell cultures, competition systems, structured populations, chemotaxis, chemical precipitation, space-time oscillations in chemical reactors, patterns in flames and fluids and mathematical methods. The discussions between experimentalists and theoreticians were especially interesting and effective. The editors hope that these proceedings reflect at least partially the atmosphere of this workshop. For the convenience of the reader, the papers are ordered alpha betically according to authors. However, the table of contents can easily be grouped into the main topics of the workshop. For practical reasons it was not possible to reproduce in colour the beautiful pictures of patterns shown at the workshop. Since a larger number of half-tone pictures could be included in this volume, the loss of information has, however, been kept to a minimum. The workshop has already stimulated cooperation between its parti cipants and this volume is intended to spread this effect.
INGLÊS

Cell Kinetic Modelling And The Chemotherapy Of Cancer

de Helmut Knolle

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 A new approach, in which the effects of multiple doses on the proliferation kinetics of the tumor in vivo as well as of cell lines in vitro are investigated, has been outlined by Skipper and his co-workers in a series of papers beginning in 1964 (Skipper, Schabel and Wilcox, 1964 and 1965).
INGLÊS

Differential Equations Models In Biology, Epidemiology And Ecology - Proceedings Of A Conference Held In Claremont California, January 13-16, 1990

59,61€ + 10% EM CARTÃO

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 Highlighting the question of how much detail is relevant when modelling and analyzing biological phenomena, this volume contains a series of essays which explore current research in population problems and dynamics, epidemiology, ecology and mathematical biology.
INGLÊS

Stochastic Model For Immunological Feedback In Carcinogenesis: Analysis And Approximations

de N. Dubin

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 Stochastic processes often pose the difficulty that, as soon as a model devi ates from the simplest kinds of assumptions, the differential equations obtained for the density and the generating functions become mathematically formidable. Worse still, one is very often led to equations which have no known solution and don''t yield to standard analytical methods for differential equations. In the model considered here, one for tumor growth with an immunological re sponse from the normal tissue, a nonlinear term in the transition probability for the death of a tumor cell leads to the above-mentioned complications. Despite the mathematical disadvantages of this nonlinearity, we are able to consider a more sophisticated model biologically. Ultimately, in order to achieve a more realistic representation of a complicated phenomenon, it is necessary to examine mechanisms which allow the model to deviate from the more mathematically tractable linear format. Thus far, stochastic models for tumor growth have almost exclusively considered linear transition probabilities.
INGLÊS

Models Of The Stochastic Activity Of Neurones

de A. V. Holden

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 These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\/~~'';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the final typescript and Mr. Peter Hargreaves for preparing the figures.
INGLÊS

Renewable Resource Management - Proceedings Of A Workshop On Control Theory Applied To Renewable Resource Management And Ecology Held In Christchurch, New Zealand January 7 - 11, 198

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 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.
INGLÊS

Optimization Of Human Cancer Radiotherapy

de G.W. Swan

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 The mathematical models in this book are concerned with a variety of approaches to the manner in which the clinical radiologic treatment of human neoplasms can be improved. 4 Spatial Distribution of the Radiation Dose 20 Chapter 2 SURVIVAL CURVES FROM STATISTICAL MODELS 24 2. 2 The Target Model 26 2.
INGLÊS

Mathematical Modeling Of The Hearing Process - Proceedings Of The Nsf-Cbms Regional Conference Held In Troy, Ny, July 21-25, 1980

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 The articles of these proceedings arise from a NSF-CBMS regional conference on the mathematical modeling of the hearing process, that was held at Rensselaer Polytechnic Institute in the summer of 1980. To put the a=ticles in perspective, it is best to briefly review the history of suc~ modeling. It has proceeded, more or less, in three stages. The first was initiated by Herman Helmholtz in the 1880''s, whose theories dominated the subject for years. However, because of his lack of accurate experimental data and his heuristic arguments it became apparent that his models needed revision. Accordingly, based on the experimental observations of von Bekesy, the "long wave" theories were developed in the 1950''s by investigators such as Zwislocki, Peterson, and Bogert. However, as the ex?eri~ents became more refined (such as Rhode''s ~wssbauer Measurements) even these models came into question. This has brought on a flurry of ''activity in recent years into how to extend the models to account for these more recent eXT. lerimental observations. One approach is through a device co~monly refered to as a second filter (see Allen''s article) and another is through a more elaborate hydroelastic model (see Chadwick''s article). In conjunction with this latter approach, there has been some recent work on developing a low frequency model of the cochlea (see Holmes'' article).
INGLÊS

Competition And Cooperation In Neural Nets - Proceedings Of The U.S.-Japan Joint Seminar Held At Kyoto, Japan February 15-19, 1982

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 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.
INGLÊS

Oscillations In Mathematical Biology - Proceedings Of A Conference Held At Adelphi University, April 19, 1982

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 The papers in this volume are based on talks given at a one day conference held on the campus of Adelphi University in April 1982. The conference was organized with the title "Oscillations in Mathematical Biology;" however the speakers were allowed considerable latitutde in their choice of topics. In the event, the talks all concerned the dynamics of non-linear systems arising in biology so that the conference achieved a good measure of cohesion. Some of the speakers cho~e not to submit a manuscript for these proceedings, feeling that their material was too conjectural to be committed to print. Also the paper of Rinzel and Troy is a distillation of the two separate talks that the authors gave. Otherwise the material reproduces the conference proceedings. The conference was made possible by the generous support of the Office of the Dean of the College of Arts and Sciences at Adelphi. The bulk of the organization of the conference was carried out by Dr. Ronald Grisell whose energy was in large measure responsible for the success of the conference.
INGLÊS

Resource Management - Proceedings Of The Second Ralf Yorque Workshop Held In Ashland, Oregon, July 23–25, 1984

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 These are the proceedings of the Second R. Yorque Workshop on Resource Management which took place in Ashland, Oregon on July 23-25, 1984. The purpose of the workshop is to provide an informal atmosphere for the discussion of resource assessment and management problems. Each participant presented a one hour morning talk; afternoons were reserved for informal chatting. The workshop was successful in stimulating ideas and interaction. The papers by R. Deriso, R. Hilborn and C. Walters all address the same basic issue, so they are lumped together. Other than that, the order to the papers in this volume was determined in the same fashion as the order of speakers during the workshop -- by random draw. Marc Mangel Department of Mathematics University of California Davis, California June 1985 TABLE OF CONTENTS A General Theory for Fishery Modeling Jon Schnute Data Transformations in Regression Analysis with Applications to Stock-Recruitment Relationships David Ruppert and Raymond J. Carroll ••••••. ••. ••. . •••••••••••••••. • 29 A Conceptual Model for Multispecies, Multifleet Fisheries Wayne M. Getz, Gordon L. Swartzman, and Robert C. Francis . ••. •••. ••• 49 Risk Adverse Harvesting Strategies Richard Der iso . . •. . ••••. . •. . . . . . . . ••••••. •. . . . . •. ••. •••••••••. •. ••• 65 A Comparison of Harvest Policies for Mixed Stock Fisheries Ray Hilborn . . •••••••. ••. ••. ••••••. ••••••••••••. . ••••••. . . . . ••••••. . • 75 Pathological Behavior of Managed Populations When Production Relationships are Assessed from Natural Experiments Carl J. Walters••••••. ••••••••••. •. ••. ••••••. •. ••••••••••. •••••. . .
INGLÊS

Mathematical Structure Of The Human Sleep-Wake Cycle

de Steven H. Strogatz

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 Over the past three years I have grown accustomed to the puzzled look which appears on people''s faces when they hear that I am a mathematician who studies sleep. They wonder, but are usually too polite to ask, what does mathematics have to do with sleep? Instead they ask the questions that fascinate us all: Why do we have to sleep? How much sleep do we really need? Why do we dream? These questions usually spark a lively discussion leading to the exchange of anecdotes, last night''s dreams, and other personal information. But they are questions about the func tion of sleep and, interesting as they are, I shall have little more to say about them here. The questions that have concerned me deal instead with the timing of sleep. For those of us on a regular schedule, questions of timing may seem vacuous. We go to bed at night and get up in the morning, going through a cycle of sleeping and waking every 24 hours. Yet to a large extent, the cycle is imposed by the world around us.
INGLÊS

Stochastic Methods In Biology - Proceedings Of A Workshop Held In Nagoya, Japan July 8-12 1985

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 This proceedings volume collects a selection of the research and/or survey papers presented at a workshop by biologists and probabilists, and thus provides an account of the latest developments in their respective fields, with particular emphasis on population genetics, neurophysiology and stochastic and other mathematical methods.
INGLÊS

Applications Of Control Theory In Ecology - Proceedings Of The Symposium On Optimal Control Theory Held At The State University Of New York, Syracuse, New York, August 10-16, 1986

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 Control theory can be roughly classified as deterministic or stochastic. Each of these can further be subdivided into game theory and optimal control theory. The next two papers deal with deterministic optimal control, and the final two deal with applications of game theory to ecological problems.
INGLÊS

Mathematical Approaches To Problems In Resource Management And Epidemiology - Proceedings Of A Conference Held At Ithaca, Ny, Oct. 28-30, 1987

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 Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth.
INGLÊS

Acanthaster And The Coral Reef: A Theoretical Perspective - Proceedings Of A Workshop Held At The Australian Institute Of Marine Science, Townsville, Aug. 6-7, 1988

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 In August 1988. the Sixth International Coral Reef Symposium was held in Townsville resulting in an influx of most of the world''s coral reef sCientists to the city. We seized this opportunity at the Australian Institute of Marine Science to run a small workshop immediately before the symposium on the outbreaks of the crown-of-thorns starfish. Aeanthaster planei. We invited that small band of mathematicians who had been modelling the phenomenon, (and who may not have normally attended an international meeting so thoroughly dedicated to natural science) to meet with those SCientists who had been been actively working on the phenomenon in the field. John Casti notes in his delightful new book Alternate Realities (Wiley, 1989): ''If the natural role of the experimenter is to generate new observables by which we know the processes of Nature, and the natural role of the mathematician is to generate new formal structures by which we can represent these processes. then the system SCientist finds his niche by serving as a broker between the two. '' I think our book shows the fruits of that brokerage through the wide range of models explored within its pages. the high level of collaboration and interaction across disciplines evident in the individual papers, and in the emerging synthesis that reflects a far deeper understanding of this complex phenomenon than was possible even a few years ago.
INGLÊS

Stochastic Transport Processes In Discrete Biological Systems

de Eckart Frehland

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 These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio logical ''transport systems can be complex. For example, the transport process can be coupled to other processes such as chemical reactions and take place in discontinuous structures of molecular dimensions. Furthermore, since there are strong electric fields or high concentration gradients across biological membranes ion transport processes of biological relevance are mostly processes far from equilibrium. For these reasons the development of new theoretical concepts has been necessary. The concept of transport in discrete systems has turned out to be more appropriate than continuum models.
INGLÊS

Population Genetics In Forestry - Proceedings Of The Meeting Of The Iufro Working Party “Ecological And Population Genetics” Held In Göttingen, August 21-24, 1984

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 When we consider the main object of forestry, the tree, it immediately becomes clear why experimental population geneticists have been so hesitant in making this object a primary concern of their research. Trees are very long-living organisms with generation intervals frequently exceeding those of their investigators by multiples. They virtually exclude, therefore, application of the classical methods of population genetics since these are based on observing genetic structures over generations. This situation, where the limits set to observation are so severe, particularly requires close cooperation between theory and experiment. It also requires careful consideration of results obtained for organisms other than trees, in order to gain additional insights by comparing the results for trees with those for other organisms. Yet, the greatest challenge to population and ecological genetics probably originates from the fact that forests are very likely to be the most complex ecosystems of all, even in some cases where they are subject to intense management. This complexity, which equally comprises biotic and abiotic factors varying both in time and space, makes extremely high demands on the adaptational capacity and thus flexibility of the carriers of such an ecosystem. Longevity combined with immobility during the vegetative phase, however, appears to contradict the obvious necessity of adaptational flexibility in forest tree populations when compared with short lived and/or mobile organisms.
INGLÊS

Stochastic Models For Spike Trains Of Single Neurons

de Gopalan Sampath e S.K. Srinivasan

59,61€ + 10% EM CARTÃO

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 1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic deletion model 45 5. 1. 2 Higher-order properties of the sequence of r-events 55 5. 1. 3 Extended version of Model 5. 1 - Model 60 5. 2 5. 2 Models with dependent interaction of excitatory and inhibitory sequences - MOdels 5. 3 and 5.
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