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A Stochastic Model For Immunological Feedback In Carcinogenesis Analysis And Approximations
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Book Synopsis A Stochastic Model for Immunological Feedback in Carcinogenesis: Analysis and Approximations by : N. Dubin
Download or read book A Stochastic Model for Immunological Feedback in Carcinogenesis: Analysis and Approximations written by N. Dubin and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Stochastic Model for Immunological Feedback in Carcinogenesis by : Neil Dubin
Download or read book A Stochastic Model for Immunological Feedback in Carcinogenesis written by Neil Dubin and published by Springer Verlag. This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A stochastic model for immunological feedback in carcinogenesis by : Neil Bubin
Download or read book A stochastic model for immunological feedback in carcinogenesis written by Neil Bubin and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Systems Theory in Immunology by : C. Bruni
Download or read book Systems Theory in Immunology written by C. Bruni and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the contributions presented at the "Working Conference on System Theory in Immunology", held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under standing of basic immunological facts. Conversely, the complexity of experimental results and of interpretative models should stimulate mathematicians to formulate new problems and to design appropriate procedures of analysis. The multitude of scientific publications in theoretical biology, appeared in recent years, confirms this trend and calls for extensive interaction between mat- matics and immunology. The material of this volume is divided into five sections, along the scheme of the Conference program.
Book Synopsis Stochastic Models for Spike Trains of Single Neurons by : S.K. Srinivasan
Download or read book Stochastic Models for Spike Trains of Single Neurons written by S.K. Srinivasan and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cell Kinetic Modelling and the Chemotherapy of Cancer by : Helmut Knolle
Download or read book Cell Kinetic Modelling and the Chemotherapy of Cancer written by Helmut Knolle and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 30 years, many chemical compounds that are active against tumors have been discovered or developed. At the same time, new methods of testing drugs for cancer therapy have evolved. nefore 1964, drug testing on animal tumors was directed to observation of the incfease in life span of the host after a single dose. 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). They also investigated the influence of the time schedule in the treatment of experimental tumors. Since the publication of those studies, cell population kinetics cannot be left out of any discussion of the rational basis of chemotherapy. When clinical oncologists began to apply cell kinetic concepts in practice about 15 years ago, the theoretical basis was still very poor, in spite of Skipper's progress, and the lack of re levant cytokinetic and pharmacologic data was apparent. Subsequently, much theoretical work has been done and many cell kinetic models have been elaborated (for a review see Eisen, 1977).
Book Synopsis Mathematical Models in Cell Biology and Cancer Chemotherapy by : M. Eisen
Download or read book Mathematical Models in Cell Biology and Cancer Chemotherapy written by M. Eisen and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.
Book Synopsis Stochastic Methods in Biology by : Motoo Kimura
Download or read book Stochastic Methods in Biology written by Motoo Kimura and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis cipline with its own repertoire of techniques. The purpose of the Workshop on sto chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important feature of the Workshop and one of the reasons for organizing it has been the fact that the theory of stochastic differential equations (SDE's) has found a rich source of new problems in the fields of population genetics and neuro biology. This is especially so for the relatively new and growing area of infinite dimensional, i. e. , measure-valued or distribution-valued SDE's. The papers in II and III and some of the papers in the remaining categories represent these areas.
Book Synopsis Stochastic Processes in Epidemic Theory by : Jean-Pierre Gabriel
Download or read book Stochastic Processes in Epidemic Theory written by Jean-Pierre Gabriel and published by Springer. This book was released on 2014-03-11 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimization of Human Cancer Radiotherapy by : G.W. Swan
Download or read book Optimization of Human Cancer Radiotherapy written by G.W. Swan and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. These improvements comprise ways of delivering radiation to the malignan cies so as to create considerable damage to tumor cells while sparing neighboring normal tissues. There is no unique way of dealing with these improvements. Accord ingly, in this book a number of different presentations are given. Each presentation has as its goal some aspect of the improvement, or optimization, of radiotherapy. This book is a collection of current ideas concerned with the optimization of human cancer radiotherapy. It is hoped that readers will build on this collection and develop superior approaches for the understanding of the ways to improve therapy. The author owes a special debt of thanks to Kathy Prindle who breezed through the typing of this book with considerable dexterity. TABLE OF CONTENTS Chapter GENERAL INTRODUCTION 1. 1 Introduction 1 1. 2 History of Cancer and its Treatment by Radiotherapy 8 1. 3 Some Mathematical Models of Tumor Growth 12 1. 4 Spatial Distribution of the Radiation Dose 20 Chapter 2 SURVIVAL CURVES FROM STATISTICAL MODELS 24 2. 1 Introduction 24 2. 2 The Target Model 26 2. 3 Single-hit-to-kill Model 27 2. 4 Multitarget, Single-hit Survival 29 2. 5 Multitarget, Multihit Survival 31 2. 6 Single-target, Multihit Survival 31 2.
Book Synopsis Analysis of Neural Networks by : U. an der Heiden
Download or read book Analysis of Neural Networks written by U. an der Heiden and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modeling and Management of Resources under Uncertainty by : Thomas L. Vincent
Download or read book Modeling and Management of Resources under Uncertainty written by Thomas L. Vincent and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This vol ume contains the proceedings of the second U. S. -Austral ia workshop on Renewable Resource Management held at the East-West Center, Honolulu, Hawaii, December 9-12, 1985. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Science and Technology (Austral ia) under the U. S. -Austral ia Cooperative Science Program. The objective of the workshop was to focus on problems associated with the management of renewable resource systems. A particular emphasis was given to methods for handling uncertain elements whieh are present in any real system. Toward this end, the partiei pants were chosen so that the collective expertise included mathematical modeling, dynamical control/game theory, ecology, and practical management of real systems. Each participant was invited to give an informal presentation in his field of expertise as related to the overall theme. The formal papers (contained in this vo 1 ume) were written after the workshop so that the authors coul d util ize the workshop experience in relating their own work to others. To further encourage this exchange, each paper contained in this volume was reviewed by two other participants who then wrote formal comments. These comments (with author's reply in some cases) are attached to the end of each paper.
Book Synopsis Gonorrhea Transmission Dynamics and Control by : H. W. Hethcote
Download or read book Gonorrhea Transmission Dynamics and Control written by H. W. Hethcote and published by Springer. This book was released on 2014-03-11 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modelling of Patterns in Space and Time by : W. Jäger
Download or read book Modelling of Patterns in Space and Time written by W. Jäger and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Przemyslaw Prusinkiewicz Publisher :Springer Science & Business Media ISBN 13 :1475714289 Total Pages :127 pages Book Rating :4.4/5 (757 download)
Book Synopsis Lindenmayer Systems, Fractals, and Plants by : Przemyslaw Prusinkiewicz
Download or read book Lindenmayer Systems, Fractals, and Plants written by Przemyslaw Prusinkiewicz and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Carlos Castillo-Chavez Publisher :Springer Science & Business Media ISBN 13 :3642934544 Total Pages :416 pages Book Rating :4.6/5 (429 download)
Book Synopsis Mathematical and Statistical Approaches to AIDS Epidemiology by : Carlos Castillo-Chavez
Download or read book Mathematical and Statistical Approaches to AIDS Epidemiology written by Carlos Castillo-Chavez and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 18 research articles of this volume discuss the major themes that have emerged from mathematical and statistical research in the epidemiology of HIV. The opening paper reviews important recent contributions. Five sections follow: Statistical Methodology and Forecasting, Infectivity and the HIV, Heterogeneity and HIV Transmission Dynamics, Social Dynamics and AIDS, and The Immune System and The HIV. In each, leading experts in AIDS epidemiology present the recent results. Some address the role of variable infectivity, heterogeneous mixing, and long periods of infectiousness in the dynamics of HIV; others concentrate on parameter estimation and short-term forecasting. The last section looks at the interaction between the HIV and the immune system.
Book Synopsis The Dynamics of Physiologically Structured Populations by : Johan A. Metz
Download or read book The Dynamics of Physiologically Structured Populations written by Johan A. Metz and published by Springer. This book was released on 2014-03-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
