Cambridge Studies in Mathematical Biology – serie

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Del 15 - Cambridge Studies in Mathematical Biology
Epidemic Modelling
An Introduction
AvD. J. Daley,J. Gani
Häftad, Engelska, 2001
688 kr
Skickas inom 11-20 vardagar
This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.
Del 8 - Cambridge Studies in Mathematical Biology
Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories
AvHenry C. Tuckwell,C. Canningsm. fl.
Häftad, Engelska, 2005
849 kr
Skickas inom 11-20 vardagar
The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.
Del 8 - Cambridge Studies in Mathematical Biology
Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure
AvHenry C. Tuckwell,C. Cannings
Häftad, Engelska, 2006
1 069 kr
Skickas inom 11-20 vardagar
The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differential equations and linear algebra is desirable.
Del 9 - Cambridge Studies in Mathematical Biology
Biological Delay Systems
Linear Stability Theory
AvN. MacDonald,C. Canningsm. fl.
Häftad, Engelska, 2008
1 678 kr
Skickas inom 11-20 vardagar
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.
Del 7 - Cambridge Studies in Mathematical Biology
Mathematical Aspects of Hodgkin-Huxley Neural Theory
AvJane Cronin
Häftad, Engelska, 2008
739 kr
Skickas inom 11-20 vardagar
This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.
Del 12 - Cambridge Studies in Mathematical Biology
Biological Kinetics
AvLee A. Segel
Häftad, Engelska, 2008
616 kr
Skickas inom 11-20 vardagar
As interest in theoretical biology grows, so does the need for an accessible link between these theories and experiments. The central purpose of this book is to illustrate the premise that examination of the kinetics of biological processes can give valuable information concerning the underlying mechanisms that are responsible for these processes. Topics covered range from co-operativity in protein binding, through receptor-infector coupling, to theories of biochemical oscillations in yeast and slime mould. In addition, an introduction to the explosively growing theoretical topic of chaos details attempts to apply this theory in physiology. The material of this book originally appeared as part of the volume Mathematical Models in Molecular and Cellular Biology (edited by L. A. Segel). However each article has been revised and updated.
Del 13 - Cambridge Studies in Mathematical Biology
The Theory of the Chemostat
Dynamics of Microbial Competition
AvHal L. Smith,Paul Waltman
Häftad, Engelska, 2008
902 kr
Skickas inom 11-20 vardagar
The chemostat is a basic piece of laboratory apparatus, yet it has occupied an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying inputs. Models which take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modelled and analysed using the dynamical systems approach. Directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools. Teachers, researchers, and students in applied mathematics, chemical engineering and ecology will find this book a welcome resource.
Del 10 - Cambridge Studies in Mathematical Biology
Mathematical Ecology of Plant Species Competition
AvAnthony G. Pakes,R. A. Maller
Häftad, Engelska, 2009
576 kr
Skickas inom 11-20 vardagar
Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology and to agronomists and botanists interested in population dynamics.
Del 2 - Cambridge Studies in Mathematical Biology
Mechanics of Swimming and Flying
AvStephen Childress
Häftad, Engelska, 1981
658 kr
Skickas inom 11-20 vardagar
This book provides a clear and concise summary of the fluid dynamics of the locomotion of living organisms. The biological phenomena described in detail range from the swimming of bacteria and fish to the flying of insects and birds. The breadth of treatment requires the study of two basic fluid-dynamical regimes. In the first case, that of small organisms, the viscosity of the fluid is paramount in deciding the most effective swimming strategy. However, for larger insects, birds, and most fish, the viscosity of the air or water may be treated as if it were zero, and resulting mechanisms of propulsion are very different. Both these types are studied, with emphasis on the unsteady character of natural movements. Written for the advanced student, this volume assumes familiarity with basic fluid mechanics, although some elementary topics are included. It will be readily accessible to students of applied mathematics and biologists who have engineering or physics backgrounds.
Del 4 - Cambridge Studies in Mathematical Biology
Mathematical Methods of Population Biology
AvFrank C. Hoppensteadt,C. Cannings
Häftad, Engelska, 1982
417 kr
Skickas inom 11-20 vardagar
This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those derived and studied in the text.
Del 3 - Cambridge Studies in Mathematical Biology
Genealogical Genetic Structure
AvC. Cannings
Häftad, Engelska, 1981
549 kr
Skickas inom 11-20 vardagar
Although the long-term processes of evolution are selection and mutation, the infrastructure of a population is a no less important force in determining the distributions of genetic characteristics observable within populations. In small populations, and in particular in human populations, complex patterns of genealogical relationship between individuals can be an important factor in the maintenance of genetic variability. The aim of this book is to develop the quantitative theory of the interrelationship between the genealogical and the genetic structures of a population. Aspects of other structural features, such as migration patterns, are also discussed, but are not central to the development. There are three major aspects; each comprises two chapters of the text. First, genealogical relationships are characterized in a way which can illuminate their genetic consequences. Second, the evolutionary aspects of genealogical structure are developed. Finally, the last two chapters present methods of characterizing the complete structure of a genealogy, and of computing relevant parameters of genealogical structure; these topics are of relevance to genetic epidemiology as well as to population genetics.
Del 7 - Cambridge Studies in Mathematical Biology
Mathematical Aspects of Hodgkin-Huxley Neural Theory
AvJane Cronin,C. Canningsm. fl.
Inbunden, Engelska, 1987
1 633 kr
Skickas inom 11-20 vardagar
This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.
Del 9 - Cambridge Studies in Mathematical Biology
Biological Delay Systems
Linear Stability Theory
AvN. MacDonald,C. Canningsm. fl.
Inbunden, Engelska, 1989
1 724 kr
Skickas inom 11-20 vardagar
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.
Del 8 - Cambridge Studies in Mathematical Biology
Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure
AvHenry C. Tuckwell,C. Canningsm. fl.
Inbunden, Engelska, 1988
1 972 kr
Skickas inom 11-20 vardagar
The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differential equations and linear algebra is desirable.
Del 8 - Cambridge Studies in Mathematical Biology
Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories
AvHenry C. Tuckwell,C. Cannings
Inbunden, Engelska, 1988
1 972 kr
Skickas inom 11-20 vardagar
The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.
Del 10 - Cambridge Studies in Mathematical Biology
Mathematical Ecology of Plant Species Competition
AvAnthony G. Pakes,R. A. Maller
Inbunden, Engelska, 1990
1 633 kr
Skickas inom 11-20 vardagar
Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology and to agronomists and botanists interested in population dynamics.
Del 12 - Cambridge Studies in Mathematical Biology
Biological Kinetics
AvSegel,Lee A. Segel
Inbunden, Engelska, 1992
1 200 kr
Skickas inom 11-20 vardagar
As interest in theoretical biology grows, so does the need for an accessible link between these theories and experiments. The central purpose of this book is to illustrate the premise that examination of the kinetics of biological processes can give valuable information concerning the underlying mechanisms that are responsible for these processes. Topics covered range from co-operativity in protein binding, through receptor-infector coupling, to theories of biochemical oscillations in yeast and slime mould. In addition, an introduction to the explosively growing theoretical topic of chaos details attempts to apply this theory in physiology. The material of this book originally appeared as part of the volume Mathematical Models in Molecular and Cellular Biology (edited by L. A. Segel). However each article has been revised and updated.
Del 11 - Cambridge Studies in Mathematical Biology
Modelling Biological Populations in Space and Time
AvEric Renshaw,Eric Renshaw
Häftad, Engelska, 1993
1 173 kr
Skickas inom 11-20 vardagar
This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.
Del 14 - Cambridge Studies in Mathematical Biology
Evolution in Age-Structured Populations
AvBrian Charlesworth,C. Canningsm. fl.
Häftad, Engelska, 1994
766 kr
Skickas inom 11-20 vardagar
The populations of many species of animals and plants are age-structured, i.e. the individuals present at any one time were born over a range of different times, and their fertility and survival depend on age. The properties of such populations are important for interpreting experiments and observations on the genetics of populations for animal and plant breeding, and for understanding the evolution of features of life-histories such as senescence and time of reproduction. In this new edition Brian Charlesworth provides a comprehensive review of the basic mathematical theory of the demography and genetics of age-structured populations. The mathematical level of the book is such that it will be accessible to anyone with a knowledge of basic calculus and linear algebra.
Del 13 - Cambridge Studies in Mathematical Biology
The Theory of the Chemostat
Dynamics of Microbial Competition
AvHal L. Smith,Paul Waltmanm. fl.
Inbunden, Engelska, 1995
1 566 kr
Skickas inom 11-20 vardagar
The chemostat is a basic piece of laboratory apparatus, yet it has occupied an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying inputs. Models which take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modelled and analysed using the dynamical systems approach. Directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools. Teachers, researchers, and students in applied mathematics, chemical engineering and ecology will find this book a welcome resource.
Del 17 - Cambridge Studies in Mathematical Biology
Mathematics of Genome Analysis
AvJerome K. Percus
Häftad, Engelska, 2001
435 kr
Skickas inom 11-20 vardagar
The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. While the basic effort is of course a biological one, the description and classification of sequences also lend themselves naturally to mathematical and statistical modeling. This short textbook on the mathematics of genome analysis presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing. It will be of interest not only to students but also to professional mathematicians curious about the subject.
Del 6 - Cambridge Studies in Mathematical Biology
An Introduction to the Mathematics of Neurons
Modeling in the Frequency Domain
AvFrank C. Hoppensteadt,C. Cannings
Inbunden, Engelska, 1997
1 431 kr
Skickas inom 11-20 vardagar
This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.
Del 6 - Cambridge Studies in Mathematical Biology
An Introduction to the Mathematics of Neurons
Modeling in the Frequency Domain
AvFrank C. Hoppensteadt,C. Cannings
Häftad, Engelska, 1997
741 kr
Skickas inom 11-20 vardagar
This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.
Del 16 - Cambridge Studies in Mathematical Biology
An Introduction to Mathematical Physiology and Biology
AvJ. Mazumdar,C. Canningsm. fl.
Inbunden, Engelska, 1999
1 463 kr
Skickas inom 11-20 vardagar
This textbook is concerned with the mathematical modelling of biological and physiological phenomena for mathematically sophisticated students. A range of topics are discussed: diffusion population dynamics, autonomous differential equations and the stability of ecosystems, biogeography, pharmokinetics, biofluid mechanics, cardiac mechanics, the spectral analysis of heart sounds using FFT techniques. The last chapter deals with a wide variety of commonly used medical devices. This book is based on courses taught by the author over many years and the material is well class tested. The reader is aided by many exercises that examine key points and extend the presentation in the body of the text. All students of mathematical biology will find this book to be a highly useful resource.
Del 16 - Cambridge Studies in Mathematical Biology
An Introduction to Mathematical Physiology and Biology
AvJ. Mazumdar,C. Canningsm. fl.
Häftad, Engelska, 1999
661 kr
Skickas inom 11-20 vardagar
This textbook is concerned with the mathematical modelling of biological and physiological phenomena for mathematically sophisticated students. A range of topics are discussed: diffusion population dynamics, autonomous differential equations and the stability of ecosystems, biogeography, pharmokinetics, biofluid mechanics, cardiac mechanics, the spectral analysis of heart sounds using FFT techniques. The last chapter deals with a wide variety of commonly used medical devices. This book is based on courses taught by the author over many years and the material is well class tested. The reader is aided by many exercises that examine key points and extend the presentation in the body of the text. All students of mathematical biology will find this book to be a highly useful resource.

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Cambridge Studies in Mathematical Biology – serie

Epidemic Modelling

Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories

Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure

Biological Delay Systems

Mathematical Aspects of Hodgkin-Huxley Neural Theory

Biological Kinetics

The Theory of the Chemostat

Mathematical Ecology of Plant Species Competition

Mechanics of Swimming and Flying

Mathematical Methods of Population Biology

Genealogical Genetic Structure

Mathematical Aspects of Hodgkin-Huxley Neural Theory

Biological Delay Systems

Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure

Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories

Mathematical Ecology of Plant Species Competition

Biological Kinetics

Modelling Biological Populations in Space and Time

Evolution in Age-Structured Populations

The Theory of the Chemostat

Mathematics of Genome Analysis

An Introduction to the Mathematics of Neurons

An Introduction to the Mathematics of Neurons

An Introduction to Mathematical Physiology and Biology

An Introduction to Mathematical Physiology and Biology

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