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Mathematical Models in Biology
(Classics in Applied Mathematics)
by Leah Edelstein-Keshet
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Biomathematics
by
S. Andersson ,K. Larsson ,M. Larsson M. Jacob
"Elsevier Science
1st edition
(October 1, 1999)
| PDF | 534 pages | 45181 KB
1st edition
(October 1, 1999)
| PDF | 534 pages | 45181 KB
Product Description
This book presents new mathematics for the description of structure and dynamics in molecular and cellular biology. On an exponential scale it is possible to combine functions describing inner organisation, including finite periodicity, with functions for outside morphology into a complete definition of structure. This mathematics is particularly fruitful to apply at molecular and atomic distances. The structure descriptions can then be related to atomic and molecular forces and provide information on structural mechanisms. The calculations have been focussed on lipid membranes forming the surface layers of cell organelles. Calculated surfaces represent the mid-surface of the lipid bilayer. Membrane dynamics such as vesicle transport are described in this new language. Periodic membrane assemblies exhibit conformations based on the standing wave oscillations of the bilayer, considered to reflect the true dynamic nature of periodic membrane structures. As an illustration the structure of an endoplasmatic reticulum has been calculated. The transformation of such cell membrane assemblies into cubosomes seems to reflect a transition into vegetative states. The organisation of the lipid bilayer of nerve cells is analyzed, taking into account an earlier observed lipid bilayer phase transition associated with the depolarisation of the membrane. Evidence is given for a new structure of the alveolar surface, relating the mathematical surface defining the bilayer organisation to new experimental data. The surface layer is proposed to consist of a coherent phase, consisting of a lipid-protein bilayer curved according to a classical surface - the CLP surface. Without employing this new mathematics it would not be possible to give an analytical description of this structure and its deformation during the respiration cycle. In more general terms this mathematics is applied to the description of the structure and dynamic properties of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled.
This mathematical description of biological structure and dynamics, biomathematics, also provides significant new information in order to understand the mechanisms governing shape of living organisms
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Transport Equations in Biology
by
Benoît Perthame
November 22, 2006 |
PDF | 198 Pages |
1.9 MB
Product Description
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion). Original mathematical methods described are, among others, the generalized relative entropy method - a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.
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Basic Biostatistics for Geneticists and Epidemiologists
A Practical Approach
by
Robert C. Elston, William Johnson
Wiley | 2008-12-31 |
ISBN: 0470024895 | 384 pages | PDF | 1,53 MB
ISBN: 0470024895 | 384 pages | PDF | 1,53 MB
Product Description
Anyone who attempts to read genetics or epidemiology research literature needs to understand the essentials of biostatistics. This book, a revised new edition of the successful Essentials of Biostatistics has been written to provide such an understanding to those who have little or no statistical background and who need to keep abreast of new findings in this fast moving field. Unlike many other elementary books on biostatistics, the main focus of this book is to explain basic concepts needed to understand statistical procedures.
This Book
Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares.
Introduces methods, such as permutation testing and bootstrapping, that are becoming more widely used in both genetic and epidemiological research.
Is illustrated throughout with simple examples to clarify the statistical methodology.
Explains Bayes’ theorem pictorially.
Features exercises, with answers to alternate questions, enabling use as a course text.
Written at an elementary mathematical level so that readers with high school mathematics will find the content accessible. Graduate students studying genetic epidemiology, researchers and practitioners from genetics, epidemiology, biology, medical research and statistics will find this an invaluable introduction to statistics.
Introduces methods, such as permutation testing and bootstrapping, that are becoming more widely used in both genetic and epidemiological research.
Is illustrated throughout with simple examples to clarify the statistical methodology.
Explains Bayes’ theorem pictorially.
Features exercises, with answers to alternate questions, enabling use as a course text.
Written at an elementary mathematical level so that readers with high school mathematics will find the content accessible. Graduate students studying genetic epidemiology, researchers and practitioners from genetics, epidemiology, biology, medical research and statistics will find this an invaluable introduction to statistics.
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Essential Mathematical Biology
by
Nicholas F. Britton
Springer | 2004/10/28 | 185233536X | PDF | 4.16 MB | 370 Pages
Product Description
Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences.
A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling.
This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology
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