Download or read book Algebras in Genetics written by Angelika Wörz-Busekros and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers¢l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff in the third section of his book "Genetics and Social Structure" has included four papers by Etherington and Reiers¢l's paper. Apparently a complete review, in par ticular one comprising more recent results was lacking, and it was difficult for students to enter this field of research. I started to write these notes in spring 1978. A first german version was finished at the end of that year. Further revision and translation required another year. I hope that the notes in their present state provide a reasonable review and that they will facilitate access to this field. I am especially grateful to Professor K. -P. Hadeler and Professor P. Holgate for reading the manuscript and giving essential comments to all versions of the text. I am also very grateful to Dr. I. Heuch for many discussions during and after his stay in TUbingen. I wish to thank Dr. V. M.

Download or read book Evolution Algebras and Their Applications written by Jianjun Paul Tian and published by Springer Science & Business Media. This book was released on 2008 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Download or read book Mathematical Structures in Population Genetics written by Yuri I. Lyubich and published by Springer. This book was released on 2011-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical methods have been applied successfully to population genet ics for a long time. Even the quite elementary ideas used initially proved amazingly effective. For example, the famous Hardy-Weinberg Law (1908) is basic to many calculations in population genetics. The mathematics in the classical works of Fisher, Haldane and Wright was also not very complicated but was of great help for the theoretical understanding of evolutionary pro cesses. More recently, the methods of mathematical genetics have become more sophisticated. In use are probability theory, stochastic processes, non linear differential and difference equations and nonassociative algebras. First contacts with topology have been established. Now in addition to the tra ditional movement of mathematics for genetics, inspiration is flowing in the opposite direction, yielding mathematics from genetics. The present mono grapll reflects to some degree both patterns but especially the latter one. A pioneer of this synthesis was S. N. Bernstein. He raised-and partially solved- -the problem of characterizing all stationary evolutionary operators, and this work was continued by the author in a series of papers (1971-1979). This problem has not been completely solved, but it appears that only cer tain operators devoid of any biological significance remain to be addressed. The results of these studies appear in chapters 4 and 5. The necessary alge braic preliminaries are described in chapter 3 after some elementary models in chapter 2.

Download or read book An Introduction to the Mathematics of Biology with Computer Algebra Models written by Edward K. Yeargers and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biology is a source of fascination for most scientists, whether their training is in the life sciences or not. In particular, there is a special satisfaction in discovering an understanding of biology in the context of another science like mathematics. Fortunately there are plenty of interesting (and fun) problems in biology, and virtually all scientific disciplines have become the richer for it. For example, two major journals, Mathematical Biosciences and Journal of Mathematical Biology, have tripled in size since their inceptions 20-25 years ago. The various sciences have a great deal to give to one another, but there are still too many fences separating them. In writing this book we have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own, in which both the biology and the math ematics should be equal and complete, and should flow smoothly into and out of one another. We have taught mathematical biology with this philosophy in mind and have seen profound changes in the outlooks of our science and engineering students: The attitude of "Oh no, another pendulum on a spring problem!," or "Yet one more LCD circuit!" completely disappeared in the face of applications of mathematics in biology. There is a timeliness in calculating a protocol for ad ministering a drug.

Download or read book Algebraic and Combinatorial Computational Biology written by Raina Robeva and published by Academic Press. This book was released on 2018-10-08 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. - Integrates a comprehensive selection of tools from computational biology into educational or research programs - Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations - Contains scalable material for use in undergraduate and graduate-level classes and research projects - Introduces the reader to freely-available professional software - Supported by illustrative datasets and adaptable computer code

Download or read book Algebraic and Discrete Mathematical Methods for Modern Biology written by Raina Robeva and published by Academic Press. This book was released on 2015-05-09 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. - Examines significant questions in modern biology and their mathematical treatments - Presents important mathematical concepts and tools in the context of essential biology - Features material of interest to students in both mathematics and biology - Presents chapters in modular format so coverage need not follow the Table of Contents - Introduces projects appropriate for undergraduate research - Utilizes freely accessible software for visualization, simulation, and analysis in modern biology - Requires no calculus as a prerequisite - Provides a complete Solutions Manual - Features a companion website with supplementary resources

Download or read book Algebraic Statistics for Computational Biology written by L. Pachter and published by Cambridge University Press. This book was released on 2005-08-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Download or read book Mathematical and Statistical Methods for Genetic Analysis written by Kenneth Lange and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to equip students in the mathematical siences to understand and model the epidemiological and experimental data encountered in genetics research. This second edition expands the original edition by over 100 pages and includes new material. Sprinkled throughout the chapters are many new problems.

Download or read book Theoretical Population Genetics written by J.S. Gale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rise of the neutral theory of molecular evolution seems to have aroused a renewed interest in mathematical population genetics among biologists, who are primarily experimenters rather than theoreticians. This has encouraged me to set out the mathematics of the evolutionary process in a manner that, I hope, will be comprehensible to those with only a basic knowledge of calculus and matrix algebra. I must acknowledge from the start my great debt to my students. Equipped initially with rather limited mathematics, they have pursued the subject with much enthusiasm and success. This has enabled me to try a number of different approaches over the years. I was particularly grateful to Dr L. J. Eaves and Professor W. E. Nance for the opportunity to give a one-semester course at the Medical College of Virginia, and I would like to thank them, their colleagues and their students for the many kindnesses shown to me during my visit. I have concentrated almost entirely on stochastic topics, since these cause the greatest problems for non-mathematicians. The latter are particularly concerned with the range of validity of formulae. A sense of confidence in applying these formulae is, almost certainly, best gained by following their derivation. I have set out proofs in fair detail, since, in my experience, minor points of algebraic manipulation occasionally cause problems. To avoid loss of continuity, I have sometimes put material in notes at the end of chapters.

Download or read book Mathematical Biology written by Ronald W. Shonkwiler and published by Springer Science & Business Media. This book was released on 2009-08-04 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.

Download or read book Human Population Genetics written by John H. Relethford and published by John Wiley & Sons. This book was released on 2012-03-27 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory guide to human population genetics and microevolutionary theory Providing an introduction to mathematical population genetics, Human Population Genetics gives basic background on the mechanisms of human microevolution. This text combines mathematics, biology, and anthropology and is best suited for advanced undergraduate and graduate study. Thorough and accessible, Human Population Genetics presents concepts and methods of population genetics specific to human population study, utilizing uncomplicated mathematics like high school algebra and basic concepts of probability to explain theories central to the field. By describing changes in the frequency of genetic variants from one generation to the next, this book hones in on the mathematical basis of evolutionary theory. Human Population Genetics includes: Helpful formulae for learning ease Graphs and analogies that make basic points and relate the evolutionary process to mathematical ideas Glossary terms marked in boldface within the book the first time they appear In-text citations that act as reference points for further research Exemplary case studies Topics such as Hardy-Weinberg equilibrium, inbreeding, mutation, genetic drift, natural selection, and gene flow Human Population Genetics solidifies knowledge learned in introductory biological anthropology or biology courses and makes it applicable to genetic study. NOTE: errata for the first edition can be found at the author's website: http://employees.oneonta.edu/relethjh/HPG/errata.pdf

Download or read book Population Genetics of Multiple Loci written by Freddy B. Christiansen and published by . This book was released on 2000-01-10 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population Genetics of Multiple Loci F. B. Christiansen University of Aarhus, Denmark "This is a very beautiful and powerful study of an area that Christiansen has dominated for many years." - Marcus Feldman, Stanford University, USA Population genetics thrives on the constant interaction between theoretical and empirical knowledge. In the first instance, population genetics was developed using one-locus, two-allele models for genetic variation. The simplicity of these models opened up theoretical developments in population and evolutionary genetics to biologists without specialist training in mathematics. Population genetics of multi-allelic loci is more complex and requires more mathematical insight, and its study is predominantly undertaken by mathematical biologists. Traditional formulations of multi-locus theory do not simplify by assuming two alleles per locus. In this elegant presentation the author provides a formulation of multi-locus population genetics that retains the simplicity of two-allele models. * Provides an accessible and natural extension of classical population genetics to multiple loci * Exposes the population genetic aspects of sexual reproduction * Describes the complexity of evolutionary interactions among genes * Provides the background for insight into the functioning of genetic algorithms applied in computer science * Written by a world leader in the field The book is divided into two main sections. Part I - Recombination and Segregation - includes coverage of random mating, inbreeding, migration and mixing. Part II - Selection - covers numerous phenomena involving natural selection including viability, fertility, mutation and migration. The author has successfully presented the theory in a way that is intelligible to anyone with a reasonably good background in basic mathematics and is devoted to learning multiple loci population genetics. The text is primarily aimed at advanced undergraduate and postgraduate students and researchers interested in genetics and population biology. It is also essential reading for those working or researching in biomathematics and adaptive computing.

Download or read book Algebras Groups and Geometries written by and published by . This book was released on 2005 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Theoretical Population Genetics written by Thomas Nagylaki and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. I have tried to formulate the various models fairly generally and to state the biological as sumptions quite explicitly. I hope the choice and treatment of topics will en able the reader to understand and evaluate detailed analyses of many specific models and applications in the literature. Models in population genetics are highly idealized, often even over idealized, and their connection with observation is frequently remote. Further more, it is not practicable to measure the parameters and variables in these models with high accuracy. These regrettable circumstances amply justify the use of appropriate, lucid, and rigorous approximations in the analysis of our models, and such approximations are often illuminating even when exact solu tions are available. However, our empirical and theoretical limitations justify neither opaque, incomplete formulations nor unconvincing, inadequate analy ses, for these may produce uninterpretable, misleading, or erroneous results. Intuition is a principal source of ideas for the construction and investigation of models, but it can replace neither clear formulation nor careful analysis. Fisher (1930; 1958, pp. x, 23-24, 38) not only espoused similar ideas, but he recognized also that our concepts of intuition and rigor must evolve in time. The book is neither a review of the literature nor a compendium of results. The material is almost entirely self-contained. The first eight chapters are a thoroughly revised and greatly extended version of my published lecture notes (Nagylaki, 1977a).

Download or read book Introduction to Linear Algebra and Differential Equations written by John W. Dettman and published by Courier Corporation. This book was released on 2012-10-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Download or read book Statistics in Human Genetics and Molecular Biology written by Cavan Reilly and published by CRC Press. This book was released on 2009-06-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the roles of different segments of DNA, Statistics in Human Genetics and Molecular Biology provides a basic understanding of problems arising in the analysis of genetics and genomics. It presents statistical applications in genetic mapping, DNA/protein sequence alignment, and analyses of gene expression data from microarray experiments.

Download or read book Regular Algebra and Finite Machines written by John Horton Conway and published by Courier Corporation. This book was released on 2012-09-16 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: A world-famous mathematician explores Moore's theory of experiments, Kleene's theory of regular events and expressions, differential calculus of events, the factor matrix, theory of operators, much more. Solutions. 1971 edition.