Download or read book Information Geometry and Population Genetics written by Julian Hofrichter and published by Springer. This book was released on 2017-02-23 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.
Download or read book The Geometry of Genetics written by A. M. Findlay and published by Wiley-Interscience. This book was released on 1989-03-20 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary biology has grown from the highly controversial world-view of the days of Charles Darwin, to a complex and refined theory of nature’s expression through the deep and subtle action of the genetic code. The Geometry of Genetics is an interdisciplinary monograph that presents the mathematical basis of molecular genetics, endowing evolutionary biology with a precision not before available to the subject. To make this work accessible to biologists and physical scientists alike, the authors have divided the subject into three parts, Structure, Statics, and Dynamics. Each of these parts is further subdivided into a presentation of the relevant mathematics, a description of the biological problem, and a mathematical reformulation of the biological problem. They provide, in effect, basic mathematical and biological primers for each topic covered. In the first part of the book, Statics, the authors develop some set-theoretic and linear algebraic notions, and describe the origin and evolution of the genetic code. Here they reveal the beauty of the hidden symmetries of the standard genetic code, and of their extension of genetic coding theory, the generalized genetic code. The second part of the book, Structure, expresses the basic processes of molecular genetics—replication, transcription, and translation—as operators on a certain linear space. The final part, Dynamics, realizes the action of molecular genetics as a differential geometry, within which evolutionary motions are treated as geodesics. It is here that evolutionary biology can be seen unfolding on the rich mathematical construct of a space-time manifold. This natural progression, from statics to structure and dynamics, provides a nested cohesiveness which reveals the intricate natural hierarchy of the elementary genetic code, molecular genetic action, and macromolecular evolution, which gives rise to a variety of genetic cosmologies. The Geometry of Genetics expresses the fundamental actions of evolutionary biology with a new richness and precision that should prove illuminating to biologists and physical scientists alike.
Download or read book The Geometry of Population Genetics written by Ethan Akin and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele model of selection plus recombination even when the fitness numbers are constant (i.e. no frequency dependence). This work is addressed to two different kinds of readers which accounts for its mode of organization. For the biologist, Chapter I contains a description of the entire work with brief indications of a proof for the harder results. I imagine a reader with some familiarity with linear algebra and systems of differential equations. Ideal background is Hirsch and Smale's text [15].
Download or read book Genetics and Geometry written by Edmund Ware Sinnott and published by . This book was released on 1944 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculating the Secrets of Life written by National Research Council and published by National Academies Press. This book was released on 1995-04-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important roleâ€"in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race. In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology. The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences. This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.
Download or read book Geometry from the Genetic Point of View written by Leroy Walter Sackett and published by . This book was released on 1908 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Preserving Strength While Meeting Challenges written by National Research Council and published by National Academies Press. This book was released on 1997-08-25 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Molecular Origins of Brain and Body Geometry written by Antonio Lima-de-Faria and published by Springer. This book was released on 2014-10-07 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: New concepts arise in science when apparently unrelated fields of knowledge are put together in a coherent way. The recent results in molecular biology allow to explain the emergence of body patterns in animals that before could not be understood by zoologists. There are no ”fancy curiosities” in nature. Every pattern is a product of a molecular cascade originating in genes and a living organism arises from the collaboration of these genes with the outer physical environment. Tropical fishes are as startling in their colors and geometric circles as peacocks. Tortoises are covered with the most regular triangles, squares and concentric circles that can be green, brown or yellow. Parallel scarlet bands are placed side by side of black ones along the body of snakes. Zebras and giraffes have patterns which are lessons in geometry, with their transversal and longitudinal stripes, their circles and other geometric figures. Monkeys, like the mandrills, have a spectacularly colored face scarlet nose with blue parallel flanges and yellow beard. All this geometry turns out to be highly molecular. The genes are many and have been DNA sequenced. Besides they not only deal with the coloration of the body but with the development of the brain and the embryonic process. A precise scenario of molecular events unravels in the vertebrates. It may seem far-fetched, but the search for the origin of this geometry made it mandatory to study the evolution of matter and the origin of the brain. It turned out that matter from its onset is pervaded by geometry and that the brain is also a prisoner of this ordered construction. Moreover, the brain is capable of altering the body geometry and the geometry of the environment changes the brain. Nothing spectacular occurred when the brain arrived in evolution. Not only it came after the eye, which had already established itself long ago, but it had a modest origin. It started from sensory cells on the skin that later aggregated into clusters of neurons that formed ganglia. It also became evident that pigment cells, that decide the establishment of the body pattern, originate from the same cell population as neurons (the neural crest cells). This is a most revealing result because it throws light on the power that the brain has to rapidly redirect the coloration of the body and to change its pattern. Recent experiments demonstrate how the brain changes the body geometry at will and within seconds, an event that could be hardly conceived earlier. Moreover, this change is not accidental it is related to the surrounding environment and is also used as a mating strategy. Chameleons know how to do it as well as flat fishes and octopuses. No one would have dared to think that the brain had its own geometry. How could the external geometry of solids or other figures of our environment be apprehended by neurons if these had no architecture of their own? Astonishing was that the so called ”simple cells”, in the neurons of the primary visual cortex, responded to a bar of light with an axis of orientation that corresponded to the axis of the cell’s receptive field. We tend to consider our brain a reliable organ. But how reliable is it? From the beginning the brain is obliged to transform reality. Brain imagery involves: form, color, motion and sleep. Unintentionally these results led to unexpected philosophical implications. Plato’s pivotal concept that ”forms” exist independently of the material world is reversed. Atoms have been considered to be imaginary for 2,000 years but at present they can be photographed, one by one, with electron microscopes. The reason why geometry has led the way in this inquiry is due to the fact that where there is geometry there is utter simplicity coupled to rigorous order that underlies the phenomenon where it is recognized. Order allows variation but imposes at the same time a canalization that is patent in what we call evolution.
Download or read book The Geometry of Evolution written by George R. McGhee and published by Cambridge University Press. This book was released on 2006-12-07 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The metaphor of the adaptive landscape - that evolution via the process of natural selection can be visualized as a journey across adaptive hills and valleys, mountains and ravines - permeates both evolutionary biology and the philosophy of science. The focus of this 2006 book is to demonstrate to the reader that the adaptive landscape concept can be put into actual analytical practice through the usage of theoretical morphospaces - geometric spaces of both existent and non-existent biological form - and to demonstrate the power of the adaptive landscape concept in understanding the process of evolution. The adaptive landscape concept further allows us to take a spatial approach to the concepts of natural selection, evolutionary constraint and evolutionary development. For that reason, this book relies heavily on spatial graphics to convey the concepts developed within these pages, and less so on formal mathematics.
Download or read book Cell Biology by the Numbers written by Ron Milo and published by Garland Science. This book was released on 2015-12-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Top 25 CHOICE 2016 Title, and recipient of the CHOICE Outstanding Academic Title (OAT) Award. How much energy is released in ATP hydrolysis? How many mRNAs are in a cell? How genetically similar are two random people? What is faster, transcription or translation?Cell Biology by the Numbers explores these questions and dozens of others provid
Download or read book Algebraic Biology Matrix Genetics And Genetic Intelligence written by Sergei V Petoukhov and published by World Scientific. This book was released on 2023-08-02 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, mathematics, probability, and statistics have been widely used in the biological sciences. Recent progress in genomics has yielded many millions of gene sequences. But what do these sequences tell us and what are the generalities and rules governed by them? It seems that we understand very little about the genetic contexts required to 'read' them. There is more to life than the genomic blueprint of each organism. Life functions within the natural laws that we know and the ones we do not know. The development of modern mathematical natural sciences is based on the use of certain mathematical tools. Mathematics can be used to understand life from the molecular to the biosphere level.This book provides the foundation and latest advances for an emerging research area that uses tools from symbolic computation, computer algebra and logic, algebraic geometry, fractal geometry, probability and statistics, and matrix algebra to formalize and solve biological problems and explore its applications in algebraic biology and code biology. It introduces highly interdisciplinary topics in biomathematics such as matrix genetics, gestalt biology, bio-antenna arrays, resonance genetics, quantum biology, and more.
Download or read book New Trends In Geometry Their Role In The Natural And Life Sciences written by Luciano Boi and published by World Scientific. This book was released on 2011-05-19 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.
Download or read book Experiencing Geometry Physics and Biology written by Georg Glaeser and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding geometry, physics, and biology This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book. The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues. Includes links to around 300 video animations, accessible via QR codes Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology With numerous images and illustrations
Download or read book Topology and Robotics written by Michael Farber and published by American Mathematical Soc.. This book was released on 2007 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
Download or read book The Geometry of Biological Time written by Arthur T. Winfree and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.
Download or read book Geometry and genetics of microbial adaptation written by Matthew Jonas Brauer and published by . This book was released on 2000 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
