The Geometry Of Evolution

Author : George R. McGhee
Publisher : Cambridge University Press
Page : 185 pages
File Size : 55,6 Mb
Release : 2006-12-07
Category : Science
ISBN : 9781139459952

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The Geometry of Evolution by George R. McGhee Pdf

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.

Author : Boris A. Rosenfeld
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 49,9 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9781441986801

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A History of Non-Euclidean Geometry by Boris A. Rosenfeld Pdf

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

Author : Yoshikazu Giga
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 46,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373917

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Surface Evolution Equations by Yoshikazu Giga Pdf

This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.

Author : Arthur T. Winfree
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662224922

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The Geometry of Biological Time by Arthur T. Winfree Pdf

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.

Author : Ulf Dieckmann,Richard Law,Johan A. J. Metz
Publisher : Cambridge University Press
Page : 583 pages
File Size : 43,5 Mb
Release : 2000-05-04
Category : Mathematics
ISBN : 9780521642941

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The Geometry of Ecological Interactions by Ulf Dieckmann,Richard Law,Johan A. J. Metz Pdf

Spatial ecology, space.

Author : Raul Rabadan,Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 522 pages
File Size : 47,7 Mb
Release : 2019-12-19
Category : Science
ISBN : 9781108757492

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Topological Data Analysis for Genomics and Evolution by Raul Rabadan,Andrew J. Blumberg Pdf

Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.

Author : Julian Hofrichter,Jürgen Jost,Tat Dat Tran
Publisher : Springer
Page : 320 pages
File Size : 53,7 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9783319520452

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Information Geometry and Population Genetics by Julian Hofrichter,Jürgen Jost,Tat Dat Tran Pdf

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.

Author : Fred L. Bookstein
Publisher : Academy of Natural Sciences
Page : 277 pages
File Size : 52,5 Mb
Release : 1985
Category : Science
ISBN : 0910006482

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Morphometrics in Evolutionary Biology by Fred L. Bookstein Pdf

Author : W.R. Knorr
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401017541

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The Evolution of the Euclidean Elements by W.R. Knorr Pdf

The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.

Author : C. Childs,R.E. Holdsworth,C.A.-L. Jackson,T. Manzocchi,J.J. Walsh,G. Yielding
Publisher : Geological Society of London
Page : 539 pages
File Size : 47,9 Mb
Release : 2017-11-06
Category : Science
ISBN : 9781862399679

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The Geometry and Growth of Normal Faults by C. Childs,R.E. Holdsworth,C.A.-L. Jackson,T. Manzocchi,J.J. Walsh,G. Yielding Pdf

Normal faults are the primary structures that accommodate extension of the brittle crust. This volume provides an up-to-date overview of current research into the geometry and growth of normal faults. The 23 research papers present the findings of outcrop and subsurface studies of the geometrical evolution of faults from a number of basins worldwide, complemented by analogue and numerical modelling studies of fundamental aspects of fault kinematics. The topics addressed include how fault length changes with displacement, how faults interact with one another, the controls of previous structure on fault evolution and the nature and origin of fault-related folding. This volume will be of interest to those wishing to develop a better understanding of the structural geological aspects of faulting, from postgraduate students to those working in industry.

Author : Adrian Bejan,J. Peder Zane
Publisher : Anchor
Page : 306 pages
File Size : 41,7 Mb
Release : 2013-01-08
Category : Science
ISBN : 9780307744340

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Design in Nature by Adrian Bejan,J. Peder Zane Pdf

In this groundbreaking book, Adrian Bejan takes the recurring patterns in nature—trees, tributaries, air passages, neural networks, and lightning bolts—and reveals how a single principle of physics, the constructal law, accounts for the evolution of these and many other designs in our world. Everything—from biological life to inanimate systems—generates shape and structure and evolves in a sequence of ever-improving designs in order to facilitate flow. River basins, cardiovascular systems, and bolts of lightning are very efficient flow systems to move a current—of water, blood, or electricity. Likewise, the more complex architecture of animals evolve to cover greater distance per unit of useful energy, or increase their flow across the land. Such designs also appear in human organizations, like the hierarchical “flowcharts” or reporting structures in corporations and political bodies. All are governed by the same principle, known as the constructal law, and configure and reconfigure themselves over time to flow more efficiently. Written in an easy style that achieves clarity without sacrificing complexity, Design in Nature is a paradigm-shifting book that will fundamentally transform our understanding of the world around us.

Author : A. M. Findlay,S. P. McGlynn,G. L. Findley
Publisher : Wiley-Interscience
Page : 184 pages
File Size : 55,8 Mb
Release : 1989-03-20
Category : Mathematics
ISBN : UOM:39015014467305

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The Geometry of Genetics by A. M. Findlay,S. P. McGlynn,G. L. Findley Pdf

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.

Author : Ian Beardsley
Publisher : Lulu.com
Page : 36 pages
File Size : 51,7 Mb
Release : 2018-08-10
Category : Technology & Engineering
ISBN : 0359016324

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The Universal Geometry of Evolution by Ian Beardsley Pdf

The author puts forward his discovery of a common structure to artificial intelligence and biological life, and in Nature in general.

Author : Jan Prüss,Gieri Simonett
Publisher : Birkhäuser
Page : 609 pages
File Size : 42,5 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783319276984

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Moving Interfaces and Quasilinear Parabolic Evolution Equations by Jan Prüss,Gieri Simonett Pdf

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Author : Kirsti Andersen
Publisher : Springer Science & Business Media
Page : 837 pages
File Size : 51,8 Mb
Release : 2008-11-23
Category : Mathematics
ISBN : 9780387489469

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The Geometry of an Art by Kirsti Andersen Pdf

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.