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Author: George R. McGhee
Publisher: Cambridge University Press
ISBN: 1139459953
Category : Science
Languages : en
Pages : 185
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Book Description
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: George R. McGhee
Publisher: Cambridge University Press
ISBN: 1139459953
Category : Science
Languages : en
Pages : 185
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Book Description
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: Fred L. Bookstein
Publisher: Academy of Natural Sciences
ISBN: 9780910006484
Category : Science
Languages : en
Pages : 277
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Book Description
Author: Boris A. Rosenfeld
Publisher: Springer Science & Business Media
ISBN: 1441986804
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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: W.R. Knorr
Publisher: Springer Science & Business Media
ISBN: 9401017549
Category : Philosophy
Languages : en
Pages : 389
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Book Description
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: Julian Hofrichter
Publisher: Springer
ISBN: 3319520458
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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: Yoshikazu Giga
Publisher: Springer Science & Business Media
ISBN: 3764373911
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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: Ulf Dieckmann
Publisher: Cambridge University Press
ISBN: 0521642949
Category : Mathematics
Languages : en
Pages : 583
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Book Description
The field of theoretical ecology has expanded dramatically in the last few years. This volume gives detailed coverage of the main developing areas in spatial ecological theory, and is written by world experts in the field. Integrating the perspective from field ecology with novel methods for simplifying spatial complexity, it offers a didactical treatment with a gradual increase in mathematical sophistication from beginning to end. In addition, the volume features introductions to those fundamental phenomena in spatial ecology where emerging spatial patterns influence ecological outcomes quantitatively. An appreciation of the consequences of this is required if ecological theory is to move on in the 21st century. Written for reseachers and graduate students in theoretical, evolutionary and spatial ecology, applied mathematics and spatial statistics, it will be seen as a ground breaking treatment of modern spatial ecological theory.
Author: Shu-Cheng Chang
Publisher: American Mathematical Soc.
ISBN: 0821833618
Category : Mathematics
Languages : en
Pages : 250
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Book Description
The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.
Author: Kirsti Andersen
Publisher: Springer Science & Business Media
ISBN: 0387489460
Category : Mathematics
Languages : en
Pages : 837
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Book Description
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.
Author: A. M. Findlay
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 184
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Book Description
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.
