Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.

Considerable attention from the international scientific community is currently focused on the wide ranging applications of wavelets. For the first time, the field's leading experts have come together to produce a complete guide to wavelet transform applications in medicine and biology. Wavelets in Medicine and Biology provides accessible, detailed, and comprehensive guidelines for all those interested in learning about wavelets and their applications to biomedical problems.

* Written by an interdisciplinary group of specialists from the arts, humanities and sciences at Oxford University * Suitable for a wide non-academic readership, and will appeal to anyone with an interest in mathematics, science and philosophy.

This work provides descriptions, explanations and examples of the Bayesian approach to statistics, demonstrating the utility of Bayesian methods for analyzing real-world problems in the health sciences. The work considers the individual components of Bayesian analysis.;College or university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.

Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses:
Principles for constructing adjoint operators in nonlinear problems
Properties of adjoint operators and solvability conditions for adjoint equations
Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation
Known results on adjoint equations and perturbation algorithms in nonlinear problems
This groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.

Structured Biological Modelling presents a straightforward introduction for computer-aided analysis, mathematical modelling, and simulation of cell biological systems. This unique guide brings together the physiological, structural, molecular biological, and theoretical aspects of the signal transduction network that regulates growth and proliferation in normal and tumor cells. It provides comprehensive survey of functional and theoretical features of intracellular signal processing and introduces the concept of cellular self-organization. Exemplified by oscillatory calcium waves, strategies for the design of computer experiments are presented that can assist or even substitute for time-consuming biological experiments. The presented minimal model for proliferation-associated signal transduction clearly shows the alterations of the cellular signal network involved in neoplastic growth. This book will be useful to cell and molecular biologists, oncologists, physiologists, theoretical biologists, computer scientists, and all other researchers and students studying functional aspects of cellular signaling.

This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients

Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.

Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black-Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.

Features Provides a unique, new approach to understanding quantum mechanics. Uses basic concepts and mathematical methods accessible at the undergraduate level. Presents applications outside physics, including a newly devised and original model of cell division that shows how cancer-cell population explosions occur.

Features Provides a unique, new approach to understanding quantum mechanics. Uses basic concepts and mathematical methods accessible at the undergraduate level. Presents applications outside physics, including a newly devised and original model of cell division that shows how cancer-cell population explosions occur.

In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation.
Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application.
Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains.
Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.

The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed in depth. They comprise the necessary apparatus for examining curves.
An important and original part of the book is the Atlas, consisting of nearly 200 plane curve classes, more than 700 figures, and nearly 2,000 drawings of specific curves. The classes have been scrupulously chosen for their interesting and useful properties. The dynamics of each class is visually represented by a series of specially arranged precise drawings showing the qualitative change of a curve's behavior as the parameters defining the class vary.
The book provides numerous application examples, descriptions of mechanisms for drawing various curves, and discussions of geometric spline possibilities. It includes more than 20 various geometric and linguistic indices and an update on world literature on curve theory. The Handbook and Atlas of Curves will be an invaluable reference for researchers, practitioners, students, and amatuers of mathematics.

"Offers a comprehensive, unified presentation of statistical designs and methods of analysis for all stages of pharmaceutical development--emphasizing biopharmaceutical applications and demonstrating statistical techniques with real-world examples."

In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with his gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists.

Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.

Biology is in the midst of a era yielding many significant discoveries and promising many more. Unique to this era is the exponential growth in the size of information-packed databases. Inspired by a pressing need to analyze that data, Introduction to Computational Biology explores a new area of expertise that emerged from this fertile field- the combination of biological and information sciences.

This introduction describes the mathematical structure of biological data, especially from sequences and chromosomes. After a brief survey of molecular biology, it studies restriction maps of DNA, rough landmark maps of the underlying sequences, and clones and clone maps. It examines problems associated with reading DNA sequences and comparing sequences to finding common patterns. The author then considers that statistics of pattern counts in sequences, RNA secondary structure, and the inference of evolutionary history of related sequences.

Introduction to Computational Biology exposes the reader to the fascinating structure of biological data and explains how to treat related combinatorial and statistical problems. Written to describe mathematical formulation and development, this book helps set the stage for even more, truly interdisciplinary work in biology.

Problems in network optimization arise in all areas of technology and industrial management. The topic of network flows has applications in diverse fields such as chemistry, engineering, management science, scheduling and transportation, to name a few.

Electromagnetic scattering from complex objects has been an area of in-depth research for many years. A variety of solution methodologies have been developed and utilised for the solution of ever increasingly complex problems. Among these methodologies, the subject of impedance boundary conditions has interested the authors for some time. In short, impedance boundary conditions allow one to replace a complex structure with an appropriate impedance relationship between the electric and magnetic fields on the surface of the object. This simplifies the solution of the problem considerably, allowing one to ignore the complexity of the internal structure beneath the surface. This book examines impedance boundary conditions in electromagnetics. The introductory chapter provides a presentation of the role of the impedance boundary conditions in solving practical electromagnetic problems and some historical background. One of the main objectives of this book is to present a unified and thorough discussion of this important subject. A method based on a spectral domain approach is presented to derive the Higher Order Impedance Boundary Conditions (HOIBC). The method includes all of the existing approximate boundary conditions, such as the Standard Impedence Boundary Condition, the Tensor Impedence Boundary Condition and the Generalised Impedance Boundary Conditions, as special cases. The special domain approach is applicable to complex coatings and surface treatments as well as simple dielectric coatings. The spectral domain approach is employed to determine the appropriate boundary conditions for planar dielectric coatings, chiral coatings and corregated conductors. The accuracy of the proposal boundary conditions is discussed. The approach is then extended to include the effects of curvature and is applied to curved dielectric and chiral coatings. Numerical data is presented to critically assess the accuracy of the results obtained using various forms of the impedence boundary conditions. A number of appendices that provide more detail on some of the topics addressed in the main body of the book and a selective list of references directly related to the topics addressed in this book are also included.

This text examines the Atiyah-Singer theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The book presents a careful treatment of non-self-adjoint operators, asymptotics of the heat equation and variational formulas. It also introduces spectral geometry and provides a list of asymptotic formulas. The bibliography has been complied by Herbert Schroeder.

Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.

Covers flight mechanics, flight simulation, flight testing, flight control, and aeroservoelasticity. Features artificial neural network and fuzzy logic-based aspects in modeling and analysis of flight mechanics systems: aircraft parameter estimation, and reconfiguration of control. Focuses on a systems-based approach. Includes two new chapters, numerical simulation examples with a MATLAB® based approach, and end-of-chapter exercises. Includes a Solutions Manual and Figure Slides for adopting instructors.

• Introduces the dynamics, principles and mathematics behind ten macroeconomic models allowing students to visualise the models and understand the economic intuition behind them. • Provides a step-by-step guide, and the necessary MATLAB codes, to allow readers to simulate and experiment with the models themselves.

Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.