Bücher der Reihe Interdisciplinary Applied Mathematics

This book presents a comprehensive set of methods for quantifying geometric quantities such as the volume of a tumor, the total surface area of the alveoli in a lung, the length of plant roots, or of blood vessels, the number of neurons in a brain compartment, the connectivity number of trabecular bone, the mean size of grains in a rock, etc.. The methods, illustrated by twenty solved case studies, are based on properly sampled slices, sections, or projections of the material, observable under light, laser, or electron microscopy, or under non-invasive radiological devices such as ecography, computed tomography, or magnetic resonance imaging. Thus, the input usually consists of flat images, and the output consists of relevant quantities defined in three dimensions. Stereology is the discipline of providing sampling designs which warrant unbiased estimation of the corresponding quantities, that is, estimation with zero mean deviation from the target. Sampling is usually systematic (i.e., with regularly spaced probes), and sparse (as opposed to reconstructions) and it is thereby efficient and easy to implement.Stereology is essentially geometric sampling, grounded on integral geometry. The necessary elements of both disciplines are detailed in textbook style, and may be used for postgraduate courses, or to serve the interest of scientists in general. Hitherto no other book on stereology has appeared which encompasses the theory, methodology, and applications of stereology in an interconnected and comprehensive way. The currently available error variance prediction formulae under systematic sampling, and their (non-obvious) derivation, are all gathered, for the first time, in the last chapter. The exposition is augmented by 127 line drawings for the theory, and 27 color pictures of real materials for the case studies.

For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth.

This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control.

This book offers a new method for studying hybrid models: Generalized Principal Component Analysis. Coverage includes statistical, geometric and algebraic concepts associated with estimation and segmentation of hybrid models, especially hybrid linear models.

An Accelerated Course with Applications in Computational Sciences and Engineering

There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact of analytic advances and produced many new problems and applications which are nonlinear in an essential way.

Arising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.

Very broad overview of the field intended for an interdisciplinary audience; Suitably accessible for beginners and suitably rigorous for experts; Features extensive four-color illustrations; Appendices featuring homework assignments and reading lists complement the material in the main text

This book offers a comprehensive reference to the mathematical modeling of environmental and geophysical problems. It provides an abundance of mathematical models, both simple and complex, and elaborates them with approximation techniques.

This book is an overview of mathematical physiology. It contains a variety of physiological problems and the current and new mathematical techniques used in this area. Numerous exercises and models are included.

The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models.

This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods.

Here is a comprehensive review of the fundamental conditions for optimality for finite-dimensional, deterministic, optimal control problems. Includes worked examples ranging from minimum surfaces of revolution to cancer treatment for novel therapy approaches.

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix.

This book provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It contains a variety of physiological problems and the current and new mathematical techniques used in this area.

A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of advanced methodology used in inelastic calculations. It is of interest to researchers and graduate students in various branches of engineering.

This book offers a systematic, rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso- and macro-scales, including detailed studies of micro-structure systems and computational results for dual-porosity models.

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments.

Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others.

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. This book enables entry-level graduate students to tackle fresh problems in this rich field.

This textbook provides an introduction to dynamic modeling in molecular cell biology, taking a computational and intuitive approach. Detailed illustrations, examples, and exercises are included throughout the text. Appendices containing mathematical and computational techniques are provided as a reference tool.

This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences.

This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this bookUseful to both students and researchers

Subject area has witnessed explosive growth during the last decade and the technology is progressing at an astronomical rate. Previous edition was first to focus exclusively on flow physics within microdevices.

Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincare Map.

Written by a specialist in geophysical fluid dynamics and an applied mathematician, this book provides an accessible introduction to new methods for analysing Lagrangian motion in geophysical flows, and surveys research in geophysical fluid dynamics that makes use of them.

This monograph describes and discusses the properties of heterogeneous materials, comparing two fundamental approaches to describing and predicting materials' properties. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.