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Mathematical Models for Registration and Applications to Medical Imaging
Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume.
Mathematical Modelling of Biosystems
This volume is an interdisciplinary book, which introduces, in a very readable way, state of the art research in the fundamental topics of mathematical modelling of Biosystems. These topics include: the study of Biological Growth and its mechanisms, the coupling of pattern to form via theorems of Differential Geometry, the human immunodeficiency virus dynamics, the inverse folding problem and the possibility of analysing true protein backbone flexibility, the Biclustering techniques for the organization of microarray data, the analytical approach to the modelling of biomolecular structure via Steiner trees, the action of biocides on resistance mechanisms of mutated and phenotypic bacteria strains, a description of the fundamental processes for the distribution and abundances of species towards a unified theory of Ecology, and a special introduction to Protein Physics aiming to explain the all-or-none first order phase transitions from native to denatured states.
Mathematical Modelling for Sustainable Development
Mathematics needs Sustainable Development. When science was gradually reinvented in European medieval societies, it was legitimised as contributing to the disclosure of God’s divine creation. The conflicts that emerged became well known as a result of the clash between Galileo and the Church. Science found a new legitimacy through recognition that it was a powerful force against superstition. In the Enlightenment the argument was pushed forward by attributing Progress to the advancement of science: science could produce a better world by promoting rationality. In our modern society, science has become intimately linked to technology. Science for its own sake unfortunately rarely has positive outcomes in terms of research grant applications. Meanwhile, science and technology, and the progress they are supposed to produce, meet with wide scale scepticism. We all know of the current global problems: climate change, resource depletion, a thinning ozone layer, space debris, declining biodiversity, malnutrition, dying ecosystems, global inequity, and the risk of unprecedented nuclear wars
Mathematical Modeling of Complex Biological Systems : A Kinetic Theory Approach
This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems—comprised of large populations of interacting cells—whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. The authors propose a new biological model for the analysis of competition between cells of an aggressive host and cells of a corresponding immune system.Because the microscopic description of a biological system is far more complex than that of a physical system of inert matter, a higher level of analysis is needed to deal with such complexity. Mathematical models using kinetic theory may represent a way to deal with such complexity, allowing for an understanding of phenomena of nonequilibrium statistical mechanics not described by the traditional macroscopic approach. The proposed models are related to the generalized Boltzmann equation and describe the population dynamics of several interacting elements (kinetic population models).The particular models proposed by the authors are based on a framework related to a system of integro-differential equations, defining the evolution of the distribution function over the microscopic state of each element in a given system. Macroscopic information on the behavior of the system is obtained from suitable moments of the distribution function over the microscopic states of the elements involved. The book follows a classical research approach applied to modeling real systems, linking the observation of biological phenomena, collection of experimental data, modeling, and computational simulations to validate the proposed models. Qualitative analysis techniques are used to identify the prediction ability of specific models.
Mathematical Modeling for the Life Sciences
Proposing a wide range of mathematical models that are currently used in life sciences may be regarded as a challenge, and that is precisely the challenge that this book takes up. Of course this panoramic study does not claim to offer a detailed and exhaustive view of the many interactions between mathematical models and life sciences. This textbook provides a general overview of realistic mathematical models in life sciences, considering both deterministic and stochastic models and covering dynamical systems, game theory, stochastic processes and statistical methods. Each mathematical model is explained and illustrated individually with an appropriate biological example. Finally three appendices on ordinary differential equations, evolution equations, and probability are added to make it possible to read this book independently of other literature.
Mathematical Methods in Time Series Analysis and Digital Image Processing
The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed.
Mathematical Methods in Robust Control of Linear Stochastic Systems
Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems with a focus on robust stabilization in the mean square, linear quadratic control, the disturbance attenuation problem, and robust stabilization with respect to dynamic and parametric uncertainty.
Mathematical Methods in Electro-Magneto-Elasticity
The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. It integrates the Mechanics of Continuous Media, Heat Conductivity and the theory of Electromagnetism that are usually studied seperately. For an accurate description of the influence of static and dynamic loadings, high temperatures and strong electromagneticfields in elastic media and constructive installations, a new aproach is required; an approach that has the potential to establish a synergism between the above-mentioned fields. Throughout the book a vast number of problems are considered: two-dimensional problems of electro-magneto-elasticity as well as static and dynamical problems for piecewise homogenous compound piezoelectric plates weakened by cracks and openings. The boundary conditions, the constuctive equations and the mathematical methods for their solution are thoroughly presented, so that the reader can get a clear quantative and qualitative understnding of the phenomena taking place.
Mathematical Methods for Engineers and Geoscientists
This book introduces and explains classical and modern mathematical procedures as applied to the real problems confronting engineers and geoscientists. Written in a manner that is understandable for students across the breadth of their studies, it lays out the foundations for mastering difficult and sometimes confusing mathematical methods.
Mathematical methods and modelling in hydrocarbon exploration and production
Hydrocarbon exploration and production incorporate great technology challenges for the oil and gas industry. In order to meet the world's future demand for oil and gas, further technological advance is needed, which in turn requires research across multiple disciplines, including mathematics, geophysics, geology, petroleum engineering, signal processing, and computer science. This book addresses important aspects and fundamental concepts in hydrocarbon exploration and production. Moreover, new developments and recent advances in the relevant research areas are discussed, whereby special emphasis is placed on mathematical methods and modelling. The book reflects the multi-disciplinary character of the hydrocarbon production workflow, ranging from seismic data imaging, seismic analysis and interpretation and geological model building, to numerical reservoir simulation. Various challenges concerning the production workflow are discussed in detail.
Mathematical Masterpieces : Further Chronicles by the Explorers
Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken.
Mathematical Implications of Einstein-Weyl Causality
The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.
Mathematical Foundation of Geodesy : Selected Papers of Torben Krarup
This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. His writings are mathematically well founded and scientifically relevant. In this impressive collection of papers he demonstrates his rare innovative ability to present significant topics and concepts. Modern students of geodesy can learn a lot from his selection of mathematical tools for solving actual problems. The collection contains the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as numerous trend setting papers on the theory of adjustment.
Mathematical Events of the Twentieth Century
Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long.
Mathematical Epidemiology
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation.
Mathematical Control Theory and Finance
This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Mathematical Control Theory : An Introduction
Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.
Mathematical Aspects of Classical and Celestial Mechanics
In this book we describe the basic principles, problems, and methods of clssical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth first and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Mathematical and Computational Models for Congestion Charging
This book presents rigorous treatments of issues related to congestion pricing. The chapters describe recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact of tolls on transporation systems. The analyses and methodologies developed in this book provide Mechanisms that aid in determining and comparing congestion pricing schemes; Methodologies for evaluating the efficiency of existing and proposed congestion pricing schemes; A means to predict the impact of pricing on urban transporation systems; and Information essential to the financial and political success of congestion pricing programs.
Mathematica for Theoretical Physics : Electrodynamics, Quantum Mechanics, General Relativity, and Fractals
Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
