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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 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.
Lines of Inquiry in Mathematical Modelling Research in Education
The book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught.
Aspects of mathematical modelling : Applications in science, medicine, economics and management
The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management. The reader will find some review papers outlining current research directions in hot topics such as pattern formation and applications to medicine, and more targeted research papers on current developments in the various disciplines included.
Applied Partial Differential Equations : A Visual Approach
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables.
