Systems biology and computational biology have recently become prominent areas of research in the biomedical community, especially in the area of cell biology. Given that much information on genes and their protein products has become available, the big question is how the individual components interact and work together, and how this determines the functioning of cells, organs, and organisms. Long before the popularity of systems biology in biomedicine, however, such approaches have been used successfully in a di?erent area of biology: population ecology. Research in the area of population...
Systems biology and computational biology have recently become prominent areas of research in the biomedical community, especially in the area of cell...
The purpose of this book is to provide an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical ?ows. These methods were originally developed in the abstract mathem- ical setting of dynamical systems theory, through a geometric approach to di?erential equations that ultimately owes much to the insights of Poincar e (1892). In the 1980s and 1990s, researchers in applied mathematics and ?uid dynamics recognized the potential of this approach for the analysis of ?uid motion. Despite these developments and the existence of a substantial body of work...
The purpose of this book is to provide an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical ?ows. T...
The subject of this monograph lies in the joint areas of applied mathematics and hydrogeology. The goals are to introduce various mathematical techniques and ideas to applied scientists while at the same time to reveal to applied math- ematicians an exciting catalog of interesting equations and examples, some of which have not undergone the rigors of mathematical analysis. Of course, there is a danger in a dual endeavor-the applied scientist may feel the mathematical models lack physical depth and the mathematician may think the mathematics is trivial. However, mathematical modeling has...
The subject of this monograph lies in the joint areas of applied mathematics and hydrogeology. The goals are to introduce various mathematical techniq...
This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics...
This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well develop...
This text is an introduction to dynamical modeling in cell biology. It is not meant as a complete overview of modeling or of particular models in cell biology. Rather, we use selected biological examples to motivate the concepts and techniques used in computational cell biology. This is done through a progression of increasingly more complex cellular functions modeled with increasingly complex mathematical and c- putational techniques. There are other excellent sources for material on mathematical cell biology, and so the focus here truly is computer modeling. This does not mean that there...
This text is an introduction to dynamical modeling in cell biology. It is not meant as a complete overview of modeling or of particular models in cell...
Our goal in this book is to explore some of the connections between control theory and geometric mechanics; that is, we link control theory with a g- metric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems s- ject to motion constraints. This synthesis of topics is appropriate, since there is a particularly rich connection between mechanics and nonlinear control theory. While an introduction to many important aspects of the mechanics of nonholonomically constrained systems may be found in such sources as the...
Our goal in this book is to explore some of the connections between control theory and geometric mechanics; that is, we link control theory with a g- ...
Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. 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. This serves as a starting point for the further motivation of the transport issues through the development...
Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems...
There has been a great deal of excitement in the last ten years over the emer- gence of new mathematical techniques for the analysis and control of nonlinear systems: Witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behavior and the develop- ment of a comprehensive theory of geometric nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the implementation in real time of...
There has been a great deal of excitement in the last ten years over the emer- gence of new mathematical techniques for the analysis and control of no...
The story of this edition is a testament to an almost legendary gure in theoretical ecology and to the in uence his work and charisma has had on the eld. It is also a story that can only be told by a trip back in time, to the genesis of the First Edition and before. Akira kubo and I were students together, but never knew it at the time. He was a graduate student at The ohns Hopkins niversity, where I was an undergraduate in mathematics. e both studied modern physics, taught by Dino Franco asetti, and we decided years later that we must have been in the same class. Akira was then a chemical...
The story of this edition is a testament to an almost legendary gure in theoretical ecology and to the in uence his work and charisma has had on the e...
This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a work piece, or end-effector, of the system. The function of the device is prescribed as a set of positions to be reachable by the end-effector; and the mechanical constraints are formed by joints that limit relative movement. The goal is to find all the devices that can achieve a specific task. Formulated in this way the design problem is purely geometric in character. Robot manipulators, walking...
This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mech...