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Mathematical Models for Biological Pattern Formation
This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume ...
Dynamics of Cell and Tissue Motion
An interdisciplinary study explaining the dynamics underlying biological motion – one of the most obvious expressions of self-organization. Designed for a broad audience from bioscientists to applied mathematicians, this book considers possible synergetic mechanisms of interaction and cooperation on different microscopic levels.
Future Directions of Nonlinear Dynamics in Physical and Biological Systems
Early in 1990 a scientific committee was formed for the purpose of organizing a high-level scientific meeting on Future Directions of Nonlinear Dynamics in Physical and Biological Systems, in honor of Alwyn Scott's 60th birthday (December 25, 1991). As preparations for the meeting proceeded, they were met with an unusually broad-scale and high level of enthusiasm on the part of the international nonlinear science community, resulting in a participation by 168 scientists from 23 different countries in the conference, which was held July 23 to August 11992 at the Laboratory of Applied Mathematical Physics and the Center for Modelling, Nonlinear Dynamics and Irreversible Thermodynamics (MIDIT) ...
Biologically Inspired Physics
The workshop "Biologically Inspired Physics" was organized, with the support of the NATO Scientific Affairs Division and the Directorate-General for Science, Research and Development of the Commission of the European Communities, in order to review some subjects of physics of condensed matter which are inspired by biological problems or deal with biological systems, but which address physical questions. The main topics discussed in the meeting were: 1. Macromolecules: In particular, proteins and nucleic acids. Special emphasis was placed on modelling protein folding, where analogies with disordered systems in con densed matter (glasses, spin glasses) were suggested. It is not clear at this p...
Introduction to Reaction-Diffusion Equations
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the sprea...
Cell Biology
As the techniques of modern molecular biology continue to revolutionize experimental design in cell biology, mathematical modeling and analysis become increasingly necessary and feasible. The papers in this collection expand on invited lectures presented at the Symposium on Some Mathematical Questions in Biology: Cell Biology, held in November 1992 in Denver, Colorado. The work reviewed in the papers demonstrates the power of combining mathematics and experiment to study a number of cell processes, including: protein transport in nerve axons, formation of transport vesicles at the Golgi, molecular motion in cell membranes, cell adhesion, T lymphocyte activation, and cellular responses to receptor aggregation. The volume is an important contribution to the literature, as it introduces mathematicians to a growing application area and cell biologists to new tools and results. The individual articles can be used as readings in a course on mathematical modeling.
Information Dynamics
Proceedings of a NATO ASI held in Irsee/Kaufbeuren, Germany, June 15--26, 1990
Differential Equations and Population Dynamics I
This book presents the basic theoretical concepts of dynamical systems with applications in population dynamics. Existence, uniqueness and stability of solutions, global attractors, bifurcations, center manifold and normal form theories are discussed with cutting-edge applications, including a Holling's predator-prey model with handling and searching predators and projecting the epidemic forward with varying level of public health interventions for COVID-19. As an interdisciplinary text, this book aims at bridging the gap between mathematics, biology and medicine by integrating relevant concepts from these subject areas, making it self-sufficient for the reader. It will be a valuable resource to graduate and advance undergraduate students for interdisciplinary research in the area of mathematics and population dynamics.
Simple Mathematical Models of Gene Regulatory Dynamics
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well stu...
Mathematical Methods for Cancer Evolution
The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned wi...
