Multiscale problems in the life sciences : from microscopic to macroscopic : lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4-9, 2006

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory, and game theory. Cover......Page 1 Lecture Notes in Mathematics 1940......Page 2 Multiscale Problems in the Life Sciences......Page 4 Copyright......Page 5 Preface......Page 6 Contents......Page 10 Positivity in Natural Sciences......Page 14 Rescaling Stochastic Processes: Asymptotics......Page 103 Modelling Aspects of Cancer Growth: Insight from Mathematical and Numerical Analysis and Computational Simulation......Page 159 Lins Between Microscopic and Macroscopic Descriptions......Page 213 Evolutionary Game Theory and Population Dynamics......Page 280 List of Participants......Page 328 Index......Page 330 List of C.I.M.E. Seminars......Page 333 Lecture Notes in Mathematics......Page 337