Multiscale Problems in the Life Sciences

Jacek Banasiak, Vincenzo Capasso, Mark A. J. Chaplain, Miroslaw Lachowicz, Jacek Miekisz, Vincenzo Capasso, Miroslaw Lachowicz9783540783602, 3540783601, 3540783628

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.

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Table of contents :
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