By Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz
The target of this quantity that provides lectures given at a joint CIME and Banach heart summer time university, is to supply a huge presentation of a category of up to date tools supplying a mathematical framework for the improvement of a hierarchy of versions of complicated platforms within the typical sciences, with a different realization to biology and medication. studying complexity implies sharing diversified instruments requiring a lot larger point of verbal exchange among varied mathematical and medical colleges, for fixing sessions of difficulties of an analogous nature. at the present time greater than ever, probably the most vital demanding situations derives from the necessity to bridge components of a method evolving at various time and area scales, specifically with admire to computational affordability. hence the content material has a slightly normal personality; the most position is performed by means of stochastic tactics, confident semigroups, asymptotic research, kinetic conception, continuum thought, and video game theory.