Statistical Physics, Automata Networks and Dynamical Systems (Mathematics and Its Applications)

One service mathematics has rendered the ~Et moi, …. si j’avait su comment en revenir, je human race. It has put common sense back n’y serais point aile.’ where it belongs, on the topmost shelf next to Jules Verne the dusty canister labelled ‘discarded nonsense’. Eric T. Bell The series is divergent; therefore we may be able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: ‘One ser vice topology has rendered mathematical physics .. .’; ‘One service logic has rendered computer science .. .’; ‘One service category theory has rendered mathematics .. .’. All arguably true. And all statements obtainable this way form part of the raison d’etre of this series. Regular and Chaotic Behaviour of Dynamical Systems.- Shocks in the Burgers Equation and the Asymmetric Simple Exclusion Process.- Automata Networks Strategies for Optimization Problems.- Two Chosen Examples for Fractals: one Deterministic, the Other Random.- A Brief Account of Statistical Theories of Learning and Generalization in Neural Networks.- On the R.E.M. and the G.R.E.M..