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The book offers a new approach to information theory that is more general then the classical approach by Shannon. The classical definition of information is given for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space ) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of , i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two new concepts derived from it, designated as information and surprise, which describe opposite versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these new concepts, mostly in statistics and in neuroscience.
|Publication date:||31st August 2012|
|Publisher:||Springer-Verlag Berlin and Heidelberg GmbH & Co. K an imprint of Springer-Verlag Berlin and Heidelberg GmbH & Co. KG|
|Categories:||Applied mathematics, Artificial intelligence, Neurosciences, Algebra,|
Gunther Palm studied mathematics in Hamburg and Tubingen. After completing his studies in mathematics (Master in 1974, Ph.D. in 1975) he worked on nonlinear systems, associative memory and brain theory at the MPI for Biological Cybernetics in Tubingen. In 1983/84 he was a Fellow at the Wissenschaftskolleg in Berlin. From 1988 to 1991 he was professor for theoretical brain research at the University of Dusseldorf. Since then he has served as a professor for computer science and Director of the Institute of Neural Information Processing at the University of Ulm, where his focus is on information theory, pattern recognition, neural networks, and brain modelling.More About Gunther Palm