Nowadays it is becoming clearer and clearer that, in the description of natural phenomena, the triadic scheme - microseopie, mesoscopic, macroscopic - is only a rough approximation and that there are many levels of description, probably an infinite hierarchy, in which the specific properties of a given level express some kind of cumulative or collective behaviour of properties or sys tems corresponding to the lower levels. One of the most interesting challenges for contemporary natural sciences is the comprehension of the connections among these different levels of description of reality and...

This volume is based on the fifth international conference of quantum bio-informatics held at the QBI Center of Tokyo University of Science.This volume provides a platform to connect mathematics, physics, information and life sciences, and in particular, research for new paradigm for information science and life science on the basis of quantum theory.The following topics are discussed:

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and...

Contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence is discussed. Quantum groups are discussed from the point of view of possible applications to quantum probability.

Based on materials discussed in the various quantum probability conferences, this text aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.