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This volume is to pique the interest of many researchers in the
fields of infinite dimensional analysis and quantum probability.
These fields have undergone increasingly significant developments
and have found many new applications, in particular, to classical
probability and to different branches of physics. These fields are
rather wide and are of a strongly interdisciplinary nature. For
such a purpose, we strove to bridge among these interdisciplinary
fields in our Workshop on IDAQP and their Applications that was
held at the Institute for Mathematical Sciences, National
University of Singapore from 3-7 March 2014. Readers will find that
this volume contains all the exciting contributions by well-known
researchers in search of new directions in these fields.
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:
The purpose of this proceedings volume is to return to the starting
point of bio-informatics and quantum information, fields that are
growing rapidly at present, and to seriously attempt mutual
interaction between the two, with a view to enumerating and solving
the many fundamental problems they entail. For such a purpose, we
look for interdisciplinary bridges in mathematics, physics,
information and life sciences, in particular, research for new
paradigm for information science and life science on the basis of
quantum theory.
This book examines information processing performed by bio-systems
at all scales: from genomes, cells and proteins to cognitive and
even social systems. It introduces a theoretical/conceptual
principle based on quantum information and non-Kolmogorov
probability theory to explain information processing phenomena in
biology as a whole. The book begins with an introduction followed
by two chapters devoted to fundamentals, one covering classical and
quantum probability, which also contains a brief introduction to
quantum formalism, and another on an information approach to
molecular biology, genetics and epigenetics. It then goes on to
examine adaptive dynamics, including applications to biology, and
non-Kolmogorov probability theory. Next, the book discusses the
possibility to apply the quantum formalism to model biological
evolution, especially at the cellular level: genetic and epigenetic
evolutions. It also presents a model of the epigenetic cellular
evolution based on the mathematical formalism of open quantum
systems. The last two chapters of the book explore foundational
problems of quantum mechanics and demonstrate the power of usage of
positive operator valued measures (POVMs) in biological science.
This book will appeal to a diverse group of readers including
experts in biology, cognitive science, decision making, sociology,
psychology, and physics; mathematicians working on problems of
quantum probability and information and researchers in quantum
foundations.
This monograph provides a mathematical foundation to the theory of
quantum information and computation, with applications to various
open systems including nano and bio systems. It includes
introductory material on algorithm, functional analysis,
probability theory, information theory, quantum mechanics and
quantum field theory. Apart from standard material on quantum
information like quantum algorithm and teleportation, the authors
discuss findings on the theory of entropy in C*-dynamical systems,
space-time dependence of quantum entangled states, entangling
operators, adaptive dynamics, relativistic quantum information, and
a new paradigm for quantum computation beyond the usual quantum
Turing machine. Also, some important applications of information
theory to genetics and life sciences, as well as recent
experimental and theoretical discoveries in quantum photosynthesis
are described.
This monograph provides a mathematical foundation to the theory of
quantum information and computation, with applications to various
open systems including nano and bio systems. It includes
introductory material on algorithm, functional analysis,
probability theory, information theory, quantum mechanics and
quantum field theory. Apart from standard material on quantum
information like quantum algorithm and teleportation, the authors
discuss findings on the theory of entropy in C*-dynamical systems,
space-time dependence of quantum entangled states, entangling
operators, adaptive dynamics, relativistic quantum information, and
a new paradigm for quantum computation beyond the usual quantum
Turing machine. Also, some important applications of information
theory to genetics and life sciences, as well as recent
experimental and theoretical discoveries in quantum photosynthesis
are described.
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