Series: Nonconvex Optimization and Its Applications, Vol. 86 2006, Approx. 275 p. 1 illus., Hardcover
ISBN: 0-387-30409-6
About this book
This book is devoted to the study and optimization of spatiotemporal stochastic processes, that is, processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems, including:
- Physical and technical systems
- Population dynamics
- Neural networks
- Computer and telecommunication networks
- Complex production networks
- Flexible manufacturing systems
- Logistic networks and transportation systems
-Environmental engineering
Climate modelling and prediction
Earth surface models
Classical stochastic dynamic optimization forms the framework of the book. Taken as a whole, the project undertaken in the book is to establish optimality or near-optimality for Markovian policies in the control of spatiotemporal Markovian processes. The authors apply this general principle to different frameworks of Markovian systems and processes. Depending on the structure of the systems and the surroundings of the model classes the authors arrive at different levels of simplicity for the policy classes which encompass optimal or nearly optimal policies. A set of examples accompanies the theoretical findings, and these examples should demonstrate some important application areas for the theorems discussed.
Table of contents
Preface.- Acknowledgments.- 1. Introduction.- 2. Prerequisites from the theory of stochastic processes and stochastic dynamic optimization.- 3. Local control of discrete time interacting Markov processes with graph structured state space.- 4. Sequential stochastic games with distributed players on graphs.- 5. Local control of continuous time interacting Markov and semi-Markov processes with graph structured state space.- 6. Connections with optimization of random field in different areas.- Bibliography.- Index.
Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations. 
Based around recent lectures given at the prestigious Ritsumeikan conference,
the tutorial and expository articles contained in this volume are an essential
guide for practitioners and graduates alike who use stochastic calculus
in finance. 
This book exposes the internal structure of non-self-adjoint operators
acting on complex separable infinite dimensional Hilbert space, by analyzing
and studying the commutant of operators. A unique presentation of the theorem
of Cowen-Douglas operators is given. The authors take the strongly irreducible
operator as a basic model, and find complete similarity invariants of Cowen-Douglas
operators by using K-theory, complex geometry and operator algebra tools.