Preface -- The Problem of Quantum-Like Representation in Economy Cognitive Science, and Genetics L. Accardi, A. Khrennikov and M. Ohya -- References -- Chaotic Behavior Observed in Linea Dynamics M. Asano, T. Yamamoto and Y. Togawa -- 1. Introduction -- 2. Dynamics on Simplex and Example -- 2.1. General Form of Dynamics on Simplex -- 2.2. Scarf-Hirota Model -- 3. Log-linear Dynamics and Chaotic Behaviors on Simplex -- 3.1. Log-linear Dynamics on Simplex -- 3.2. Discrete Log-linear Dynamics -- 3.3. Chaotic Behavior -- 4. Conclusion -- References -- Complete m-Level Quantum Teleportation Based on Kossakowski-Ohya Scheme M. Asano, M. Ohya and Y. Tanaka -- 1. Introduction -- 2. Quantum Teleportation and Kossakowski-Ohya Scheme -- 3. Teleportation Map of Complete m-Ievel Teleportation -- 4. Model of Complete Two-level Quantum Teleportation -- 4.1. Case of n = 4 -- 4.2. Expansion to Model of n = 28 -- 5. Conclusion -- References -- Towards Quantum Cybernetics: Optimal Feedback Control in Quantum Bio Informatics V. P. Belavkin -- 1. Introduction -- 2. Some facts and notations -- 2.1. Quantum state geometry -- 2.2. Derivations and Hessians -- 2.3. Affine and concave costs -- 2.4. Legendre-Fenchel transform -- 3. Quantum conditionally Markov dynamics -- 3.1. Quantum controlled generator -- 3.2. Deterministic quantum Master equations -- 3.3. Output processes and continuous observation -- 3.4. Stochastic quantum Master equations -- 4. Quantum dynamical programming -- 4.1. Quantum Hamilton-Jacobi equation -- 4.2. Pontryagin's maximum principle -- 4.3. The filtered quantum Bellman equation -- 4.4. Linear-convex state costs -- 5. Optimal feedback control of purification -- 5.1. Bequest function for purification -- 5.2. Optimal feedback qubit control -- 5.3. The qubit HJB equation -- 6. Discussion -- References.

Quantum Entanglement and Circulant States D. Chruscinski -- 1. Introduction -- 2. PPT states - simple example -- 3. Circulant states -- 3.1. Two qubits -- 3.2. Two qutrits -- 4. General case - two qudits -- 5. Circulant liftings -- 6. Conclusions -- Acknowledgments -- References -- The Compound Fock Space and Its Application in Brain Models K.-H. Fichtner and W. Freudenberg -- 1. Introduction -- 2. The Space of Signals -- 2.1. The Boson Fock Space -- 2.2. Exponential Vectors - Coherent States -- 2.3. The Space of Elementary Signals -- 3. The Memory -- 3.1. The Compound Fock space -- 3.2. States of the Memory -- 3.3. Some Basic Operators -- 4. Processing - Recognition of Signals -- References -- Characterisation of Beam Splitters L. Fichtner and M. Gabler -- 1. Introduction and Main Result -- 2. The Bosonic Fock Space -- 2.1. Representation of r(L2(G)) as an L2-Space -- 2.2. M(A) and its Factorisation -- 2.3. Tensor Products of M(A) -- 2.4. Embedding M2(A) into M2(G) -- 3. Proof of Corollary 1 -- 4. Proof of Theorem 1 -- References -- Application of Entropic Chaos Degree to a Combined Quantum Baker's Map K. Inoue, M. Ohya and I. V. Volovich -- 1. Introduction -- 2. Classical Baker's Transformation -- 3. Quantum Baker's Map -- 4. Dynamics of Quantum Baker's Map -- 5. Entropic Chaos Degree -- 6. A Combined Quantum Baker's Map and Its Entropic Chaos Degree -- 7. Dependence of the Entropic Chaos Degree on the Combination Parameter a -- 8. Dependence of the Entropic Chaos Degree on N -- References -- On Quantum Algorithm for Multiple Alignment of Amino Acid Sequences S. Iriyama and M. Ohya -- 1. Introduction -- 2. Outline of Alignment -- 2.1. Language classes of alignment -- 3. Quantum Algorithm -- 3.1. Chaos Amplification -- 4. Quantum Algorithm of Multiple Alignment -- 5. Computational Complexity of Multiple Alignment -- References.

Quantum-Like Models for Decision Making in Psychology and Cognitive Science A. Khrennikov -- 1. Introduction -- 2. Prisoner's Dilemma -- 3. Contexts in Gambling Experiments -- 4. Measure of Interference -- 5. Interference in Disjunction Experiments -- 6. Quantum-like Representation Algorithm - QLRA -- 7. Hilbert-space Representation of Mental Information and Decision Making -- 8. Concluding Remarks: Accardian Models, Ohya's Adaptive Dynamics -- Acknowledgments -- References -- On Completely Positive Non-Markovian Evolution of a d-Level System A. Kossakowski and R. Rebolledo -- 1. Introduction -- 2. Notations -- 3. Non-Markovian Master Equations -- 4. Modified non-Markovian Master Equations -- Acknowledgment -- References -- Measures of Entanglement - A Hilbert Space Approach W. A. Majewski -- 1. Definitions and notations -- 2. Tomita-Takesaki scheme for transposition -- 3. PPT states on the Hilbert-space level -- 4. Effectiveness of the description of PPT states -- 5. Measures of entanglement -- Acknowledgments -- References -- Some Characterizations of PPT States and Their Relation T. Matsuoka -- 1. Introduction -- 2. Entanglement mapping and PPT condition -- 2.1. Pure state case -- 2.2. Characterization of PPT states by entanglement mapping -- 3. Characterization of CP and CCP map via St!Zirmer's isomorphism -- 4. Majewski's description of PPT states on Tomita-Takesaki scheme (see [11], [12]) -- 5. Equivalence between two types of characterization of PPT states -- References -- On the Dynamics of Entanglement and Characterization of Entangling Properties of Quantum Evolutions M. Michalski -- 1. Introduction -- 2. The Heisenberg model -- References -- Perspective from Micro-Macro Duality - Towards Non-Perturbative Renormalization Scheme I. Ojima -- 1. Micro-Macro duality -- 2. Broken scale invariance: imaginary-time vs. real-time.

2.1. How to formulate broken scale invariance -- 2.2. Scale changes on states -- 3. N udearity Condition & Renormalizability -- 3.1. Point-like fields as idealized local observables -- 3.2. Comparison between OPE & Wigner-Eckhart theorem -- Acknowledgement -- References -- A Simple Symmetric Algorithm Using a Likeness with Introns Behavior in RNA Sequences M. Regoli -- 1. Introduction -- 2. The algorithm -- 3. The boxes -- 3.1. The box Bl -- 3.2. Box B2 -- 4. Decoding message -- 5. Statistical informations about the size of output -- 6. Next step -- 7. Final considerations -- References -- Some Aspects of Quadratic Generalized White Noise Functionals Si Si and T. Hida -- 1. Introduction -- 2. Quadratic functionals of white noise -- 3. Duality in the space of quadratic generalized functionals -- 4. Quadratic forms of at'S and a -- 'So -- 5. Concluding remarks -- Acknowledgements -- References -- Analysis of Several Social Mobility Data Using Measure of Departure from Symmetry K. Tahata, K. Yamamoto, N. Miyamoto and S. Tomizawa -- 1. Introduction -- 2. Review of model and measure of symmetry -- 2.1. Symmetry model -- 2.2. Measure -- 3. Approximate confidence interval for measure -- 4. Comparison between occupational mobility data -- 5. Concluding remarks -- References -- Time in Physics and Life Science 1. V. Volovich -- 1. Introduction -- 2. Time Travel -- 3. Black Hole/Wormhole Production -- 4. Models of Life -- Acknowledgements -- References -- Note on Entropies in Quantum Processes N. Watanabe -- 1. Introduction -- 2. Quantum Channels -- 3. Quantum Mutual Entropy Type Measures -- 3.1. Ohya Mutual Entropy and Capacity -- 3.2. Coherent Entropy and Lindblad-Nielsen Entropy -- 4. Quantum Measurement Process -- 5. Quantum Communication Process -- 5.1. Attenuation Process -- 6. Quantum Teleportation Process -- 7. Quantum Computational Process.

References -- Basics of Molecular Simulation and Its Application to Biomolecules T. Ando and 1. Yamato -- 1. Introduction -- 2. Molecular Dynamics Simulation -- 2.1. Governing Equation of Molecular Dynamics -- 2.2. Potential Functions for Biomoleules -- 2.3. Integration Algorithm -- 2.4. Simulation Conditions -- 2.5. Current Limitations of Molecular Dynamics -- 3. Protein Folding Problem -- 4. Brownian Dynamics Simulation -- 4.1. Brownian Dynamics Algorithm -- 4.2. Force Field -- 4.3. Folding Simulations of a-Helical and p-Hairpin Peptides -- 4.3.1 . Folding trajectories -- 4.3.2. Energy components -- 4.3.3. Cluster analysis -- 5. Conclusions -- Acknowledgments -- References -- Theory of Proton-Induced Superionic Conduction in Hydrogen-Bonded Systems H. Kamimura -- 1. Introduction -- 2. Theory of superionic conduction in the superionic phase -- 2.1. Mechanism of proton-induced superionic conduction -- 2.2. Formula for proton-induced ionic mobility in the superionic phase -- 2.3. Comparison between quantum mechanical and classical diffusion times -- 2.4. Estimation of the quantum mechanical mobility and ionic conductivity for Rb3 H(Se04h -- 2.5. Summary of Section 2 and concluding remarks -- 3. Theory of superionic conduction below and at the ferroelastic phase transition -- 3.1. The Ginzburg-Landau theory for the ferroelastic phase transition in M3H(X04h -- 3.2. A new idea for explaining the divergent behavior of ionic conduction just below and at T = Tc in the ferroelastic phase -- 3.3. Derivation of an energy criterion for the realization of the mixed phase by a simple consideration -- 3.4. Expression of the ionic conductivity for T Tc -- 3.5. Summary of Section 3 -- Acknowledgments -- References -- Massive Collection of Full-Length Complementary DNA Clones and Microarray Analyses: Keys to Rice Transcriptome Analysis S. Kikuchi -- 1. Introduction.

1.1. Massive collection offull-length cDNA clones and their sequence information: starting materials for transcriptome analysis.