CONTENTS -- Preface -- Five Years of QBIC -- 1. Aims of QBIC -- 2. Solving the mystery of life -- 3. Some works appeared in conference of QBIC -- 3.1. Examples of researches in QBIC -- 3.1.1. Concerning of the Figure above -- 3.2. Concerning -- 3.3. Concerning -- 3.4. Concerning -- References -- Complexity Considerations Quantum Computation Luigi Accardi -- 1. Introduction -- 2. Simon's period-finding quantum algorithm -- 2.1. Ingredients of Simon's quantum period finding algorithm (QPFA) -- 3. Complexity considerations on Simon's quantum period finding algorithm (QPFA) -- 4. Classical reduction of the factorization problem to period finding -- 4.1. Classical probabilistic factorization algorithms -- References -- Quantum Markov Chains and Ising Model on Cayley Tree Luigi Accardi, Farrukh Mukhamedov and Mansoor Saburov -- 1. Introduction -- 2. Preliminaries -- 3. Construction of QMC on the Cayley tree -- 4. QMC associated with Ising model and main results -- 5. Diagonalizability of forward QMC -- Acknowledgement -- References -- Mathematical Aspects of Conserved Quantities in a General Class of Quantum Systems Asao Arai -- 1. Introduction -- 2. A Free Relativistic Quantum Particle Revisited -- 3. Uniqueness Theorem on a Decomposition of a Linear Operator and Some Consequences -- 4. Existence Theorems -- 4.1. Bounded Conserved Quantities -- 4.2. Unbounded Conserved Quantities -- Acknowledgments -- References -- Oscillations and Rolling for Duffing's Equation Irina Ya. Aref 'eva, Evgeny V. Piskovskiy and Igor V. Volovich -- 1. Introduction -- 2. Higgs equation and anharmonic oscillator -- 3. Solution to the Higgs equation -- 4. Approximate solutions -- 5. Nonlocal Nonlinear Equation -- 6. Conclusion -- Acknowledgments -- References.

General Formalism of Decision Making Based on Theory of Open Quantum Systems Masanori Asano, Masanori Ohya, Irina Basieva and Andrei Khrennikov -- 1. Introduction -- 2. Problem solving as decoherence -- 3. Dynamics of decision making -- Conclusion -- References -- Quantum-Like Representation of Non-Bayesian Inference Masanori Asano, Masanori Ohya, Irina Basieva, Andrei Khrennikov and Yoshiharu Tanaka -- 1. Bayesian inference -- 2. Prediction State Vector -- 3. Quantum-like Bayesian Updating -- 3.1. Biased Posterior Probability -- 3.2. Reliability of Knowledge -- 3.3. Irrationality -- 4. Bayesian Updating Biased by Psychological Factor -- 4.1. System of Psychological Factor -- 4.2. Bias Operator -- 4.3. Redefinition of Biased Posterior Probability -- 4.4. Biased Posterior Probability by PVM Operators -- References -- A Mathematical Treatment of Joint and Conditional Probability Masanori Asano, Masanori Ohya, Yoshiharu Tanaka, Ichiro Yamato, Irina Besieva and Andrei Khrennikov -- 1. Introduction -- 2. Conditional probability and joint probability in quantum systems -- 3. Liftng and joint probability -- 4. Adaptive Dynamics -- 5. New views of probability both in classical and quantum systems -- References -- Entangled States Preparation in Clusters of Three Resonantly Interacting Fluorescent Particles Irina Basieva -- 1. Introduction -- 2. Theoretical model -- 3. Results and discussion -- 3.1. Exact analytical solution -- 3.2. Approximate solution for the case of weak laser field -- 3.3. States dynamics under strong laser field -- 3.4. Conclusion -- References -- Minimum of Information Distance Criterion for Optimal Control of Mutation Rate in Evolutionary Systems Roman V. Belavkin -- 1. Introduction -- 2. Replicator-Mutator Dynamics -- 3. Optimal control of Markov evolution -- 3.1. Minimum information distance criterion.

3.2. Information distance and mutual information -- 3.3. General solutions of variational problems -- 4. Optimal Search of DNA Sequences -- 4.1. Stochastic search in metric spaces -- 4.2. Stochastic search in the Hamming space -- 4.3. Optimal control of mutation rates -- 5. Discussion -- Acknowledgements -- References -- On Non-Markovian Quantum Evolution Dariusz Chruscinski and Andrzej Kossakowski -- 1. Introduction -- 2. Divisible maps -- 3. Information flow vs. discrimination problem -- 4. Example: qubit dynamics -- 5. Markovianity and the generalized discrimination problem -- 6. Conclusions -- Acknowledgments -- References -- High Density Limit of the Distribution of the Outcome of EEG-Measurements Karl-Heinz Fichtner, Lars Fichtner, Wolfgang Freudenberg and Masanori Ohya -- 1. Introduction -- 2. The Space of Signals -- 3. Time Evolution of Signals -- 4. The Process of Recognition -- 5. EEG-Measurements -- 6. High Density Limit in the Case of EEG-Measurements -- References -- Internal Noise of EEG-Measurements and Certain Boson Systems Karl-Heinz Fichtner, Lars Fichtner, Kei Inoue and Masanori Ohya -- 1. Introduction -- 2. Basic notions and notations -- 2.1. The Symmetric Fock Space -- 2.2. Exponential Vectors -- 2.3. The Memory Space -- 2.4. EEG-Measurements -- 3. Main Results -- References -- Skew Information and Uncertainty Relation Shigeru Furuichi and Kenjiro Yanagi -- 1. Introduction -- 2. Uncertainty relation with the quantity including Wigner-Yanase skew information -- 3. Generalizations of Theorem 2.2 -- 3.1. Uncertainty relation with Wigner-Yanase-Dyson skew information -- 3.2. A two-parameter generalization -- 3.3. Generalization with metric adjusted correlation measure -- 4. Conclusion -- Acknowledgements -- References.

Multiple-Photon Absorption Attack on Entanglement-Based Quantum Key Distribution Protocols Guillaume Adenier, Noboru Watanabe, Irina Basieva and Andrei Khrennikov -- 1. Introduction -- 2. Single-photon absorption attack n = m = 1 -- 3. Two-photon absorption attack -- 4. Multiple-photon absorption attack -- 5. Eve's knowledge of the key -- 6. Discussion and countermeasures -- 7. Conclusion -- References -- Protein Sequence Alignment Taking the Structure of Peptide Bond Toshihide Hara, Keiko Sato and Masanori Ohya -- 1. Introduction -- 2. The measure of difference between a pair of sequences used in MTRAP -- 3. A new measure based on dihedral angles of amino acids -- 4. Results and discussion -- 5. Conclusion -- References -- Space - Time - Noise (Raum - Zeit - Rauschen) Takeyuki Hida -- 1. Introduction -- 2. Two kinds of noise -- 3. A noise with space parameter -- 4. Concluding remarks -- References -- Quantum Algorithm for Protein Folding and Its Computational Complexity Satoshi Iriyama, Masanori Ohya and Ichiro Yamato -- 1. Introduction -- 2. Quantum Algorithm -- 2.1. OV algorithm -- 2.2. Language classes -- 3. Quantum Algorithm for Binary Search -- 4. Molecular Dynamics -- 4.1. Governing equation -- 4.2. Verlet algorithm -- 5. Quantum Algorithm for Protein Folding -- 6. Computational Complexity -- 7. Conclusion -- References -- On Effective Procedures in Analyzing of Quantum Operations and Processes Andrzej Jamio lkowski -- 1. Introduction -- 2. Properties of maps which have invariant cones -- 3. Positive maps on PSD -- 4. Criteria for existence of DFS and irreducibility of completely positive maps -- References -- On Numerical Ranges of Operators Jacek Jurkowski -- 1. Restricted Numerical Ranges -- 2. Circulant Operators in C2 Cd -- 3. Product Numerical Range for a Circulant Operator -- 3.1. Product Numerical Range for d = 2 -- Acknowledgments.

References -- Partial Roc Reveals Superiority of Mutual Rank of Pearson's Correlation Coefficient as a Coexpression Measure to Elucidate Functional Association of Genes Takeshi Obayashi and Kengo Kinoshita -- 1. Introduction -- 2. A common threshold of gene coexpression to construct gene network -- 3. New assessment of coexpression measures using partial ROC -- 4. Conclusion -- Acknowledgments -- References -- QFT and Hadronic World as Dynamical Bases of Natural History Izumi Ojima -- 1. Introduction: Hadrons and Bacteria as "Unsung Heros" behind Nature -- 2. Micro-Macro Duality and Quadrality Scheme -- 3. QFT and S-Matrix -- 4. Asymptotic Condition & Yang-Feldman Equation -- 5. Micro-Macro Duality in "Central Limit Theorem" in QFT -- 6. PCT and Modular Structure -- 7. Duality in Hadronic World of Strong Coupling -- Acknowledgments -- References -- Long-Range Property in Time-Dependent Interaction with Three-Body Structure and New Aspect Shinsho Oryu -- 1. Introduction -- 2. Fourier Transform of the Three-Body Born Term -- 3. An energy average by a Laplace transform of the three-body Born term -- 4. Summary and discussion -- Acknowledgement -- Appendix A. Partial wave expansion -- Appendix B. Binomial Series -- References -- Kinetic Isotope Effect on Transport Mediated by CLC-Type H+/Cl- Exchangers Alessandra Picollo, Mattia Malvezzi and Alessio Accardi -- 1. Introduction -- 2. Materials and Methods -- 3. Results -- 3.1. Effects of deuterium on the transport rate of CLC-ec1 and CLC-5 -- 3.2. Kinetic isotope effect on the Voltage dependent H+ block of CLC-5 -- 4. Discussion -- Acknowledgments -- References -- On Positive Maps -- Finite Dimensional Case Wladyslaw A. Majewski -- 1. Introduction -- 2. The set D and its properties -- 3. A characterization of exposed points of D -- Acknowledgments -- References.

A New Noise Depending on a Space Parameter and Its Application Si Si and Win Win Htay.