Contents -- Foreword -- Preface -- Locality and Bell's Inequality -- 1 Inequalities among numbers -- 2 The Bell inequality -- 3 Implications of the Bell's inequalities for the singlet correlations -- 4 Bell on the meaning of Bell's inequality -- 5 Critique of Bell's "vital assumption" -- 6 The role of the counterfactual argument in Bell's proof -- 7 Proofs of Bell's inequality based on counting arguments -- 8 The quantum probabilistic analysis -- 9 The realism of ballot boxes and the corresponding statistics -- 10 The realism of chameleons and the corresponding statistics -- 11 Bell's inequalities and the chamaleon effect -- 12 Physical implausibility of Bell's argument -- 13 The role of the single probability space in CHSH's proof -- 14 The role of the counterfactual argument in CHSH's proof -- 15 Physical difference between the CHSH's and the original Bell's inequalities -- References -- Refutation of Bell's Theorem -- 1 Introduction -- 2 The EPRB gedanken experiment -- 3 The 'CHSH' function -- 4 Strongly objective interpretation -- 5 Weakly objective interpretation -- 6 Conclusion -- References -- Probability Conservation and the State Determination Problem -- 1 Introduction -- 2 Conservation of Probability -- 3 Determination of the phase function -- 4 Validity and range of applicability -- 5 Evolution of a Gaussian Wave Packet -- 6 Operational Issues -- Acknowledgments -- References -- Extrinsic and Intrinsic Irreversibility in Probabilistic Dynamical Laws -- 1 Introduction -- 2 Ontic and epistemic descriptions -- 3 Breaking Time-Reversal Symmetry: Extrinsic Irreversibility -- 4 Breaking Time-Reversal Symmetry: Intrinsic Irreversibility -- 5 Summary and Open Questions -- Acknowledgments -- References -- Interpretations of Probability and Quantum Theory -- 1 Introduction.

2 Interpretations of Probability -- 3 The Axioms of Probability -- 4 Probability in Quantum Mechanics -- 5 Conclusions -- References -- Forcing Discretization and Determination in Quantum History Theories -- 1 Introduction -- 2 Outcome determination via contextual models -- 3 Unitary ortho- and projective structure -- 4 Representing quantum history theory -- 5 Further discussion -- Acknowledgments -- References -- Interpretations of Quantum Mechanics and Interpretations of Violation of Bell's Inequality -- 1 Realist and empiricist interpretations of quantum mechanics -- 2 EPR experiments and Bell experiments -- 3 Bell's inequality in quantum mechanics -- 4 Bell's inequality in stochastic and deterministic hidden-variables theories -- 5 Analogy between thermodynamics and quantum mechanics -- 6 Conclusions -- References -- Discrete Hessians in Study of Quantum Statistical Systems: Complex Ginibre Ensemble -- 1 Introduction -- 2 The Ginibre ensembles -- Acknowledgements -- References -- Some Remarks on Hardy Functions Associated with Dirichlet Series -- 1 Introduction -- 2 "Hardyfication" of Dirichlet series -- 3 Factorization of n -- 4 Applications -- References -- Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit -- 1 Introduction -- 2 There is a lot to add to classical equilibrium statistics from our experience with "Small" systems: -- 3 Relation of the topology of S(E N) to the Yang-Lee zeros of Z(T u V) -- 4 The regions of positive curvature A1 of s(es ns) correspond to phase transitions of first order -- 5 Boltzmann's principle and non-equilibrium thermodynamics -- 6 Macroscopic observables imply the "EPS-probability" -- 7 On Einstein's objections against the EPS-probability -- 8 Fractal distributions in phase space Second Law -- 9 Conclusion -- Appendix -- Acknowledgement.

References -- An Approach to Quantum Probability -- 1 Introduction -- 2 Formulation -- 3 Wave Functions and Hilbert Space -- 4 Spin -- 5 Traditional Quantum Mechanics -- 6 Concluding Remarks -- References -- Innovation Approach to Stochastic Processes and Quantum Dynamics -- 1 Introduction -- 2 Review of defining a stochastic process and white noise analysis -- 3 Relations to Quantum Dynamics -- 4 Addenda to foundations of the theories. Concluding remarks -- Acknowledgements. -- References -- Statistics and Ergodicity of Wave Functions in Chaotic Open Systems -- 1 Introduction -- 2 Classical Nonergodicity and Short-Path Dynamics -- 3 Universal Description of Wave Function Statistics -- 4 Numerical Analyses and Discussions -- 5 Conclusions -- Acknowledgments -- References -- Origin of Quantum Probabilities -- 1 Introduction -- 2 Quantum formalism and perturbation effects -- 3. Probability transformations connecting preparation procedures -- 3 Hyperbolic and hyper-trigonometric probabilistic transformations -- 4 Double stochasticity and correlations between preparation procedures -- 5 Hyperbolic quantum formalism -- 6 Physical consequences -- Acknowledgements -- References -- Nonconventional Viewpoint to Elements of Physical Reality Based on Nonreal Asymptotics of Relative Frequencies -- 1 Introduction -- 2 Analysis of the foundation of probability theory -- 3 General principle of statistical stabilization of relative frequencies -- 4 Probability distribution of a collective -- 5 Model examples of p-adic statistics -- Acknowledgements -- References -- "Complementarity" or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? -- 1 Introduction -- 2 De Broglie waves as an SED effect -- 3 Schrodinger Equation -- 4 Conclusions.

A Probabilistic Inequality for the Kochen-Specker Paradox -- 1 Introduction -- 2 The Kochen-Specker theorem -- 3 The Kochen-Specker inequality -- 4 Independence -- 5 Conclusions -- Quantum Stochastics. The New Approach to the Description of Quantum Measurements -- 1 Introduction -- 2 Quantum stochastic approach -- 3 Concluding remarks -- 4 Acknowledgments -- References -- Abstract Models of Probability -- 1 What probability sets o are possible? -- 2 Uniqueness of semigroups of zeros and units. -- 3 Probabilities with hidden parameters -- 4 Probability sets with a single unit. -- 5 Acknowledgments -- References -- Quantum K-Systems and their Abelian Models -- 1 Introduction -- 2 Classical K-System -- 3 Algebraic Quantum K-Systems -- 4 Dynamical Entropy -- 5 Some General Considerations on Abelian Models -- 6 Abelian Models for Algebraic K-Systems -- 7 Continuous K-Systems -- 8 Mixing Properties Without Algebraic K-Property -- 9 Time Evolution -- References -- Scattering in Quantum Tubes -- 1 Introduction -- 2 Tubes in quantum heterostructures -- 3 Mathematical model -- 4 Reformulated scattering problem -- 5 Solution of the scattering problem -- References -- Position Eigenstates and the Statistical Axiom of Quantum Mechanics -- 1 Quantum probabilities according to Deutsch -- 2 Schrodinger's equation for a free particle as a consequence of position eigenstates -- 3 Driven particle: Weyl equation in general space-time -- 4 Realizing Deutsch's "substitution" as a time evolution -- 5 Can normalization be replaced by symmetry? -- References -- Is Random Event the Core Question? Some Remarks and a Proposal -- 1 Preface -- 2 Linguistic Model -- 3 Ensemble Model -- 4 Structural Model -- 5 Certain and Uncertain Structures -- 6 Probability -- 7 Experimental Verification -- 8 Objective and Subjective Probability -- 9 Conclusions -- References.

Constructive Foundations of Randomness -- 1 Introduction -- 2 Kolmogorov Complexity -- 3 Incompressibility -- 4 Reversible Complexity -- 5 Complexity and Information -- 6 Frequency Rates -- 7 Prefix Complexity -- 8 Universal Probability -- 9 Sequentially Coding Algorithms -- References -- Structure of Probabilistic Information and Quantum Laws -- 1 Introduction -- 2 Gaining experimental information -- 3 Efficient representation of probabilistic information -- 4 Predictions -- 5 Discussion -- Acknowledgments -- References -- Quantum Cryptography in Space and Bell's Theorem -- 1 Introduction -- 2 Bell's Inequality -- 3 Localized Detectors -- 4 Quantum Key Distribution -- 5 Gaussian Wave Functions -- 6 Conclusions -- 7 Acknowledgments -- References -- Interacting Stochastic Process and Renormalization Theory -- 1 Introduction -- 2 Acknowledgments -- References.