Explicated is a role of the space (Z/dZ)^<2n> equipped with a symplectic bilinear form in quantum information theory. Specifically, quantum error-correcting codes, quantum teleportation, entanglement distillation, quantum cryptography and so on are explained from a unified algebraic point of view. The symplectic bilinear form naturally emerges in the commutation relation for Weyl's ray (projective) representation of (Z/dZ)^<2n>.

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This paper reviews statistical asymptotic theory for time series. The asymptotic optimality of inference and testing is described in terms of the local asymptotic normality. The results have been applied to financial engineering, biomedical sciences and econometrics etc.

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Hierarchical simulation for systematic calculation from the scale at a molecular level to the scale at a macroscopic level through mesoscopic scale must become important technique for realization of practical material design. In this paper, some concepts of coarse-graining, which is indispensable process for hierarchical simulation, were described based on recent investigations studied by the present author et al. As a simple and basic example of coarse-graining process, an analysis of the local structure in liquid carbon tetrachloride was introduced for the description of finite value of depolarization ratio on a complete polarized Raman band of carbon tetrachloride molecule. A more complicated and practical example of hierarchical simulation was described on a simulation for structure formation of polyelectrolyte-water composite membrane system. Available processes were shown for mesoscopic structure formation based on the structure formula of the polyelectrolyte molecule, local molecular arrangements in the mesoscopic structure derived from a mesoscopic simulation, and the electronic structure at a molecular level in mesoscopic inhomogeneous field.

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[in Japanese]

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[in Japanese]

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