1994 Fiscal Year Final Research Report Summary
Mathematical Study of Information Dynamics and its Applications
| Project/Area Number |
05640224
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Science University of Tokyo |
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Principal Investigator |
OHYA Masanori Science University of Tokyo Faculty of Science and Technology Profeesor, 理工学部, 教授 (90112896)
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| Co-Investigator(Kenkyū-buntansha) |
SUYARI Hiroki Science University of Tokyo Faculty of Science and Technology Assistant, 理工学部, 助手 (70246685)
WATANABE Noboru Science University of Tokyo Faculty of Science and Technology Assistant Professo, 理工学部, 講師 (70191781)
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| Project Period (FY) |
1993 – 1994
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| Keywords | Information Dynamics / Complexity / Quantum Entropy / Mutual Entropy / Quantum Channel / Markov Process / K-S entropy / Optical Communication |
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| Research Abstract |
For mathematical sytudy in many fields such as physics, mathematics, engeneering, biology and recognization science each dynamics is described by its state of each system.One of the important studies is to discuss the change of the state and its complexity. Examples of these complexities are entropy, fractal, chaos, fuzzy and uncertainty, and these meaning has different in each field. However these complexities have the similar scientific meaning, so that it can be applied to unify these complexities. From this standing point we try to find the concept of complexities well related to its information and we construct "Information Dynamics" to deal with each dynamics. By using "Information Dynamics" we can solve some problems in physics, mathematics, engeneering, biology and recognization science from the same point of view. Moreover these resuls can be applied to each field, so that we can get the new idea about each problem. Concretely we can get the following results in the framework of "Information Dynamics". (1) We discussed quantum entropy in detail. (2) We diiscussed a maximization of entropy and we apply it to the Gaussian process. (3) We discussed the dyanmical change of mutual entropy with respect to the times of the channel describing the attenuation process. (4) We applied an open system to a quantum Markov chain and we compute the mutual entropy rigorously. We discuss the irreversibility in the open system. (5) Under the above results we investigate the property of the complexities in "Information Dynamics".
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