| Project/Area Number |
25400188
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Ibaraki University |
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Principal Investigator |
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| Research Collaborator |
Scarfone Antonio M. トリノ工科大学, 応用科学工学科, 准教授
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | κ-指数型分布 / 情報幾何 / κ-エントロピ－ / ダイバージェンス / 双対平坦 / 揺動応答関係 / κ-エントロピ / フィーシャー情報計量 / κ-統計力学 / エスコート期待値 / 一般化エントロピー / κエントロピー / フィッシャー情報計量 / 情報幾何学 |
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| Outline of Final Research Achievements |
We found the conjugate representations for constructing the statistical manifold associated with a family of the kappa-generalized exponential distributions. We have obtained the explicit expressions of the kappa-generalized geometrical quantities (e.g, Fisher metric, affine connections, divergence functions) which characterize the information geometric structures. We also showed that the kappa-statistical manifold is dually flat, which is an important feature in information geometry.
From these results we derive a kappa-generalization of the fluctuation-response relations, and pointed out the importance of an escort expectation value in addition to the conventional linear expectation.
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