Elucidation of information structure behind complex systems using continued fraction and scale invariant generalized exponential function
| Project/Area Number |
25540106
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Soft computing
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| Research Institution | Chiba University |
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Principal Investigator |
Suyari Hiroki 千葉大学, 融合科学研究科(研究院), 教授 (70246685)
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| Research Collaborator |
Naudts Jan アントワープ大学, 教授
Scarforne Antonio トリノ工科大学, 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 |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | q-指数関数 / スケール不変 / 自己相似 / 自己相似性 / Tsallisエントロピー / α-ダイバージェンス / 大偏差原理 |
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| Outline of Final Research Achievements |
Power distribution is ubiquitous in complex systems such as chaos and fractals. A power distribution can be represented as a generalization of an exponential function, so that the information structure behind complex systems can be systematically expressed in terms of a generalized exponential function. In this work, using the self-similarity in the q-exponential function, the relation between continued fraction and q-exponential function is found, but the the relation to the multi-scaled cantor set is still missing. However, in the process of this work, we obtain the important result on the large deviation principle generalized for the q-exponential function. Concretely, we derive the generalized binomial distribution uniquely determined by the q-exponential function and obtain the alpha-divergence as the rate function for the first time.
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Report
(4 results)
Research Products
(10 results)
