| Project/Area Number |
23540134
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Fukui |
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Principal Investigator |
OHARA Atsumi 福井大学, 工学(系)研究科(研究院), 教授 (90221168)
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| Co-Investigator(Renkei-kenkyūsha) |
FUJIWARA Akio 大阪大学, 理学研究科, 教授 (30251359)
MATSUZOE Hiroshi 名古屋工業大学, 工学研究科, 准教授 (90315177)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 情報幾何学 / 一般化熱統計学 / 正定値対称行列 / 力学系 / 共形平坦化 / 一般化指数型分布 |
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| Outline of Final Research Achievements |
Generalizing concepts such as probability density functions or entropies, which play important roles in statistical physics and information sciences, we study their mathematical structure from information geometrical viewpoints and obtain several results for its new application in such fields.
First, we have proved that geometrically nice properties, which are related to flatness in differential geometrical sense, are still maintained, even if the ordinary exponential and logarithmic functions in probability densities or entropies are replaced with power functions. Second, utilizing this nice geometrical structure, we developed several methods to analyze physical phenomena and statistical data those such stochastic structure governs.
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