| Project/Area Number |
26800077
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TAKEUCHI Kota 筑波大学, 数理物質系, 助教 (50722485)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Akito 筑波大学, 数理物質系, 教授 (30180045)
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| Research Collaborator |
CHERNIKOV Artem University of California Los Angeles, Mathematics, Assistant Professor
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | n-dependent / 2-order property / Ramsey property / indiscernible / VC-dimension / n-dependent property / Random graph / Ramsey class / monochromatic subgraph / n-dependence / VCn-dimension / PACn-learning |
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| Outline of Final Research Achievements |
Several interactions between model theory in logic and finite combinatorics were studied in this project. It was well-known that No Independent Property defined in model theory coincides with the finiteness of VC-dimension in combinatorics. The same concept appears in Machine Learning theory. We studied NIPn, which is a generalization of No Independent Property, and the Ramsey property of infinite graphs, then we applied such results and obtained 2-order property, a generalization of order property. In addition, some applications for combinatorics on hypergraph and higher dimensional PAC-learning were found by this research.
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