2013 Fiscal Year Final Research Report
Duality of statistical optimality and physical optimality for spherical designs and their constructions
| Project/Area Number |
23654031
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
JIMBO Masakazu 名古屋大学, 情報科学研究科, 教授 (50103049)
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| Co-Investigator(Kenkyū-buntansha) |
SAWA Masanori 名古屋大学, 大学院・情報科学研究科, 助教 (50508182)
MASE Shigeru 東京工業大学, 情報理工学研究科, 教授 (70108190)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 球面デザイン / 組合せデザイン |
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| Research Abstract |
When we integrate some polynomial function on a n-dimensional sphere, if the integrand polynomial is at most degree 2, we clarified the condition on an optimal Euclidean design with two concentric spheres. Conditions on an optimal Euclidean design is given by (i) the ratio the radius of two spheres, (ii) the number of points chosen from each sphere and (iii) the configuration of points for each concentric sphere. We obtained such conditions that a cubature formula is optimal and gave constructions of Euclidean designs which satisfy the conditions. These results were accepted as papers for Sankha Indian Journal of Statistics, etc.
Moreover, we introduced a notion of mutually orthogonal t-designs (t-MOD) over
the complex number field. We examined some conditions for a t-MOD to be optimal. And we find that t-MOD is equivalent to a quantum jump code.
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