Duality of statistical optimality and physical optimality for spherical designs and their constructions

球形设计及其构造的统计最优性和物理最优性的对偶性

• 批准号: 23654031
• 负责人: JIMBO Masakazu
• 金额: $ 2.25万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654031/
• 关键词: 球面デザイン; 組合せデザイン; １因子分解; ユークリディアンデザイン; ユークリッドデザイン; 統計的最適性; 最適性

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) overthe 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.

当我们在n维球面上积分多项式函数时，如果被积多项式的次数至多为2，我们阐明了两个同心球面的最优欧氏设计的条件。最优欧氏设计的条件由（i）两个球的半径之比，（ii）从每个球中选择的点的数目和（iii）每个同心球的点的配置给出。给出了求积公式为最优的条件，并给出了满足这些条件的欧氏设计的构造。这些结果被接受为论文Sankha印度统计杂志等。此外，我们引入了一个概念，相互正交的t-设计（t-MOD）在复数域。我们研究了t-MOD最优的一些条件。并且我们发现t-MOD等价于一个量子跳跃码。

项目成果

Optimal equi-difference conflict-avoiding codes of length n=2^a3^bm and weight four

长度n=2^a3^bm、权重4的最优等差冲突避免码

• 发表时间: 2013
• 作者: Y. Lin;M. Mishima;M. Jimbo
• 通讯作者: M. Jimbo

A q-Analogue of the Addressing Problem of Graphs by Graham and Pollak

• DOI: 10.1137/110831520
• 发表时间: 2012-04
• 期刊: SIAM J. Discret. Math.
• 作者: Saori Watanabe;Kota Ishii;M. Sawa

Journal of Statistical Theory and Practice Special Issue: Combinatorial Configurations and Information Sciences

统计理论与实践杂志特刊：组合配置和信息科学

• 发表时间: 2012
• 作者: M. Jimbo;S. Kageyama 編
• 通讯作者: S. Kageyama 編

Tight Equi-Difference Conflict-Avoiding Codes of Odd Length and Weight Three

奇长奇重三紧等差冲突避免码

• 发表时间: 2012
• 作者: Y. Lin;M. Mishima;J. Sato;M. Jimbo
• 通讯作者: M. Jimbo

A t-spontaneous emission error design and its application to secret sharing scheme

t-自发发射误差设计及其在秘密共享方案中的应用

• 作者: 林怡伶;神保雅一
• 通讯作者: 神保雅一