Spectral analysis of complex networks and modeling methods by statistics

复杂网络的谱分析和统计建模方法

• 批准号: 23654046
• 负责人: OBATA Nobuaki
• 金额: $ 2.33万
• 依托单位: Tohoku 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-23654046/
• 关键词: ネットワーク; 量子確率; 量子ウォーク; ランダムグラフ; スペクトル; 局在化; 有向グラフ; 固有値分布

(1) Spectral analysis of networks: The asymptotic spectral distribution of the distance-k graph of the cartesian product graph is derived as a combinatorial central limit theorem. The asymptotic spectral distribution of weighted hypercubes are described in terms of q-deformed Hermite polynomials. The spectral distribution is completely determined for the Manhattan product of directed paths of small orders, and thier asymptotic behaviors are obtained in the infinite length.(2) Statistical and asymptotic behaviors of dynamics for the modeling methods: A quantum probabilistic method is applied to classical random walks for reconstructing transition probability and recurrence probability. A necessary and sufficient condition is obtained for a quantum walk (Grover walk) on a spidernet in order to exhibit the localization.

（1）网络的光谱分析：笛卡尔产品图的距离K图的渐近光谱分布被推导为组合中央限制定理。用Q呈现的Hermite多项式描述了加权高管的渐近光谱分布。对于小订单的有向路径的曼哈顿产物，光谱分布是完全确定的，并且在无限的长度上获得了渐近行为。（2）建模方法的统计和渐近行为：量子概率的方法适用于经典的随机步行，用于重新构建过渡概率和再生。为了展示定位，在蜘蛛网上获得量子步行（Grover Walk）的必要条件。

项目成果

Distance-k graphs of hypercube and q-Hermite polynomials

超立方体和 q-Hermite 多项式的距离 k 图

• DOI: 10.1142/s0219025713500112
• 发表时间: 2013
• 期刊: Infin. Dimens. Anal. Quantum Probab. Relat. Top.
• 作者: S. Kinoshita;M. Iwamoto;K. Tateishi;N.J. Suematsu;and D. Ueyama;野呂正行;Hun Hee Lee and Nobuaki Obata
• 通讯作者: Hun Hee Lee and Nobuaki Obata

One-mode interacting Fock spaces and random walks on graphs

• DOI: 10.1080/17442508.2010.550919
• 发表时间: 2012-04
• 期刊: Stochastics
• 作者: N. Obata

Manhattan Products of Digraphs: Characteristic polynomials and examples

有向图的曼哈顿积：特征多项式和示例

• 发表时间: 2012
• 期刊: Ann. Funct. Anal.
• 作者: 間淵 聡;藤代 一成;大野 義夫;Nobuaki Obata
• 通讯作者: Nobuaki Obata

Asymptotic spectral analysis of growing Graphs: a quantum probabilistic approach

生长图的渐近谱分析：一种量子概率方法

• 发表时间: 2006
• 期刊: Methods and applications of infinite Dimensional analysis
• 作者: Obata;Nobuaki
• 通讯作者: Nobuaki

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