Spectral analysis of complex networks and modeling methods by statistics
| Project/Area Number |
23654046
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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 |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
OBATA Nobuaki 東北大学, 情報科学研究科, 教授 (10169360)
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| Co-Investigator(Renkei-kenkyūsha) |
HORA Akihito 北海道大学, 大学院・理学研究院, 教授 (10212200)
KONNO Norio 横浜国立大学, 大学院・工学研究院, 教授 (80205575)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 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 |
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| Research Abstract |
(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.
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Report
(4 results)
Research Products
(44 results)
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[Presentation] Localization of quantum walks on spidernets2012
Author(s)
Nobuaki Obata
Organizer
15th Workshop on Non-Commutative Harmonic Analysis : Random Matrices, representation theory and free probability
Place of Presentation
with applications Mathematical Research and Conference Center (MRCC), Bedlewo, Poland
Year and Date
2012-09-24
Related Report
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[Presentation] Spectral analysis of digraphs2012
Author(s)
Nobuaki Obata
Organizer
Workshop on Non-Commutative Harmonic Analysis with Applications to Real World Complex Phenomena
Place of Presentation
Hanyang University, Korea
Year and Date
2012-01-16
Related Report
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