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| Presentation | 2008-03-27 14:25 New developments in large deviation statistics and time correlation calculations in chaotic dynamics and stochastic processes Syuji Miyazaki, Miki Kobayashi, Kei Ejima, Mika Izuo, Taro Takaguchi, Kai Morino (Kyoto Univ.)  NLP2007-160 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | First, spectra statistics of transition matrices of the Watts-Strogatz model are studied. Different statistics are observed between regular and random graphs. Rewiring rate dependence of the distance between the largest eigenvalue and the second largest one follows a power law. In this sense, small world is a kind of critical state between regular and random graphs. Secondly, large deviation statistics are applied to a random walk on the subgraph of the {\em mixi} network which is truncated at distance two from the specific user. Dynamical structure functions reflect distributions of node-dependent characteristic quantities, $q$-phase transitions are observed, which are phenomenologically explained by use of diagonal block strucrue of transition matrices. Finally, regarding state variables at different times as independent ones, we explain an approximate calculation method of correlation functions, in which memory terms appearing in the Mori's projection operator method are ignored. This calculation is applied to a chaotic diffusion model, in which fractal diffusion coefficients are observed. Our approximations agree with the exact calculation. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | spectra statistics / small world / large deviation statistics / social networking service / level dynamics / Frobenius-Perron operator / chaotic diffusion / fractal diffusion coefficient | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 560, NLP2007-160, pp. 37-42, March 2008. | |
| Paper # | NLP2007-160 | |
| Date of Issue | 2008-03-20 (NLP) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | NLP2007-160 |
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| Conference Information | |
| Committee | NLP |
| Conference Date | 2008-03-27 - 2008-03-28 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | NLP |
| Conference Code | 2008-03-NLP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | New developments in large deviation statistics and time correlation calculations in chaotic dynamics and stochastic processes |
| Sub Title (in English) | |
| Keyword(1) | spectra statistics |
| Keyword(2) | small world |
| Keyword(3) | large deviation statistics |
| Keyword(4) | social networking service |
| Keyword(5) | level dynamics |
| Keyword(6) | Frobenius-Perron operator |
| Keyword(7) | chaotic diffusion |
| Keyword(8) | fractal diffusion coefficient |
| 1st Author's Name | Syuji Miyazaki |
| 1st Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 2nd Author's Name | Miki Kobayashi |
| 2nd Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 3rd Author's Name | Kei Ejima |
| 3rd Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 4th Author's Name | Mika Izuo |
| 4th Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 5th Author's Name | Taro Takaguchi |
| 5th Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 6th Author's Name | Kai Morino |
| 6th Author's Affiliation | Kyoto University (Kyoto Univ.) |
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| Speaker | Author-1 |
| Date Time | 2008-03-27 14:25:00 |
| Presentation Time | 25 minutes |
| Registration for | NLP |
| Paper # | NLP2007-160 |
| Volume (vol) | vol.107 |
| Number (no) | no.560 |
| Page | pp.37-42 |
| #Pages | 6 |
| Date of Issue | 2008-03-20 (NLP) |
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