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Paper Abstract and Keywords
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
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.
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
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

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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Date Time 2008-03-27 14:25:00 
Presentation Time 25 
Registration for NLP 
Paper # IEICE-NLP2007-160 
Volume (vol) IEICE-107 
Number (no) no.560 
Page pp.37-42 
#Pages IEICE-6 
Date of Issue IEICE-NLP-2008-03-20 

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