Paper Abstract and Keywords |
Presentation |
2016-07-21 15:20
An evaluation of the shape of the Lorenz attractor embedded in the delay coordinate space with persistent homology Shotaro Tsuji, Kazuyuki Aihara (Univ. Tokyo) NLP2016-37 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
We conducted a numerical evaluation of the geometric shapes of the Lorenz attractor and the recon-
structed Lorenz attractors in the delay-coordinate space with persistent homology. Takens' embedding theorem
ensures that the reconstructed attractor embeded in the delay-coordinate space with sufficiently high dimension is
diffeomorphic to the original attractor. However, under the condition of differmorphism, the shape of the attractor
may deform greatly depending on the delay time. Then, we evaluated the relation between the shapes of the recon-
structed attractors and the delay time with persistent homology. Moreover, we observed that there are a signicant
difference between the optimal delay time calculated with persistent homology and that calculated from the mutual
information. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
delay-coordinate space / Takens' theorem / Persistent homology / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 116, no. 151, NLP2016-37, pp. 17-20, July 2016. |
Paper # |
NLP2016-37 |
Date of Issue |
2016-07-14 (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) |
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NLP2016-37 |
Conference Information |
Committee |
NLP |
Conference Date |
2016-07-21 - 2016-07-22 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Hokkaido Univ. Centennial Hall |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
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Paper Information |
Registration To |
NLP |
Conference Code |
2016-07-NLP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
An evaluation of the shape of the Lorenz attractor embedded in the delay coordinate space with persistent homology |
Sub Title (in English) |
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Keyword(1) |
delay-coordinate space |
Keyword(2) |
Takens' theorem |
Keyword(3) |
Persistent homology |
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1st Author's Name |
Shotaro Tsuji |
1st Author's Affiliation |
The University of Tokyo (Univ. Tokyo) |
2nd Author's Name |
Kazuyuki Aihara |
2nd Author's Affiliation |
The University of Tokyo (Univ. Tokyo) |
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Speaker |
Author-1 |
Date Time |
2016-07-21 15:20:00 |
Presentation Time |
25 minutes |
Registration for |
NLP |
Paper # |
NLP2016-37 |
Volume (vol) |
vol.116 |
Number (no) |
no.151 |
Page |
pp.17-20 |
#Pages |
4 |
Date of Issue |
2016-07-14 (NLP) |
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