Faculty Profiles - Obayashi Ippei

Papers - Obayashi Ippei

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A Cyclone Identification Algorithm with Persistent Homology and Merge-Tree Reviewed

Masaru Inatsu, Hayato Kato, Yuta Katsuyama, Yasuaki Hiraoka, Ippei Ohbayashi

SOLA 13 214 - 218 2017

Language：English Publishing type：Research paper (scientific journal) Publisher：Meteorological Society of Japan

<p>This paper addresses a cyclone identification algorithm with the superlevel set filtration of the persistent homology together with the merge-tree reconstruction of data. Based on the information of peaks and saddles of the scaler field, the newly developed algorithm divides the analysis area into several homology classes, each of which satisfies the peak-to-saddle difference larger than a criterion that should be set in advance. Applied to the 850-hPa relative vorticity in the western North Pacific at 1200 UTC on 2 March 2013, 3 homology classes were found with the criterion of 100 × 10⁻⁶ s⁻¹ and 17 homology classes were found with the criterion of 50 × 10⁻⁶ s⁻¹. The merge-tree restructuring clarified the neighbour relation among homology classes. The result suggests that the weak criterion detected too much homology classes, some of which are small peaks inside of a single cyclone. The climatology feature density provides the Pacific storm track with the strict criterion. Finally, a possible way to extend toward cyclone tracking with the persistent homology is discussed.</p>

DOI： 10.2151/sola.2017-039

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Inverse Problems for Persistence Diagrams Invited Reviewed

Ippei Obayashi

Bulletin of the Japan Society for Industrial and Applied Mathematics 26 ( 4 ) 7 - 14 2017

Continuation of point clouds via persistence diagrams Reviewed

Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi

PHYSICA D-NONLINEAR PHENOMENA 334 ( 1 ) 118 - 132 2016.11

Language：English Publishing type：Research paper (scientific journal) Publisher：ELSEVIER SCIENCE BV

In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D', we gradually move from D to D', by successively computing intermediate point clouds until we finally find a point cloud P' having D' as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data. (C) 2015 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physd.2015.11.011

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Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity Reviewed

Ippei Obayashi, Shinya Aoi, Kazuo Tsuchiya, Hiroshi Kokubu

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 472 ( 2190 ) 20160028 2016.6

Language：English Publishing type：Research paper (scientific journal) Publisher：ROYAL SOC

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.

DOI： 10.1098/rspa.2016.0028

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Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics Reviewed

Ippei Obayashi, Shinya Aoi, Kazuo Tsuchiya, Hiroshi Kokubu

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 32 ( 2 ) 315 - 332 2015.7

Language：English Publishing type：Research paper (scientific journal) Publisher：SPRINGER JAPAN KK

In this paper, we investigate the mathematical structures and mechanisms of bipedal walking from a dynamical viewpoint. Especially, we focus on the basin of attraction since it determines the stability of bipedal walking. We treat two similar but different bipedal walking models (passive and active dynamic walking models) and examine common mathematical structure between these models. We find that the saddle hyperbolicity and hybrid system play important roles for the shape of the basin of attraction in both models, which are quite common for more general bipedal models and important for understanding the stability mechanism of bipedal walking.

DOI： 10.1007/s13160-015-0181-9

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Capturing the Global Behavior of Dynamical Systems with Conley-Morse Graphs Reviewed

Zin Arai, Hiroshi Kokubu, Ippei Obayashi

Advances in Cognitive Neurodynamics (III) 665 2013

Combinatorial-topological framework for the analysis of global dynamics Reviewed

Justin Bush, Marcio Gameiro, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Ippei Obayashi, Pawel Pilarczyk

CHAOS 22 ( 4 ) 047508 2012.12

Language：English Publishing type：Research paper (scientific journal) Publisher：AMER INST PHYSICS

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

DOI： 10.1063/1.4767672

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Computer-Assisted Verification Method for Invariant Densities and Rates of Decay of Correlations Reviewed

Obayashi Ippei

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 10 ( 2 ) 788 - 816 2011

Exponential decay of correlations for surface semiflows with an expanding direction Reviewed

Ippei Obayashi

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY 49 ( 2 ) 427 - 440 2009

Language：English Publishing type：Research paper (scientific journal) Publisher：KINOKUNIYA CO LTD

Dolgopyat [4] showed that a class of Axiom A flows has exponential decay of correlations for smooth observables, and Baladi-Vallee [2] gave a nice interpretation of it on suspension semiflows of one-dimensional expanding countable Markov maps. Avila-Gouezel-Yoccoz [1] extends the result of Baladi-Vallee to higher dimensional systems.
In this paper we show that a class of non-Markov semiflows also has exponential decay of correlations.
We prove that such exponential decay can be shown on an open dense condition for the suspensions of piecewise expanding maps.

DOI： 10.1215/kjm/1256219166

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