論文 - 彭　林玉

Information geometric characterization of the complexity of fractional Brownian motions

Peng L., Sun H., Xu G.

Journal of Mathematical Physics （AMER INST PHYSICS）  53 （ 12 ） 123305 2012年12月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  00222488

　概要を見る

The complexity of the fractional Brownian motions is investigated from the viewpoint of information geometry. By introducing a Riemannian metric on the space of their power spectral densities, the geometric structure is achieved. Based on the general construction, for an example, whose power spectral density is obtained by use of the normalized Mexican hat wavelet, we show its information geometric structures, e.g., the dual connections, the curvaturesthe geodesics. Furthermore, the instability of the geodesic spreads on this manifold is analyzed via the behaviors of the length between two neighboring geodesics, the average volume element as well as the divergence (or instability) of the Jacobi vector field. Finally, the Lyapunov exponent is obtained. © 2012 American Institute of Physics.

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Geometry of hamiltonian dynamics with conformal Eisenhart metric

Sun H., Peng L., Sun X.

International Journal of Mathematics and Mathematical Sciences 2011 （ 1 ） 710274 2011年09月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  01611712

　概要を見る

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads. © 2011 Linyu Peng et al.

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The geometric structures and instability of entropic dynamical models

Peng L., Sun H., Sun D., Yi J.

Advances in Mathematics （ELSEVIER）  227 （ 1 ） 459 - 471 2011年05月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  00018708

　概要を見る

In this paper, we characterize two entropic dynamical (ED) models from the viewpoint of information geometry and give the geometric structures of the associated statistical manifolds of the models. The scalar curvatures and the geodesics are obtained. Also the instability of entropic dynamical models is studied from the behavior of the geodesics lengths, statistical volume elements and Jacobi vector fields. © 2011.

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Information geometry and its applications

Sun H, Peng L, Zhang Z

Advances in Mathematics (China) 40 （ 3 ） 257 - 269 2011年

研究論文（学術雑誌）, 共著, 査読有り

3D object recognition based on linear lie algebra model

Li F., Wu P., Sun H., Peng L.

Journal of Beijing Institute of Technology 18 （ 1 ） 46 - 50 2009年03月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  10040579

　概要を見る

A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given. © A paper published in JBIT is protected by copyright.

On fibre bundle surfaces and their curvatures

Li F., Peng L., Sun H.

Journal of Beijing Institute of Technology 17 （ 4 ） 451 - 454 2008年12月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  10040579

　概要を見る

A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves: a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.

The geometric structure of the inverse Gamma distribution

Tongzhu L., Linyu P., Huafei S.

Contributions to Algebra and Geometry 49 （ 1 ） 217 - 225 2008年04月

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  01384821

　概要を見る

In the present paper we study the geometric structure of the inverse Gamma manifold from the viewpoint of information geometry and give the Kullback divergence, the J-divergence and the geodesic equations. Also, some applications of the inverse Gamma distribution are provided. © 2008 Heldermann Verlag.

Surface model based on a fibre bundle of Hamiltonian Lie algebra and Gaussian curvature

Li F, Wu P, Peng L, Sun H

Science & Technology Review 26 （ 8 ） 37 - 39 2008年

研究論文（学術雑誌）, 共著, 査読有り

The geometric structure of the Pareto distribution

L Peng, H Sun, L Jiu

Boletın de la Asociación Matemática Venezolana 14 （ 1-2 ） 5 - 13 2007年

研究論文（学術雑誌）, 共著, 査読有り