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Galaxy Evolution with Manifold Learning. [PDF]

open access: yesEntropy (Basel)
Takeuchi TT, Cooray S, Kano RR.
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The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry

Canadian Mathematical Bulletin, 2002
AbstractA partial differential equation, the local Möbius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Möbius equation and an additional partial ...
Fernández-López, Manuel   +2 more
openaire   +2 more sources

Composition of Local Normal Coordinates and Polyhedral Geometry in Riemannian Manifold Learning

International Journal of Natural Computing Research, 2015
The Local Riemannian Manifold Learning (LRML) recovers the manifold topology and geometry behind database samples through normal coordinate neighborhoods computed by the exponential map. Besides, LRML uses barycentric coordinates to go from the parameter space to the Riemannian manifold in order to perform the manifold synthesis.
Gastão Florêncio Miranda Jr.   +3 more
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Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry

Sbornik: Mathematics, 1998
The paper is devoted to the classification of integrable geodesic flows on two-dimensional surfaces. The authors restrict themselves to the following four important equivalence relations on the set of all geodesic flows: (1) isometry, (2) geodesic equivalence, (3) orbital equivalence, (4) Liouville equivalence.
Fomenko, A., Bolsinov, A., Matveev, V.
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Stochastic matched-field localization of an acoustic source based on principles of Riemannian geometry

The Journal of the Acoustical Society of America, 2018
Passive localization of acoustic sources is treated within a geometric framework where non-Euclidean distance measures are computed between a cross-spectral density estimate of received data on a vertical array and a set of stochastic replica steering matrices, rather than traditional replica steering vectors.
Steven, Finette, Peter C, Mignerey
openaire   +2 more sources

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