Results 1 to 10 of about 1,183,540 (276)
Pseudo-Riemannian geometry encodes information geometry in optimal transport. [PDF]
Inf Geom, 2022 Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from ...
Wong TL, Yang J.
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Geometry without topology as a new conception of geometry [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points).
Yuri A. Rylov
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The geometry of Riemannian spaces [PDF]
Transactions of the American Mathematical Society, 1934 The primary purpose of this paper is to expose, in as simple and clear a form as is possible, the fundamentals of the geometric structure of a Riemannian space. It is a general truth that the methods which pierce most deeply into the heart of a geometric theory are invariant methods, that is, methods which are independent of the choice of the ...
W. C. Graustein
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Discrete Riemannian geometry [PDF]
Journal of Mathematical Physics, 1999 Within a framework of noncommutative geometry, we develop an analog of (pseudo-) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation. The latter is based on a correspondence between first order differential calculi and digraphs (the vertices of ...
Folkert Müller-Hoissen +1 more
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Decoding Multi-Class Motor Imagery and Motor Execution Tasks Using Riemannian Geometry Algorithms on Large EEG Datasets [PDF]
Sensors, 2023 The use of Riemannian geometry decoding algorithms in classifying electroencephalography-based motor-imagery brain–computer interfaces (BCIs) trials is relatively new and promises to outperform the current state-of-the-art methods by overcoming the noise
Zaid Shuqfa +2 more
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Motor Imagery EEG Classification Based on Decision Tree Framework and Riemannian Geometry. [PDF]
Comput Intell Neurosci, 2019 This paper proposes a novel classification framework and a novel data reduction method to distinguish multiclass motor imagery (MI) electroencephalography (EEG) for brain computer interface (BCI) based on the manifold of covariance matrices in a ...
Guan S, Zhao K, Yang S.
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Riemannian geometry of Lie algebroids
Journal of the Egyptian Mathematical Society, 2011 We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting.
Mohamed Boucetta
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Poisson-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2017 We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter λ, using a functorial approach. This leads us to field equations of ‘Poisson–Riemannian geometry’ between the classical metric, the Poisson bracket and a certain Poisson-compatible connection needed as initial data for the ...
E. Beggs, S. Majid
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A bridge between complex geometry and Riemannian geometry [PDF]
Proceedings of the American Mathematical Society, 1993 Every complex manifold M n {M^n} with holomorphic metric can be obtained (at least locally) from a complex manifold E 2 ∙ n − 2 {E^{2 \bullet n - 2}} and one of its C
Antonio Cassa
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The Geometry of Modified Riemannian Extensions [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009 We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent.
Peter B. Gilkey +3 more
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