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Journal of the Optical Society of America A, 2010
It is generally accepted that hues can be arranged so as to make a circle. The circular representation of hue has been supported by multidimensional scaling, which allows for the representation of a set of colored papers as a configuration in a Euclidean space where the distances between the papers correspond to the perceptual dissimilarities between ...
Tokunaga, Rumi, Logvinenko, Alexander D.
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It is generally accepted that hues can be arranged so as to make a circle. The circular representation of hue has been supported by multidimensional scaling, which allows for the representation of a set of colored papers as a configuration in a Euclidean space where the distances between the papers correspond to the perceptual dissimilarities between ...
Tokunaga, Rumi, Logvinenko, Alexander D.
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Journal of the London Mathematical Society, 1995
As is well known, a 1-form \(\eta\) on a \((2n +1)\)-dimensional differentiable manifold \(M\) is said to be a contact form if \(\eta \wedge (d\eta)^n \neq 0\) everywhere on \(M\). In the present paper, it is proposed to study the following quaternionic analogue of contact manifolds.
Geiges, Hansjörg, Thomas, Charles B.
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As is well known, a 1-form \(\eta\) on a \((2n +1)\)-dimensional differentiable manifold \(M\) is said to be a contact form if \(\eta \wedge (d\eta)^n \neq 0\) everywhere on \(M\). In the present paper, it is proposed to study the following quaternionic analogue of contact manifolds.
Geiges, Hansjörg, Thomas, Charles B.
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Journal of Mathematical Physics, 1984
The concept of a probability manifold M is introduced. The global properties of M inherited from its local structure are then considered. It is shown that a deterministic spin model due to Pitowski falls within this general framework. Finally, we construct a phase-space model for nonrelativistic quantum mechanics.
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The concept of a probability manifold M is introduced. The global properties of M inherited from its local structure are then considered. It is shown that a deterministic spin model due to Pitowski falls within this general framework. Finally, we construct a phase-space model for nonrelativistic quantum mechanics.
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Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005
Manifold learning has become a vital tool in data driven methods for interpretation of video, motion capture, and handwritten character data when they lie on a low dimensional, nonlinear manifold. This work extends manifold learning to classify and parameterize unlabeled data which lie on multiple, intersecting manifolds.
Souvenir, Richard, Pless, Robert
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Manifold learning has become a vital tool in data driven methods for interpretation of video, motion capture, and handwritten character data when they lie on a low dimensional, nonlinear manifold. This work extends manifold learning to classify and parameterize unlabeled data which lie on multiple, intersecting manifolds.
Souvenir, Richard, Pless, Robert
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Bulletin of the London Mathematical Society, 1972
Abstract Differentiable manifolds and their geometry appear naturally in the study of diverse areas of mathematics, including Lie group theory, homogeneous spaces, probability theory, differential equations, the theory of functions of a single complex variable and of several complex variables, algebraic geometry, classical mechanics ...
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Abstract Differentiable manifolds and their geometry appear naturally in the study of diverse areas of mathematics, including Lie group theory, homogeneous spaces, probability theory, differential equations, the theory of functions of a single complex variable and of several complex variables, algebraic geometry, classical mechanics ...
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