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Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.


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Patent
14 Feb 1994
TL;DR: In this paper, a fluid distribution manifold is described, where the input piping is inserted in through the manifold's circular intake opening and onto its cylindrical input port, and the manifold has the further utility of being expandable to larger sizes.
Abstract: This invention relates to a fluid distribution manifold, where the input piping is inserted in through the manifold's circular intake opening and onto its cylindrical input port. The manifold's intake opening leads through a cylindrical path to a closed terminal end. Along the inner manifold wall, there are arranged in a sequence, which may be in a straight line, a series of straight lines or rows, a spiral, or an alternating 90- or 180-degree arrangement, a number of distribution outlet openings and their respective ports, which may be barbed or ribbed on their outer surface. The manifold has the further utility of being expandable to larger sizes. This is achieved by removing the closed terminal end from one manifold and then inserting and connecting that open terminal end in through another manifold's circular intake opening and into its intake port. To achieve a more uniform fluid flow pressure at each of the distribution outlet ports, two or more manifold devices may be fitted and connected to intake piping which is fitted with a T-joint or Y-joint. In a preferred embodiment, the manifold is composed of acrylonitrile-butadiene-styrene, and is used to distribute air in spas and hydrotherapy baths.

66 citations

Journal ArticleDOI
TL;DR: This paper proposes a novel unsupervised manifold learning method termed Laplacian Auto-Encoders (LAEs), which regularizes training of auto-encoders so that the learned encoding function has the locality-preserving property for data points on the manifold.

65 citations

Journal ArticleDOI
TL;DR: In this paper, a study of generic submanifolds in a Kahler manifold from a differential geometric point of view is presented. And fundamental results in this respect are obtained.
Abstract: LetN be a real submanifold in a complex manifoldM. If the maximal complex subspaces of the tangent spaces ofM contained in the tangent spaces ofN are of constant dimension and they define a differentiable distribution, thenN is called a generic submanifold. The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds andCR-submanifolds. In this paper we initiate a study of generic submanifolds in a Kahler manifold from differential geometric point of view. Some fundamental results in this respect will be obtained.

64 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a method to compute the joint probability distribution of the eigenvalues of the one-body reduced density matrices of a random quantum state of multiple distinguishable or indistinguishable particles.
Abstract: Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced density matrices. As a corollary, by taking the distribution’s support, which is a convex moment polytope, we recover a complete solution to the one-body quantum marginal problem. We obtain the probability distribution by reducing to the corresponding distribution of diagonal entries (i.e., to the quantitative version of a classical marginal problem), which is then determined algorithmically. This reduction applies more generally to symplectic geometry, relating invariant measures for the coadjoint action of a compact Lie group to their projections onto a Cartan subalgebra, and can also be quantized to provide an efficient algorithm for computing bounded height Kronecker and plethysm coefficients.

61 citations

Journal ArticleDOI
TL;DR: In this article, an optimal transportation (OT) view of GANs is introduced, where the generator computes the OT map and the discriminator computes Wasserstein distance between the generated data distribution and the real data distribution.

58 citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202159
202067
201953
201843
201733