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Showing 1 to 6 of 6 for “"hyper-sphere"”.
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Nonparametric Modelling for Directional Data
… with corresponding support space on a circle, a hyper-sphere, and a torus, respectively. As conventional statistical tools and algorithms are mostly designed for data in an Euclidean space, it motivates us to develop special techniques for directional data to accommodate their general support on …
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Fock's representation for molecular orbitals
… by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R<sub>4</sub> spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter …
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Beran Estimation of the Fisher-Bingham and Curved Kent Distributions
… be considered as a point incident to the unit hyper-sphere S^(p-1). Techniques for developing statistical tools to analyze directional data have a long and established history. Due to this interest in directional statistics, several probability distributions have been developed for data over …
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Efficient and Robust Black-box Integral-approximation and Optimization
… points set for integral approximation on hyper-sphere. Our structured point sets can serve as a good initialization for black-box optimization. Moreover, we propose stochastic black-box optimization with implicit natural gradients for black-box optimization. Our method is very simple and …
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Motor Imagery Based Brain Computer Interfaces
… of input signal on a dense uniformly sampled hyper-sphere. A novel non-uniform sampling scheme is proposed to estimate the local mean of multivariate signals. The non-uniform samples are generated by linearly transforming the hypersphere into an N dimensional ellipsoid using singular value …
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Spatiotemporal random bipartite matching problems and applications in mobility systems
… uniformly distributed on the surface of a hyper-sphere in a D-dimensional Euclidean space; and (iii) RBMP-B, where the vertices are uniformly distributed in a hyper-ball within a D-dimensional Lp space. All derived formulas are verified by a series of Monte-Carlo simulation experiments, …