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The Gauss map can be defined for hypersurfaces in R n as a map from a hypersurface to the unit sphere S n − 1 ⊆ R n. For a general oriented k - submanifold of R n the Gauss map can also be defined, and its target space is the oriented Grassmannian G ~ k , n {\displaystyle {\tilde {G}}_{k,n}} , i.e. the set of all oriented k -planes in R n .
Cobweb plot of the Gauss map for = and =. This shows an 8-cycle. This shows an 8-cycle. In mathematics , the Gauss map (also known as Gaussian map [ 1 ] or mouse map ), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function :
2x mod 1 map, Bernoulli map, doubling map, sawtooth map Exponential map: discrete: complex: 2: 1: ... Gaussian map Generalized Baker map: Genesio-Tesi chaotic ...
The Gaussian curvature is the product of the two principal curvatures Κ = κ 1 κ 2. The sign of the Gaussian curvature can be used to characterise the surface. If both principal curvatures are of the same sign: κ 1 κ 2 > 0, then the Gaussian curvature is positive and the surface is said to have an elliptic point. At such points, the surface ...
The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior density over the quantity one wants to estimate.
t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map.
Eberflus acknowledged that the Bears did a poor job of blocking, but believes that the Packers made illegal contact with long snapper Scott Daly on the play and wants the NFL to take a second look.
Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, or kriging; extending Gaussian process regression to multiple target variables is known as cokriging. [26] Gaussian processes are thus useful as a powerful non-linear multivariate interpolation tool. Kriging is also used to extend Gaussian ...