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First, the underlying manifold structure of data is not considered in process modeling.
The structure of the linearized flow can then be translated into the manifold structure of the nonlinear flow.
The proposed LRMO algorithm analyzes the manifold structure of the overlay data and computes accurate overlay variations with a low computational complexity.
Our approach characterizes the manifold structure of each sample point using the geodesic distances between the sample point and given correspondences.
The proposed method preserves the manifold structure of labeled and unlabeled samples in addition to separating labeled samples in different classes from each other.
These approaches are instances of generative model, whereas they all ignore the manifold structure of data distribution, which is generally useful for preserving the nonlinear information.
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We present a construction of a Banach manifold structure on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space.
However, the effect of the manifold structure on the flow distribution in the lumen side appears to be negligible.
Taking the two basic structure units into account, new quaternary structure model describing the manifold structures of hiPP particles has been proposed.
The group and manifold structures of G are meshed together by the condition that the product operation is a differentiable mapping of G × G into G.
We propose to take advantage of this manifold structure for the effective classification of the object represented by the observation set.
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Justyna Jupowicz-Kozak
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