Sentence examples for same manifold from inspiring English sources

Contact constraints are thus enforced on the same manifold as the accompanying structural problem.

The linear sub-arrays that are parallel to x-axis in the rectangular array share the same manifold when only the estimation of α is taken into account.

There is, however, a subtlety due to the fact that in general a manifold can be seen as many connected sums of the same manifold with spheres.

Sparse manifold clustering and embedding (SMCE) adaptively selects neighbor points from the same manifold and approximately spans a low-dimensional affine subspace, but it does not explicitly give a projection matrix and encounters the out-of-sample problem.

We selected waves with spike-like patterns that satisfy the shape constraints set in the 1st step of the method as the negative class, instead of choosing random background segments, because the more similar the two classes are, the more possible it is to occupy the same manifold and thus to allow learning the separation between them.

In fact, when we do a cut on a sphere, for instance in the n = 1 case, what we are doing is the following: take a manifold and remove a ball B3 from it, then take the same manifold, reverse the orientation, carve a ball B3, and identify the boundaries between the two.

Under the alternative rescaling to a (2F, 3SS) system, the projections of the solution trajectory are as shown in Fig. 16C and D. This system has the same critical manifold (mathscr {M}_{s}) as the original system.

These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold.

Moreover, it gives support to the notion of using multiple embeddings as a potentially efficient way of extracting information from time series data of limited length, but where there are potentially many simultaneous observations of dynamics on the same attractor manifold.

When R is not sterically demanding, or when the second olefin is too substituted, the evolution of B syn into C is more difficult and the formation of D becomes competitive, thus leading to the formation of 3.[ 3d– f,  10] The same mechanistic manifold is operative for substrate 4 a, thus leading to the formation of 5 and 6.

The time series have two properties: (1) a pair of time series lies on the same sub-manifold, (2) the sub-manifold of a pair of time series is smooth.