Sentence examples for manifold directions from inspiring English sources

Moreover, the local linearity assumption around certain data points may be violated, at least anisotropically (i.e. only in some manifold directions).

Based on normal form theory and center manifold theorem, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied.

The is th signal's direction manifold vector, superscript is the transpose operation and the symbol denotes the Kronecker tensor.

By the theory of normal form and the center manifold method, the direction and stability of the bifurcating periodic solution are discussed.

The multivalued density and higher moments are thus resolved by integrating f along the n-dimensional manifold in the phase directions.

While Eq. (2) provides the set of Lyapunov exponents of an attractor, Eq. (3) provides the Lyapunov exponents of the synchronization manifold and its transversal directions.

The angle ∅ can be interpreted as the relative amplitude of signal energy along the 1D which manifolds in two orthogonal directions.

The scattering relation maps the point and direction of a geodesic entering the manifold to the point and direction of exit of the geodesic.

Judging by her recent work the directions will be manifold and pursued with imagination and passion.

and z, z ¯ are the local coordinates of the center manifold Ω 0 in the directions of q ∗ and q ¯ ∗ respectively.

An example is given below, where the pdf is concentrated on a non-linear manifold due to fast, contracting directions.