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We expect traversal along the identity manifold to result in gradual shape transition and valid shape interpolation between known targets.
The system implemented using these operations guarantees a unique and valid shape for each intermediate LOD in the simultaneous multiresolution modeling environment.
However it cannot be said with certainty that any arbitrary vector i∈ span i1,..., i N ) will result in a valid shape interpolation due to the sparse nature of the training set in terms of the identity variation.
The manifold topology T * defined in (1) tends to group targets of similar 3D shapes and/or the same class together, enforcing the best local semantic smoothness along the identity manifold, which is essential for a valid shape interpolation between target types.
We refer to this 1D structure as the identity manifold denoted by M ⊂ ℝ N. Then an arbitrary identity vector i ∈ M would be semantically meaningful due to its proximity to the basis vectors, and should support a valid shape interpolation.
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Through selectively emphasising particular issues, the media can shape what views and interpretations are seen to be most valid, shaping people's perceptions of reality, risk and blame which, in turn, may influence their health behaviours [ 6– 8].
In order to be classified as valid, the shape of the candidate brushstroke should be comprised within a range of aspect ratios.
In particular, the continuous nature of the proposed identity manifold makes it possible to interpolate valid target shapes between known targets in the training data.
In comparison to conventional coating methods, polyelectrolyte multilayers are easy to prepare and the procedure is valid whatever the shape of the solid.
The expression is valid for any shape of cross-section, subjected to combined axial loads and biaxial bending, both for short-time and sustained loads, normal and high strength concretes, but it is only suitable for columns with equal effective buckling lengths in the two principal bending planes.
We now point out that the result can be valid for any shape of the hole in the aperture, and, furthermore, it requires only that the electric field is equal and opposite at large distances above and below the aperture, respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com