Sentence examples for manifold mapping from inspiring English sources

In this paper, we propose a comprehensible framework for nonlinear classifier design, called Manifold Mapping Machine (M3).

Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N.

In these cases it is possible to ask empirically how motions on this low dimensional manifold map into movements relative to the outside world.

We repair this discrepancy by exploiting the correspondence with defect-correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the exact solution.

The Neumann operator is an operator on the boundary of a smooth manifold which maps the boundary value of a harmonic function to its normal derivative.

We then obtain a set of equations that, while defined on the whole Euclidean space, are intrinsic to the implicitly defined target manifold and map into it.

In particular, the key notion of invariant manifold for maps in nonlinear discrete-time dynamics is shown to be conceptually insightful and technically quite effective to address important issues related to the deterministic observerbased nonlinear state estimation problem in the discrete-time domain.

This is illustrated in Figure 1(c), where two different pieces of the original manifold are mapped to the same piece of the immersed manifold, producing an immersion that is not an embedding.

When creating the subspace, each input domain is treated as a manifold and the mapping function is constructed for each input domain while preserving the topology of each one.

Our method can be generalized to compute two-dimensional unstable manifolds of maps with three-dimensional state spaces.

Numerical simulations of the stable and unstable manifolds, Poincaré maps, Lyapunov exponents and fractal basin boundaries are performed.