Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anisotropically Weighted and Nonholonomically Constrained Evolutions on
  Manifolds   We present evolution equations for a family of paths that results from
anisotropically weighting curve energies in non-linear statistics of manifold
valued data. This situation arises when performing inference on data that have
non-trivial covariance and are anisotropic distributed. The family can be
interpreted as most probable paths for a driving semi-martingale that through
stochastic development is mapped to the manifold. We discuss how the paths are
projections of geodesics for a sub-Riemannian metric on the frame bundle of the
manifold, and how the curvature of the underlying connection appears in the
sub-Riemannian Hamilton-Jacobi equations. Evolution equations for both metric
and cometric formulations of the sub-Riemannian metric are derived. We
furthermore show how rank-deficient metrics can be mixed with an underlying
Riemannian metric, and we relate the paths to geodesics and polynomials in
Riemannian geometry. Examples from the family of paths are visualized on
embedded surfaces, and we explore computational representations on finite
dimensional landmark manifolds with geometry induced from right-invariant
metrics on diffeomorphism groups.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga