Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, the singular set is an embedded one dimensional manifold and there are three type of points: Riemannian points where the two vector fields are linearly independent, Gr...

This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first consider the case of a strongly equiregular submanifold, i.e., a smooth submanifold N for which the growth vector of the distribution D and the growth vector of the intersection of D with TN are constant on N...

This paper proposes a novel signature based on singular value decomposition (SVD) for video sequence matching. By considering the input image as a matrix, a partition procedure is first performed to separate the matrix into non-overlapping sub-images of a fixed size. The SVD process then individually decomposes each partitioned sub-image into an singular value and the corresponding singular vec...

We investigate the local conjugacy, at a partially hyperbolic fixed point, of a diffeomorphism (vector field) to its normally linear part in the presence of constraints, where the change of variables also must satisfy the constraints. The main result is applied to vector fields respecting a singular foliation, encountered, by F. Dumortier and R. Roussarie, in the desingularization of families o...

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems. It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a Cauchy matrix-vector product. With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank1 perturbed ma...

The aim of this paper is to address computational aspects of the total energy singular vector analysis of atmospheric chemical transport models. We discuss the symmetry of the tangent-linear/adjoint operator for stiff systems. Results for a 3D simulation with real data reveal that the total energy singular vectors depend on the target domain, simulation window, chemical reactions, and meteorolo...