We present a Lie algebraic framework for vortex sheets as singular 2-forms with support of codimension 1, i.e. singular elements of a completion of the dual to the Lie algebra of divergence-free vector fields. This framework allows one to define the Poisson and symplectic structures on the space of vortex sheets, which interpolate between the corresponding structures on filaments and smooth vor...

In this work we pursue the singular-vector analysis of the integrable perturbations of conformal theories that was initiated in [1]. Here we consider the detailed study of the N = 1 superconformal theory and show that all integrable perturbations can be identified from a simple singular-vector argument. We identify these perturbations as theories based on affine Lie superalgebras and show that ...

We study the omega-limit sets ωX(x) in an isolating block U of a singular-hyperbolic attractor for three-dimensional vector fields X. We prove that for every vector field Y close to X the set {x ∈ U : ωY (x) contains a singularity} is residual in U . This is used to prove the persistence of singular-hyperbolic attractors with only one singularity as chain-transitive Lyapunov stable sets. These ...

In this paper, we propose a novel technique for video shot segmentation and classiication based on the Singular Value Decomposition (SVD). For the input video sequence, we create a feature-frame matrix A, and perform the SVD on it. From this SVD, we are able to not only derive the reened feature space to better segment the video sequence along time axis, but also deene metrics to enable classii...

An improved version of the well-known Poincaré-Dulac’s normal form theorem is first proposed. It is shown that, for a nonlinear vector field, a normal form near a singular point can always be chosen so that the number of nonlinear components is at most equal to the number of Jordan blocks in the normalized leading matrix, thus leading to the “simplest” form in which a formal vector field can be...

In an orthogonal vector space of type l)/(4n, q), a spread is a family of q2n-l+ totally singular 2n-spaces which induces a partition of the singular points; these spreads are closely related to Kerdock sets. In a 2m-dimensional vector space over GF(q), a spread is a family of q + subspaces of dimension m which induces a partition of the points of the underlying projective space; these spreads ...

We propose a rank-k variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation (1-SVD) in Frank-Wolfe with a top-k singular-vector computation (k-SVD), which can be done by repeatedly applying 1-SVD k times. Our algorithm has a linear convergence rate when the objective function is smooth and str...

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral operator, acting on LpX(R ) with p ∈ (1,∞). Moreover, replacing equality by a linear equivalence, this is fo...

We study the omega-limit sets ω X (x) in an isolating block U of a singular-hyperbolic attractor for three-dimensional vector fields X. We prove that for every vector field Y close to X the set {x ∈ U : ω Y (x) contains a singularity} is residual in U. This is used to prove the persistence of singular-hyperbolic attractors with only one singularity as chain-transitive Lyapunov stable sets. Thes...

A novel feature set for low-dimensional signal representation, designed for classification or clustering of non-stationary signals with complex variation in time and frequency, is presented. The feature representation of a signal is given by the first left and right singular vectors of its ambiguity spectrum matrix. If the ambiguity matrix is of low rank, most signal information in time directi...