A Gagliardo–Nirenberg inequality, with application to duality-based a posteriori error estimation in the L 1 norm Dedicated to Professor Boško S. Jovanovi´c on the occasion of his sixtieth birthday Endre Süli We establish the Gagliardo–Nirenberg-type multiplicative interpolation inequality v L 1 (R n) ≤ Cv 1/2 Lip (R n) v 1/2 BV(R n) ∀v ∈ BV(R n), where C is a positive constant, independent of ...

The generalized lasso problem penalizes the `1 norm of a matrix D times the coefficient vector to be modeled, and has a wide range of applications, dictated by the choice of D. Special cases include the trend filtering and fused lasso problem classes. We consider in this talk highly efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor [1]. This covers ...

A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green’s function and its firstand second-order derivatives are established in the L1 norm by employing the parametrix method. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be...

We consider the problem of representing individual faces by maximum L1-norm projection subspaces calculated from available face-image ensembles. In contrast to conventional L2-norm subspaces, L1-norm subspaces are seen to offer significant robustness to image variations, disturbances, and rank selection. Face recognition becomes then the problem of associating a new unknown face image to the “c...

Let Σ be the algebraic universal cover of a closed surface of genus g > 1, T (Σ) its Teichmüller space, M(Σ,ℓ) the group of mapping classes stabilizing a fixed leaf ℓ. The L 1 Ehrenpreis conjecture asserts that M(Σ,ℓ) acts on T (Σ) with dense orbits in the L 1 topology (the topology coming from the L 1 norm on quadratic differentials). We give a proof of this weaker version of the Ehrenpreis co...

In this paper we investigate the large-time behavior of solutions to the first initial-boundary value problem for the non-linear diffusion ut = (u )xx, m > 0. In particular, we prove exponential decay of u(x, t) towards its own steady state in L1-norm for long times and we give an explicit upper bound for the rate of decay. The result is based on a new application of entropy estimates, and on d...

Resource discovery in a Grid environment is a critical problem and also a fundamental task which provides searching and locating necessary resources for given processes. Based on the domain and resource routing nodes, a grid resource discovery model of multilayer overlay network is given in this paper. And on this basis, using a linear combination of the block distance and chessboard distance i...

This paper studies trajectory generation for a mothership that tows a drogue using a flexible cable. The contributions of this paper include model validation for the towed cable system described by a lumped mass extensible cable using flight data, and optimal trajectory generation for the towed cable system with tension constraints using model predictive control. The optimization problem is for...

The two dimensional bandwidth problem under the distances of L∞-norm and L1-norm has only been studied for a limited number of graphs. In this paper, I analyze the two dimensional bandwidth for a few different families of graphs.

I apply the iterative hyperbolic Radon transform to CMP gathers to create a velocity panel where multiples and primaries are separable. The velocity panel is created using three different inversion schemes: (1) l2 norm inversion, (2) l1 norm inversion and (3) l1 norm with l1 regularization inversion. The third technique is particularly efficient at separating primaries and multiples in the pres...