We study analytical and numerical properties of the L1−L2 minimization problem for sparse representation of a signal over a highly coherent dictionary. Though the L1 −L2 metric is non-convex, it is Lipschitz continuous. The difference of convex algorithm (DCA) is readily applicable for computing the sparse representation coefficients. The L1 minimization appears as an initialization step of DCA...

Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional that are not only subject noise along their y axis but also random warping x axis, we refer as the time axis. Conventional distances functions, such L2 distance, under these conditions. The Fisher–Rao metric...

We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk . The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best approximates the given measurements in the directions u1, . . . , uk (in the least squares sense). ...

The variance of a fuzzy random variable plays an important role as a measure of central tendency. Some of the main contributions in this topic are consolidated and discussed in this paper. In case of the hypothesis testing problem, bootstrap techniques (Efron and Tibshirani, 1993) have empirically been shown to be efficient and powerful. Algorithms to apply these techniques in practice and some...

In [20] we presented a semantic study of a language LJ that extends Hoares CSP model with communication on multiple channels and synchronization based on join patterns in the style of Join calculus. In this paper we consider a language L2 J that extends LJ with second order communication: sending and receiving of statements rather than values. We employ the mathematical methodology of metric se...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...

In the last lecture we defined metric spaces, normed spaces, and considered the distortion resulting from certain embeddings. In particular, we proved that l1 norms cannot always be embedded isometrically into l2 by considering a specific four-point l1 norm and showing that it requires at least √ 2 distortion. Today’s lecture further explores the 1 norm. We see a couple of interesting examples ...

Typical measures for closed loop systems are so-called gaps between two systems, classically either L2 or H2 gap. Here, the distance between to candidate models for a plant can be measured taking all possible combinations of bounded input and output signals into account. Rather recently, a variant of theses gaps, the ν − gap, gained interest in the “identification for control” community. This r...

We prove a variational principle for stochastic flows on manifolds. It extends V. Arnold’s description of Lagrangian Euler flows, which are geodesics for the L2 metric on the manifold, to the stochastic case. Here we obtain stochastic Lagrangian flows with mean velocity (drift) satisfying the NavierStokes equations. We study the stability properties of such trajectories as well as the evolution...