of such an edge-preserving regularization. Under these conditions, we show that it is possible to introduce an auxiliary variable whose role is twofold. First, it marks the discontinuities and ensures their preservation from smoothing. Second, it makes the criterion half-quadratic. The optimization is then easier

Abstract We establish five facts about prices in the U.S. economy: 1) The median frequency of nonsale price change is 9-12% per month, roughly half of what it is including sales. This implies an uncensored median duration of regular prices of 8-11 months. Product turnover plays an important role

Variable selection plays an important role in high dimensional statistical modeling which nowa-days appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper

the original data exactly, and play an important role in fast multiresolution and wavelet techniques. Dyn, Gregory, and Levin introduced the Butterfly scheme, which yields C 1 surfaces in the topologically regular setting. Unfortunately it exhibits undesirable artifacts in the case of an irregular topology. We

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years several pioneering works suggested such a separation based on variational formulation, and others using independent component analysis

and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or tree-like data structures in which each level in the tree corresponds to a particular scale of representaion. Noting that scale plays the role of a time

Rational vertex operator algebras, which play a fundamental role in rational conformal field theory (see [BPZ] and [MS]), single out an important class of vertex operator algebras. Most vertex operator algebras which have been studied so far are rational vertex operator

problems including some kind of noisy tasks provided that the regularization parameter is chosen well. In particular we derive a simple su#cient condition for this parameter in the case of Gaussian RBF kernels. On the one hand our considerations are based on an investigation of an approximation property

role of prior knowledge is put forward, and we discuss the important notion of input-dependent regularization. We postulate a number of baseline methods, being algorithms or algorithmic schemes which can more or less straightforwardly be applied to the problem, without the need for genuinely new

of an ffl-free NFA due to to Glushkov [Glu61] is a natural representation of the regular expression, because it can be described in terms of the Brzozowski derivatives [Brz64] of the expression. Moreover, the Glushkov construction also plays a significant role in the document processing area: The SGML