In [6], an adaptive method to approximate unorganized clouds of points by smooth surfaces based on wavelets has been described. The general fitting algorithm operates on a coarse-to-fine basis. It selects on each refinement level in a first step a reduced number of wavelets which are appropriate to represent the features of the data set. In a second step, the fitting surface is constructed as the linear combination of the wavelets which minimizes the distance to the data in a least squares sense. This is followed by a thresholding procedure on the wavelet coefficients to discard those which are too small to contribute much to the surface representation.
In this paper, we firstly generalize this strategy to a classically regularized least squares functional by adding a Sobolev norm, taking advantage of the capability of wavelets to characterize Sobolev spaces of even fractional order. After recalling the usual cross-validation technique to determine the involved smoothing parameters, some examples of fitting severely irregularly distributed data, synthetically produced and of geophysical origin, are presented. In order to reduce computational costs, we then introduce a multilevel generalized cross-validation technique which goes beyond the Sobolev formulation and exploits the hierarchical setting based on wavelets. We illustrate the performance of the new strategy on some geophysical data.
AMS subject classification 65T60, 62G09, 93E14, 93E24We gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft (KU 1028/7 1 and SFB 611) and by the Basque Government. 相似文献
The reaction between N1-acylacetamidrazones 1 and enol ether 2 is described. Depending on the reaction conditions and on the substitution pattern of amidrazones 2-acylhydrazino-4-methyl-6-trifluoro-methylpyridines 3 and/or 2-acylhydrazino-6-methyl-4-trifluoromethylpyridines 4 were obtained. 相似文献
Abstract In this paper we consider the problem of global analytic and Gevrey hypoellipticity and solvability for a class of partial
differential operators on a torus. We prove that global analytic and Gevrey hypoellipticity and solvability on the torus is
equivalent to certain Diophantine approximation properties.
Keywords: Global hypoellipticity, Global solvability, Gevrey classes, Diophantine approximation property
Mathematics Subject Classification (2000): 35D05, 46E10, 46F05, 58J99 相似文献
We study different qualitative properties of the semigroup generated by some degenerate differential elliptic operators on the standard simplex of Rd. Some methods are new and are based on the representation formulas of the semigroup in terms of iterates of suitable positive operators. The main result is the ultracontractivity property which is obtained in the setting of weighted Lp-spaces. We describe the asymptotic behavior of the semigroup and obtain the compactness property in the same setting and also in spaces of continuous functions. 相似文献
Summary We characterize the existence of proper holomorphic mappings between pseudoellipsoids of the form
. If f:()() is any such mapping, the existence of a subgroup of Aut (()) such that
is shown equivalent to a condition on the branch locus of f. 相似文献
Textiles represent an attractive class of materials for realizing wearable biosensors. Electronic textiles, or smart textiles, describe the convergence of electronics and textiles into fabrics, which are able to sense, compute, communicate, and actuate. As many different electronic systems can be connected to any clothing, a wearable system becomes more versatile, and the user can change its look depending on environmental changes and individual preference. In this review, we want to explain how it is possible to develop the sensing component of a wearable sensor by sol–gel method based on the use of opportune organofunctional trialkoxysilane precursors, such as 3-glycidoxypropyltrimethoxysilane. Results show that the halochromic dyestuffs are completely entrapped in the sol–gel coatings, both through chemical and physical interactions with the textile fabric. Moreover, a certain washing fastness was observed. Sensor films show excellent reproducibility, reversibility, and short response times, with dynamic ranges from pH 4.4–6.0 (Methyl Red), pH 6.0–7.0 (Nitrazine Yellow), and pH 4.5–8.3 (Litmus), respectively.
Analyzing mass spectrometry imaging data can be laborious and time consuming, and as the size and complexity of datasets grow, so does the need for robust automated processing methods. We here present a method for comprehensive, semi-targeted discovery of molecular distributions of interest from mass spectrometry imaging data, using widely available image similarity scoring algorithms to rank images by spatial correlation. A fast and powerful batch search method using a MATLAB implementation of structural similarity (SSIM) index scoring with a pre-selected reference distribution is demonstrated for two sample imaging datasets, a plant metabolite study using Artemisia annua leaf, and a drug distribution study using maraviroc-dosed macaque tissue.
