Correction to: On the Stability and Accuracy of Least Squares Approximations

Foundations of Computational Mathematics - The inequality on line 8 of page 826 is stated in the wrong direction     

The degree of shape preserving weighted polynomial approximation

We analyze the degree of shape preserving weighted polynomial approximation for exponential weights on the whole real line. In particular, we establish a Jackson type estimate.     

Phenotyping of CYP450 in human liver microsomes using the cocktail approach

The cocktail approach is an advantageous strategy used to monitor the activities of several cytochromes P450 (CYPs) in a single test to increase the throughput of in vitro phenotyping studies. In this study, a cocktail mixture was developed with eight CYP-specific probe substrates to simultaneously evaluate the activity of the most important CYPs, namely, CYP1A2, CYP2A6, CYP2B6, CYP2C9, CYP2C19, CYP2D6, CYP2E1, and the CYP3A subfamily. After cocktail incubation in the presence of human liver microsomes (HLMs), the eight selected substrates and their specific metabolites were analyzed by ultra-high-pressure liquid chromatography and electrospray ionization quadrupole time-of-flight mass spectrometry. Qualitative and quantitative data were simultaneously acquired to produce an overview of the extended phase I biotransformation routes for each probe substrate in the HLMs and to generate phenotypic profiles of various HLMs. A comparison of the cocktail strategy with an individual substrate assay for each CYP produced similar results. Moreover, the cocktail was tested on HLMs with different allelic variants and/or in the presence of selective inhibitors. The results were in agreement with the genetic polymorphisms of the CYPs and the expected effect of the alterations. All of these experiments confirmed the reliability of this cocktail assay for phenotyping of the microsomal CYPs.     

NAIMA as a solution for future GMO diagnostics challenges

In the field of genetically modified organism (GMO) diagnostics, real-time PCR has been the method of choice for target detection and quantification in most laboratories. Despite its numerous advantages, however, the lack of a true multiplexing option may render real-time PCR less practical in the face of future GMO detection challenges such as the multiplicity and increasing complexity of new transgenic events, as well as the repeated occurrence of unauthorized GMOs on the market. In this context, we recently reported the development of a novel multiplex quantitative DNA-based target amplification method, named NASBA implemented microarray analysis (NAIMA), which is suitable for sensitive, specific and quantitative detection of GMOs on a microarray. In this article, the performance of NAIMA is compared with that of real-time PCR, the focus being their performances in view of the upcoming challenge to detect/quantify an increasing number of possible GMOs at a sustainable cost and affordable staff effort. Finally, we present our conclusions concerning the applicability of NAIMA for future use in GMO diagnostics.     

Logic and Colour

In this paper evidence will be provided that Wittgenstein??s intuition about the logic of colour relations is to be taken near-literally. Starting from the Aristotelian oppositions between propositions as represented in the logical square of oppositions on the one hand and oppositions between primary and secondary colors as represented in an octahedron on the other, it will be shown algebraically how definitions for the former carry over to the realm of colour categories and describe very precisely the relations obtaining between the known primary and secondary colours. Linguistic evidence for the reality of the resulting isomorphism will be provided. For example, the vertices that resist natural single-item lexicalization in logic (such as the O-corner, for which there is no natural lexicalization *nall (=not all)) are not naturally lexicalized in the realm of colour terms either. From the perspective of the architecture of cognition, the isomorphism suggests that the foundations of logical oppositions and negation may well be much more deeply rooted in the physiological structure of human cognition than is standardly assumed.     

Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway

Many terpenes used as fragrance compounds autoxidize when exposed to air, forming allylic hydroperoxides that have the potential to be skin contact allergens. To trigger the immunotoxicity process that characterizes contact allergy, these hydroperoxides are supposed to bind covalently to proteins in the skin via radical pathways. We investigated the formation of reactive radical intermediates from 7-hydroperoxy-3,7-dimethylocta-1,5-dien-3-ol and 2-hydroperoxylimonene, responsible for the sensitizing potential acquired by autoxidized linalool and limonene. Both compounds were synthesized through new short and reproducible synthetic pathways. The hydroperoxide decomposition catalyzed by Fe(II)/Fe(III) redox systems, playing a key role in degradating peroxides in vivo, was examined by spin-trapping-EPR spectroscopy. Alkoxyl and carbon-centered free radicals derived from the hydroperoxides were successfully trapped by the spin-trap 5,5-dimethyl-1-pyrroline N-oxide, whereas peroxyl radicals were characterized by spin-trapping studies with 5-diethoxyphosphoryl-5-methyl-1-pyrroline N-oxide. Using liquid chromatography combined with mass spectrometry, we demonstrated the formation of adducts, via radical mechanisms induced by Fe(II)/Fe(III), between the hydroperoxides and N-acetylhistidine methyl ester, a model amino acid that is prone to radical reactions. Free radicals derived from these hydroperoxides can thus induce amino acid chemical modifications via radical mechanisms. The study of these mechanisms will help to understand the sensitizing potential of hydroperoxides.     

Time reversal of flexural waves in a beam at audible frequency

There has been very limited work on the application of time reversal to the propagation of audible frequency waves in mechanical structures. The present work concentrates on the application of time reversal to the focusing of audible range, flexural waves in an infinite beam, and to the detection of local heterogeneity in such a beam. Practical applications of time reversal of flexural waves in structures include vibration energy focusing, detection of vibratory or acoustic sources, and detection of defects in mechanical structures. An analytical model of flexural wave propagation in the beam as well as sensing and emission using piezoelectric transducers is presented. Time reversal experiments are conducted and compared to the model results in either a homogeneous beam or a beam with point mass heterogeneities. In the various situations tested, it is shown that time reversal effectively compensates the spreading in time of the impulse due to the dispersive propagation of flexural waves. One interesting aspect of this property is the generation of large amplitude impulsive responses in the beam using remote actuators. Finally, the "Decomposition de l'Operateur de Retournement Temporel" approach is examined to detect and localize point mass scatterers in the beam.     

Stability and optimization of dispersion-managed soliton control

Dispersion-managed solitons with in-line all-optical regeneration are shown to be subject to amplitude and timing-jitter instabilities. We identify and discuss the different natures of these instabilities by means of a linear stability analysis, which is in good agreement with the full numerical solutions of the governing equations. Stable pulse propagation can be achieved through appropriate choices of dispersion map and pulse energy.     

On the Theoretical and Numerical Control of a One-Dimensional Nonlinear Parabolic Partial Differential Equation

This paper deals with the analysis of the internal and boundary control of a one-dimensional parabolic partial differential equation with nonlinear diffusion. First, we prove a local null controllability result with distributed controls, locally supported in space. The proof relies on local inversion (more precisely, we use Liusternik’s Inverse Function Theorem), together with some appropriate specific estimates. We also establish a similar result with controls on one side of the boundary. Then, we consider an iterative algorithm for the computation of null controls, we prove the convergence of the iterates, and we perform some numerical experiments.