Outlier detection and robust covariance estimation using mathematical programming

The outlier detection problem and the robust covariance estimation problem are often interchangeable. Without outliers, the classical method of maximum likelihood estimation (MLE) can be used to estimate parameters of a known distribution from observational data. When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them. Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions. However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance. An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given smaller weights and can be detected. This method produces a covariance estimator that has the following properties: First, it is affine equivariant. Second, it is computationally efficient even for large problem sizes. Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method is tested for different contamination models, including recently proposed ones. The method is not only faster than the Fast-MCD method for high dimensional data but also has reasonable accuracy for the tested cases.     

Laser conditioning and nonlinear absorption of LaF3/MgF2 dielectric multilayers at 193 nm

A sensitive and simple pulsed surface thermal lens (TL) technique is used in situ to investigate the laser conditioning and to measure the nonlinear absorption of LaF₃/MgF₂ dielectric multilayers deposited on CaF₂ substrates at 193 nm. Due to the high single-shot sensitivity of the surface TL technique, the laser conditioning can be monitored from the first shot of irradiation on a shot-by-shot basis. The LaF₃/MgF₂ multilayers show a very strong conditioning effect. The ratio of the absorption before and after the laser irradiation is in the range 4–8 for a highly reflective (LH)²⁰ LaF₃/MgF₂ multilayer, and 3–4 for (1L3H)⁷ and (3L1H)⁷ multilayers. In comparison, a (LH)²⁰ LaF₃/AlF₃ multilayer shows only a weak conditioning effect, with an absorption ratio of approximately 1.4. Our experimental results suggest that the strong conditioning effect of the LaF₃/MgF₂ multilayer is due to the absorption conditioning of the LaF₃ layers. However, the MgF₂ layers are shown to be responsible for the considerable increase in LaF₃ absorption as well as the ability to condition the absorption. The fluoride multilayers present non-negligible nonlinear absorption and the two-photon absorption coefficient of the multilayers is estimated to be approximately 5×10^-7 cm/W. Received: 11 December 2000 / Accepted: 20 February 2001 / Published online: 25 July 2001     

Zur Quantentheorie der stimulierten RAMAN-Streuung in Molekülkristallen. I. Einige Bemerkungen zur Theorie nach K. GROB

Stimulated RAMAN scattering in molecular crystals is quantum theoretically described as stimulated polariton scattering. The quantum theoretical treatment of molecular crystals is given within the framework of a second quantization described in an earlier work. In the HEISENBERG picture the equations of motion for the operators of the polaritons are derived and specialized for RAMAN scattering. By supposing quasi-stationary behaviour the operators of the polaritons that are mixtures of phonons and photons are eliminated. The resulting equations are shown to have the same structure but a generalized physical meaning as those derived by GROB on other way.     

Molekülstruktur und Retentionsverhalten I. Strukturelle Zuordnssung von thermischen Umlagerungsprodukten der Cyclododecatriene (1.5.9) mittles Gas-Adsorptions-Chromatographie

Zusammenfassung In der vorliegenden Arbeit wurden für einige durch thermischen Umlagerung von cyclododecatrien-(1.5.9) erhaltene Kohlenwasserstoffe und ihre Hydrierungs-produkte Retentionsdaten an graphitiertem thermischen Ru? bestimmt. In Verbindung mit semiempirischen Berechnungen und durch Vergleich mit Retentionsdaten, die an Squalan-bzw. Ucon 50 HB 280×polar-Trennkapillaren gemesen wurden, konnte aus diesen, Werten eine konfigurative Zuordnung getroffen werden.

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Molecular structure and retention data I. Structure determination of thermal rearrangement products of 1.5.9-cyclododecatrienes by gas adsorption chromatography

Summary In the present paper, retention data on graphitized thermal carbon black were determined for some hydrocarbons obtained by thermal rearragement of 1.5.9-cyclododecatrienes, and their hydrogenation products. Thus, by semiempirical calculations and by comparison with retention data on open tubular columns coated with squalane or Ucon 50 HB 280×polar respectively, an assignment of configuration was possible.

     

Zur fraktalen Oberfl?chendimension chromatographisch relevanter Kieselgele

Ohne Zusammenfassung

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On the fractal surface dimension of silica used in liquid chromatography

     

Self-diffusion of lithium in LiAlSi2O6 glasses studied using mass spectrometry

In order to improve our understanding of the transport mechanisms of lithium in glasses, we have performed diffusion and ionic conductivity studies on spodumene composition (LiAlSi(2)O(6)) glasses. In diffusion couple experiments pairs of chemically identical glasses with different lithium isotopy (natural Li vs pure (7)Li) were processed at temperatures between 482 and 732 K. Profiles of lithium isotopes were measured after the diffusion runs innovatively applying femtosecond UV laser ablation combined with inductively coupled plasma mass spectrometry (LA ICP-MS). Self-diffusion coefficients of lithium in the glasses were determined by fitting the isotope profiles. During some of the diffusion experiments the electrical conductivity of the samples was intermittently measured by impedance spectrometry. Combining ionic conductivity and self-diffusivity yields a temperature-independent correlation factor of ~0.50, indicating that motions of Li ions are strongly correlated in this type of glasses. Lithium self-diffusivity in LiAlSi(2)O(6) glass was found to be very similar to that in lithium silicate glasses although Raman spectroscopy demonstrates structural differences between these glasses; that is, the aluminosilicate is completely polymerized while the lithium silicate glasses contain large fractions of nonbridging oxygen.     

Optical microcavities formed by semiconductor microtubes using a bottlelike geometry

We report on the realization of optical microtube resonators with a bottlelike geometry. The measured eigenenergies and the measured axial field distributions of the modes can be described by a straight and intuitive model using an adiabatic separation of the circulating and the axial propagation. The dispersion of the axial mode energies follows a photonic quasi-Schr?dinger equation including a quasipotential which can be determined for the actual geometry of the microtube in a precise and simple way. We show that tailoring the geometry of the microtube bottle resonators enables the realization of a wide variety of mode distributions and dispersion relations.     

Optimization of grating size in chirped-pulse-amplification. laser system

We performed calculations for a chirped-pulse-amplification laser system with a sub-100-fs pulse duration including the finite size of gratings in an aberration-free stretcher/compressor design. Both the higher-order phase dispersion and the spectral clipping, which is due to the finite size of the optics in the stretcher and the compressor, are taken into account in the calculation. We discuss the influence of both phase dispersion and spectral clipping on the important parameters of the recompressed pulse, such as pulse duration, pulse contrast, and peak intensity, employing different phase-dispersion compensation methods. The calculations show that the use of a small compressor grating reduces the higher-order phase errors and smoothes the sharp spectral cut-off caused by spectral clipping in the stretcher, which consequently improves the pulse contrast ratio of the main pulse to the pedestal. Received: 1 April 2000 / Published online: 8 November 2000     

Electrostatic ultra-low-energy antiproton recycling ring

There is a strong need to push forward developments in the storage and control of ultra-low-energy antiproton beams to enable important scientific research. To this end, a small electrostatic ring, and associated electrostatic acceleration section, is being designed and developed by the QUASAR group. The ring will be placed on the MUSASHI beamline at the CERN-AD. It will serve as a prototype for the future ultra-low energy storage ring (USR), to be integrated at the facility for low-energy antiproton and ion research (FLAIR) and will enable various components of the USR to be tested and optimised. A reaction microscope will be integrated in the ring to enable partial ionisation cross section measurements to be made. This small recycler ring will be unique due to its combination of size, electrostatic nature and energy and type of circulating particles (ca 3?C30 keV antiprotons). A short electrostatic accelerating section is also being developed, which will be placed between the beamline and the ring to accelerate the antiprotons from the trap extraction energy (typically 250 eV) to the final required (re-circulating) energy. The AD recycler project will be described, including ring design, accelerating injection section and the inclusion of a reaction microscope and the experiments it will enable.     

The Influence of Intramolecular Coupling between v(XH) and v(XH…Y) Modes on the IR Absorption Spectra of Hydrogen Bonded Species XH…Y

By modifying the simple Morse oscillator model usually used for describing the vibrational motion of a linear XH…Y complex a more realistic model is proposed, which is in better agreement with experimental results. The potential energy surface is derived by fitting the bond length, the dissociation energy of the H-bond, the bond length shortening, and the normal frequency of the v(XH) vibration to their observed values. From the resulting values of the transition matrix elements between low excited v(XH) and high excited v(XH…Y) quantum states it is shown, that for explaining the smoothness of the IR absorption bands the intramolecular coupling between v(XH) and v(XH…Y) stretching modes of vibration should be taken into account.