Support vector channel selection in BCI

Designing a brain computer interface (BCI) system one can choose from a variety of features that may be useful for classifying brain activity during a mental task. For the special case of classifying electroencephalogram (EEG) signals we propose the usage of the state of the art feature selection algorithms Recursive Feature Elimination and Zero-Norm Optimization which are based on the training of support vector machines (SVM). These algorithms can provide more accurate solutions than standard filter methods for feature selection. We adapt the methods for the purpose of selecting EEG channels. For a motor imagery paradigm we show that the number of used channels can be reduced significantly without increasing the classification error. The resulting best channels agree well with the expected underlying cortical activity patterns during the mental tasks. Furthermore we show how time dependent task specific information can be visualized.     

RHF and two-configuration SCF calculations are inappropriate for conjugated diradicals

Restricted Hartee Fock (RHF) and two-configuration self-consistent field (TCSCF) calculations provide qualitatively correct molecular orbitals for the two open-shell electrons in diradicals. Nevertheless, these calculations fail to give correct relative energies and in some cases they even lead to incorrect geometries. Examples of these failures are given for both singlet and triplet states of some conjugated diradicals. In several cases these failures are related to the “doublet instability problem” in RHF calculations on radicals. It is argued that unrestricted Hartee-Fock (UHF) calculations on triplet states are more likely that RHF to provide accurate geometries.     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

A comparison of various methods for calculating unimolecular reaction rate constants

A test of the Kassel quantum expressions for unimolecular rate constants and densities of vibrational states is described. Rate constants are calculated for nine reactions previously used in such tests, over a wide range of temperatures and pressures. The Kassel expression using the geometric mean of the molecular vibration frequencies is generally found to give better results than that using the arithmetic mean.     

Studies in qualitative inorganic analysis. XIX

Summary A procedure for the separation of magnesium in the final (soluble) Group of the systematic qualitative semimicro inorganic analysis scheme is described which uses a solvent extraction technique with 8-hydroxy-quinoline in chloroform. Magnesium is detected in the ignition residue of the extract by means of the Titan yellow test. The method has several advantages over other means for the separation of magnesium in qualitative analysis.

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Zusammenfassung Ein Verfahren für die Abtrennung des Magnesiums von der letzten Gruppe des systematischen anorganischen Halbmikroanalysenganges wird beschrieben. Es beruht auf der Extraktion des Magnesiums mit chloroformischer 8-Hydroxy-chinolinlösung. Der Extraktrückstand wird verglüht und das Magnesium mit Titangelb nachgewiesen. Die Methode hat gegenüber anderen Möglichkeiten zur Abtrennung des Magnesiums in der qualitativen Analyse verschiedene Vorteile.

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Résumé On décrit un procédé de séparation du magnésium dans le groupe final (soluble) du schéma d'analyse minérale qualitative systématique à l'échelle semimicro, utilisant une technique d'extraction par solvant avec l'hydroxy-8 quinoléine dans le chloroforme. On recherche le magnésium dans le résidu de combustion de l'extrait en effectuant l'essai au jaune titane. La méthode présente plusieurs avantages sur les autres procédés de séparation du magnésium en analyse qualitative.

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Part XVIII. Mikrochim. Acta [Wien]1961, 88.

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Dedicated to Prof.A. A. Benedetti-Pichler on the occasion of his 70th birthday.     

Photon structure functions beyond the SUSY threshold

We evolve virtual photon parton densities up to the SUSY threshold and higher using coupled inhomogeneous DGLAP differential equations. Reliable input parameterizations were available from the c-quark threshold. Limited (target photon virtuality) dependence is observed. The difference to the photon structure function is shown to be significant with the introduction of SUSY dependent splitting functions. A negligible difference is observed by letting the gluino mass enter after the squark mass. An effort is made to include the squark threshold effect in such a way that both the renormalization group equations are satisfied and the perturbative calculation is reproduced. Received: 25 August 2000 / Revised version: 1 November 2000 / Published online: 21 December 2000     

Mass spectra of boron compounds

The infrared and Raman spectra of six compounds (trimethylsiloxyethylene, (CH₃)₃SiOCHCH₂, methoxytrimethylsilane, (CH₃)₃SiOCH₃, and their deuterated derivatives: (CD₃)₃SiOCHCH₂, (CH₃)₃SiOCDCD₂, (CD₃)₃SiOCH₃, (CH₃)₃SiOCD₃ have been analysed.The majority of the bands observed have been assigned, in particular those due to ν(SiO).The study of the vinyl compounds shows that the enoxysilane exists in two conformers, the major being the gauche and the minor the s-cis one.     

Strict <Emphasis Type="Italic">p</Emphasis>-negative type of a metric space

Doust and Weston (J Funct Anal 254:2336–2364, 2008) have introduced a new method called enhanced negative type for calculating a non-trivial lower bound \({\wp_{T}}\) on the supremal strict p-negative type of any given finite metric tree (T, d). In the context of finite metric trees any such lower bound \({\wp_{T} >1 }\) is deemed to be non-trivial. In this paper we refine the technique of enhanced negative type and show how it may be applied more generally to any finite metric space (X, d) that is known to have strict p-negative type for some p ≥ 0. This allows us to significantly improve the lower bounds on the supremal strict p-negative type of finite metric trees that were given in Doust and Weston (J Funct Anal 254:2336–2364, 2008, Corollary 5.5) and, moreover, leads in to one of our main results: the supremal p-negative type of a finite metric space cannot be strict. By way of application we are then able to exhibit large classes of finite metric spaces (such as finite isometric subspaces of Hadamard manifolds) that must have strict p-negative type for some p > 1. We also show that if a metric space (finite or otherwise) has p-negative type for some p > 0, then it must have strict q-negative type for all \({q \in [0, p)}\) . This generalizes Schoenberg (Ann Math 38:787–793, 1937, Theorem 2) and leads to a complete classification of the intervals on which a metric space may have strict p-negative type.