A PAC-Bayesian margin bound for linear classifiers

We present a bound on the generalization error of linear classifiers in terms of a refined margin quantity on the training sample. The result is obtained in a probably approximately correct (PAC)-Bayesian framework and is based on geometrical arguments in the space of linear classifiers. The new bound constitutes an exponential improvement of the so far tightest margin bound, which was developed in the luckiness framework, and scales logarithmically in the inverse margin. Even in the case of less training examples than input dimensions sufficiently large margins lead to nontrivial bound values and-for maximum margins-to a vanishing complexity term. In contrast to previous results, however, the new bound does depend on the dimensionality of feature space. The analysis shows that the classical margin is too coarse a measure for the essential quantity that controls the generalization error: the fraction of hypothesis space consistent with the training sample. The practical relevance of the result lies in the fact that the well-known support vector machine is optimal with respect to the new bound only if the feature vectors in the training sample are all of the same length. As a consequence, we recommend to use support vector machines (SVMs) on normalized feature vectors only. Numerical simulations support this recommendation and demonstrate that the new error bound can be used for the purpose of model selection.     

Synthese und Molekülstruktur von Li[(Me2NCH2CH2CH2)4Yb]

Preparation and Structure of Li[(Me₂NCH₂CH₂CH₂)₄Yb] YbCl₃ reacts with dimethylaminopropyl lithium in tetrahydrofuran with formation of Li[(Me₂NCH₂CH₂CH₂)₄Yb]. The X-ray structure determination proves the formation of chelat rings by two of the ligands. The nitrogens of the other two ligands are coordinated to the lithium. The compound crystallizes in the monoclinic space group C2/c with the unit cell parameters a = 27.854(8) Å, b = 9.183(3) Å, c = 20.125(8) Å, β = 96.40° and Z = 8.     

Motorkraftstoffe

Ohne Zusammenfassung     

Berechnung der Molmasseverteilung und der Verteilung der Monomerarten

Ohne Zusammenfassung     

Darstellung und Eigenschaften von 3-(N,N-Dimethylamino)propyl-Verbindungen des Thalliums

Preparation and Properties of 3-(N,N-Dimethylamino)propyl Thallium Compounds TlCl₃ reacts with Me₂NCH₂CH₂CH₂Li in molar ratio 1:2 with formation of (Me₂NCH₂CH₂CH₂)₂TlCl ( 1 ) which can be transfered with MeLi into (Me₂NCH₂CH₂CH₂)₂TlMe ( 2 ) and with excess of Me₂NCH₂CH₂CH₂Li into (Me₂NCH₂CH₂CH₂)₃Tl ( 3 ) respectively. Comproportionation of 1 with TlCl₃ yields rather instable Me₂NCH₂CH₂CH₂TlCl₂ ( 4 ) from which Me₂NCH₂CH₂CH₂TlMe₂ ( 5 ) can be obtained by alkylation with MeLi. 1–3 and 5 were characterized by elemental analysis, mass spectra, ¹H- and ¹³C-n.m.r. spectra.     

Label-Free Spatial Analysis of Free and Enzyme-Bound NAD(P)H in the Presence of High Concentrations of Melanin

The analysis of autofluorescence, often regarded as undesired noise during the imaging of biological samples, allows label free, unbiased detection of NAD(P)H and melanin in native samples. Because both the emission and absorption spectra of these fluorophores overlap and they can hence not be differentiated using emission filters or with different excitation wavelengths, fluorescence lifetime imaging microscopy (FLIM) is used to differentiate between them. In the present paper the application of two-photon excitation microscopy is presented to investigate the autofluorescence of fungal spores. The model organism which was examined is Aspergillus ochraceus. Furthermore a strategy is developed which allows to quantitatively analyze the fluorescence lifetimes of melanin, free NAD(P)H and protein-bound NAD(P)H using forward convolution of a multiexponential decay function with the instrument response function (IRF) and subsequent fitting to the experimental fluorescence data. As a consequence proteins, which are able to bind NAD(P)H, are located with sub-cellular resolution. Furthermore a spatial differentiation of the fluorophores NAD(P)H and melanin inside the spores, is revealed.     

Berechnung der Teilums?tze der Monomeren, der mittleren Zusammensetzung und des mittleren Polymerisationsgrades des Copolymeren sowie der optimalen Seiteneinspeisung

Ohne Zusammenfassung     

Die 3-(N,N-Dimethylamino)prop-1-enyl-Gruppe als Chelatligand in Organoindium-Verbindungen

The 3-(N,N-Dimethylamino)prop-1-enyl Group as a Chelate Ligand in Indium Organyls InBr₃ reacts with Me₂NCH₂CH?CHMgCl (molar ratio 1 : 2) to form (Me₂NCH₂CH?CH)₂InBr ( 1 ) as the first indium alkenyl compound with amino-functionalized alkenyl groups. The X-ray structure determination shows the formation of a chelate complex. 1 crystallizes in the orthorhombic space group Fddd with the unit cell parameters a = 14.904(2) Å, b = 17.140(1) Å and c = 21.035(2) Å. By reaction of Me₂InBr with Me₂NCH₂CH?CHMgCl (molar ratio 1 : 1) (Me₂NCH₂CH?CH)InMe₂ ( 2 ) is formed as a colorless, at room temperature liquid, monomeric compound. The n.m.r. and mass spectra are discussed.