Lower tail dependence for Archimedean copulas: Characterizations and pitfalls

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution. For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the lower tail dependence copulas to the Clayton copula. In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable. Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas still do not need to converge to the independent copula.     

Nonparametric estimation of an extreme-value copula in arbitrary dimensions

Inference on an extreme-value copula usually proceeds via its Pickands dependence function, which is a convex function on the unit simplex satisfying certain inequality constraints. In the setting of an i.i.d. random sample from a multivariate distribution with known margins and an unknown extreme-value copula, an extension of the Capéraà-Fougères-Genest estimator was introduced by D. Zhang, M. T. Wells and L. Peng [Nonparametric estimation of the dependence function for a multivariate extreme-value distribution, Journal of Multivariate Analysis 99 (4) (2008) 577-588]. The joint asymptotic distribution of the estimator as a random function on the simplex was not provided. Moreover, implementation of the estimator requires the choice of a number of weight functions on the simplex, the issue of their optimal selection being left unresolved.A new, simplified representation of the CFG-estimator combined with standard empirical process theory provides the means to uncover its asymptotic distribution in the space of continuous, real-valued functions on the simplex. Moreover, the ordinary least-squares estimator of the intercept in a certain linear regression model provides an adaptive version of the CFG-estimator whose asymptotic behavior is the same as if the variance-minimizing weight functions were used. As illustrated in a simulation study, the gain in efficiency can be quite sizable.     

Assessing the suitability of capillary electrophoresis‐mass spectrometry for biomarker discovery in plasma‐based metabolomics

The actual utility of capillary electrophoresis‐mass spectrometry (CE‐MS) for biomarker discovery using metabolomics still needs to be assessed. Therefore, a simulated comparative metabolic profiling study for biomarker discovery by CE‐MS was performed, using pooled human plasma samples with spiked biomarkers. Two studies have been carried out in this work. Focus of study I was on comparing two sets of plasma samples, in which one set (class I) was spiked with five isotope‐labeled compounds, whereas another set (class II) was spiked with six different isotope‐labeled compounds. In study II, focus was also on comparing two sets of plasma samples, however, the isotope‐labeled compounds were spiked to both class I and class II samples but with concentrations which differ by a factor two between both classes (with one compound absent in each class). The aim was to determine whether CEMS‐based metabolomics could reveal the spiked biomarkers as the main classifiers, applying two different data analysis software tools (MetaboAnalyst and Matlab). Unsupervised analysis of the recorded metabolic profiles revealed a clear distinction between class I and class II plasma samples in both studies. This classification was mainly attributed to the spiked isotope‐labeled compounds, thereby emphasizing the utility of CE‐MS for biomarker discovery.     

Silane-silanol condensation catalyzed by organotin compounds

The rate of condensation of H–SiR₂–(OSiR₂)_n–H (n=2, 3 or 4 and R=CH₃) and HO-SiRR–(OSiRR)₃–OH (R=C₆H₅) in xylene at 100 °C, catalyzed by dibutyltin diacetate, dilaurate and di-(2-ethyl)hexanoate, has been studied by infrared spectroscopy. The kinetic law is first order in each reactant and the reaction is accompanied by autocondensation of the silanol. The mecha nism involves complexation of the silanol with the catalyst, followed by the attack of a silane or silanol molecule.

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H–SiR₂–(OSiR₂)_n–H ( n=2,3 4 R=CH₃) HO–SiRR–(OSiRR)₃–OH ( R=C₆H₅) 100° C, , -(2-) , . . .

     

Positron trapping in indium

The positron annihilation lineshape was measured in indium in the temperature range between 74 K and the melting point (430 K). A model based on self-trapping of positrons and trapping by vacancies was fitted through the data. A vacancy formation enthalpy of (0.48±0.03) eV was obtained.     

Temperature dependence of positron annihilation parameters in solid gallium

Positron annihilation measurements between 80 and 300 K indicate that in gallium positrons are not trapped in thermally induced vacancies. Also no clear evidence is obtained for self-trapping of positrons in gallium. The slight temperature dependence of the lineshape measurements is probably due to thermal expansion.     

Formation of a metallic contact: jump to contact revisited

The transition from tunneling to metallic contact between two surfaces does not always involve a jump, but can be smooth. We have observed that the configuration and material composition of the electrodes before contact largely determine the presence or absence of a jump. Moreover, when jumps are found preferential values of conductance have been identified. Through a combination of experiments, molecular dynamics, and first-principles transport calculations these conductance values are identified with atomic contacts of either monomers, dimers, or double-bond contacts.     

Ein Beitrag zum Einfluß des Stoffüberganges auf eine erzwungene Konvektion an einer fluiden Phasengrenze

The interfacial-dynamic behaviour of a fluid two-phase-system with mass transfer was investigated under influence of forced convection in the manner of flat jets directed to the interface. The tangential velocities were measured at a characteristic point near to the interface air/water or in the interface itself using a Laser-Doppler-Velocimeter in dependence on the velocities of jets into two phases in both cases with and without transfer of acetone. The variations of velocities due to the interfacial effects are only detectable at small velocities of the jets. They are discussed by model conceptions and compared with the results of a theoretical research of heat transfer in a fluid two-phase-system (Interfacial-dynamic surface renewal model).     

Determination of the ferromagnetic vacancy-formation enthalpy in α-iron by the positron method using the carbon-vacancy pair as a probe

The 511 keV positron annihilation lineshape was measured as a function of temperature between 600 and 1183 K in extremely pure and carbon-doped (50 and 750 appm C) iron. Whereas in pure iron no trapping of positrons is observed below the Curie temperature (1043 K), trapping in carbon-vacancy pairs is observed in this temperature range in the carbon-doped samples. This allowed us to determine the ferromagnetic vacancy-formation enthalpy as 2.0 ± 0.2 eV.     

Study of fast-neutron irradiated vitreous silica by positron annihilation methods

The nature of the glass-like structure as obtained by fast neutron irradiation of vitreous silica has been investigated by positron annihilation lifetime and Doppler broadening experiments. Comparing the annihilation parameters obtained in the unirradiated sample to those obtained in irradiated ones we observed that in the irradiated SiO₂ glasses the probability of positronium formation is reduced and the orthopositronium lifetime is increased. The decrease of the positronium formation probability is mainly attributed to the reduction of the amount of free-volume in compacted domains. The orthopositronium lifetime increase is explained by large free spaces generated along trajectories of fast knocked-on particles.