Weak properties and robustness of t-Hill estimators

We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile.     

Observation of the spin alignment of the ϱ0-meson produced in ¯pp interactions at 22.4 and 5.7 GeV/c

Studying the ⁰-meson production in ¯pp interactions at 22.4 GeV/c and in 4-prong anníhilation channels of ¯pp interactions at 5.7 GeV/c, we have observed an essential ⁰-meson spin alignment. The values of the ₀₀ element of the ⁰-meson spin density matrix (thez-axis is directed along the normal to the production plane) are equal to 0.08 ± 0.07 and 0.55 ± 0.03, respectively, i.e. the ⁰-meson spin lies preferably in the production plane. The absence of such an effect in pp interactions at 12 and 24 GeV/c and also the essentially larger ⁰ production cross section in ¯pp interactions at these energies make it possible to connect the observed ⁰-meson spin alignment with the annihilation processes. The character of the observed spin alignment is unexpected from the point of view of usual models, e.g. multiperipheral models. This effect could be described by the spontaneous polarization of quarks and antiquarks during the state preceding their recombination into mesons.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.The authors would like to express their gratitude to the CERN-Prague collaboration for permission to use their data on ¯pp interactions at 5.7 GeV/c. The authors are also indebted to A. M. Baldin, S. B. Gerasimov and H. I. Miettinen for valuable discussions, to the technicians and assistants at all laboratories for their work.     

Weighted estimates for the Hilbert transform of odd functions

The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak, or extra-weak type estimates in Orlicz classes for the integral operator $$H_0 f(x) = \frac{2}{\pi }\int_0^\infty {\frac{{yf(y)}}{{x^2 - y^2 }}dy, x \in (0,\infty )}$$ .     

No effect and lack-of-fit permutation tests for functional regression

This paper proposes statistical procedures to check if a real-valued covariate X has an effect on a functional response Y(t). A non-parametric kernel regression is considered to estimate the influence of X on Y(t) and two test statistics based on residual sums of squares and smoothing residuals are proposed. Their acceptance levels are determined by means of permutations. The lack-of-fit test for a class of parametric models is then discussed as a consequence of the no effect procedure. Monte Carlo simulations provide an insight into the level and the power of the no effect tests. A study of atmospheric radiation illustrates the behavior of the proposed methods in practice.     

Computer Simulation of In Vitro Formation of PHB Granules: Particulate Polymerization

The kinetics of poly(3‐hydroxybutyrate) granules formed in vitro from [R]‐(–)‐3‐hydroxybutyryl–Coenzyme A (CoA) monomer in the presence of PHA synthase were followed using transmission electron microscopy (TEM) and Cryo‐TEM. Round granules were formed rapidly at the beginning of the experiment, growing from the initially observed diameter of 0.1 μm to about 1 μm within a few minutes. In contrast to the rapid granule growth, the initial conversion (polymerization) rate was slow. After a lag phase lasting several minutes, the conversion rate reached its maximum value while the total number of granules steadily declined. We account for these observations as follows: • The initial granules are vesicle‐like, being stabilized by a monomolecular enzyme layer on their surface. • The initial granules are microporous, i.e., contain some polymer but are mainly filled with water. • The granules collide due to Brownian motion and coalescence occurs accounting for most of the diameter growth. • The polymerization is topotactic and is hindered by the surface energy required to extrude the hydrophobic polymer into the largely aqueous environment inside the granules. • As the granules accumulate PHB, polymerization is increasingly favored and its rate reaches a maximum. A computer program was written to test the model. The dynamic display simulates the in vitro growth of the granules in three‐dimensional space. The simulation mimics granule formation, monomer conversion, Brownian motion, and coalescence. The sizes and compositions of all particles are recorded and simulated data are plotted and compared with experimental observations. The computer simulation approximated the experimental data and validated the mechanistic hypotheses.     

On the mechanism of the laccase-mediator system in the oxidation of lignin

In an effort to elucidate the role of phenolic and non-phenolic lignin subunits in a laccase mediator (LM) system, vanillyl alcohol was oxidized with laccase in the presence and absence of the mediator 1-hydroxybenzotriazol (HBT). Furthermore, the role of phenolic, aliphatic hydroxyl, and carboxylic acid moieties in lignin degradation was elucidated by selectively blocking them. The modified samples were then subjected to laccase and laccase-HBT treatments. On the basis of this data it was possible to establish the role of this mediator. HBT mediates the oxidation of lignin by inducing side-chain oxidation and oxygen-addition products rather than oxidative coupling reactions.     

Analysis of human blood plasma and hen egg white by chiroptical spectroscopic methods (ECD, VCD, ROA)

Chiroptical methods are widely used in structural and conformational analyses of biopolymers. The application of these methods to investigations of biofluids would provide new avenues for the molecular diagnosis of protein-misfolding diseases. In this work, samples of human blood plasma and hen egg white were analyzed using a combination of conventional and chiroptical methods: ultraviolet absorption/electronic circular dichroism (UV/ECD), Fourier transform infrared absorption/vibrational circular dichroism (FTIR/VCD), and Raman scattering/Raman optical activity (Raman/ROA). For comparison, the main components of these substances—human serum albumin (HSA) and ovalbumin (Ova)—were also analyzed by these methods. The ultraviolet region of the ECD spectrum was analyzed using the CDNN CD software package to evaluate the secondary structures of the proteins. The UV/ECD, FTIR/VCD, and Raman/ROA spectra of the substances were quite similar to those of the corresponding major proteins, while some differences were also detected and explained. The conclusions drawn from the FTIR/VCD and Raman/ROA data were in good agreement with the secondary structures calculated from ECD. The results obtained in this work demonstrate that the chiroptical methods used here can be applied to analyze not only pure protein solutions but also more complex systems, such as biological fluids.