Strong Central Limit Theorem for isotropic random walks in {\mathbb{R}^d}

We prove an optimal Gaussian upper bound for the densities of isotropic random walks on ${\mathbb{R}^d}$ in spherical case (d ?? 2) and ball case (d ?? 1). We deduce the strongest possible version of the Central Limit Theorem for the isotropic random walks: if ${\tilde S_n}$ denotes the normalized random walk and Y the limiting Gaussian vector, then ${\mathbb{E} f(\tilde S_{n}) \rightarrow \mathbb{E} f(Y)}$ for all functions f integrable with respect to the law of Y. We call such result a ??Strong CLT??. We apply our results to get strong hypercontractivity inequalities and strong Log-Sobolev inequalities.     

On solving the dual for portfolio selection by optimizing Conditional Value at Risk

This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk (CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general purpose LP solvers. However, in the case of more advanced simulation models employed for scenario generation one may get several thousands of scenarios. This may lead to the LP model with huge number of variables and constraints thus decreasing the computational efficiency of the model. To overcome this difficulty some alternative solution approaches are explored employing cutting planes or nondifferential optimization techniques among others. Without questioning importance and quality of the introduced methods we demonstrate much better performances of the simplex method when applied to appropriately rebuilt CVaR models taking advantages of the LP duality.     

Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency

Scalar diffraction theory is applied to analyze the intensity distribution in the fiber core during fiber Bragg grating (FBG) fabrication using an apodized phase mask. The averaged diffraction field distribution in fiber core was calculated as a function of optical fiber position. The results show that in a case of apodized FBGs fabrication, averaged field intensity profile, and thus refractive index changes in fiber core have complex form. Moreover, it was shown that the influence of optical fiber position behind the phase mask on average intensity distribution in fiber core decreases with increasing of its diameter.     

Δ(1232) axial charge and form factors from lattice QCD

We present the first calculation on the Δ axial?vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to Δ axial transition coupling constant and Δ axial charge.     

The observable pressure of light in dielectric fluids

By considering a perfect reflector submerged in a dielectric fluid, we show that the Minkowski formulation describes the optical momentum transfer to submerged objects. This result is required by global energy conservation, regardless of the phase of the reflected wave. While the electromagnetic pressure on a submerged reflector can vary with phase of the mirror reflection coefficient between twice the Abraham momentum and twice the Minkowski momentum, the Minkowski momentum is always restored due to the additional pressure on the dielectric surface. This analysis also gives further evidence for use of the Minkowski stress tensor at the boundary of a dielectric interface, which has been the subject of a long-standing debate in physics and the source of uncertainty in the modeling of optical forces on submerged particles.     

Thermostability of glucose oxidase in silica gel obtained by sol-gel method and in solution studied by fluorimetric method

The thermostability of glucose oxidase entrapped in silica gel obtained by sol-gel method was studied by thermostimulated fluorescence of FAD at pH 5 and 7 and compared with that of the native enzyme in the solution and at the presence of ethanol. The unfolding temperatures were found to be lower for the enzyme immobilised in gel as compared with the native enzyme but higher as for the enzyme at the presence of ethanol. In gel, the thermal denaturation of glucose oxidase is independent on pH while in solution the enzyme is more stable at pH 5. The investigation the enzyme in different environment by steady-state fluorescence of FAD and tryptophan, synchronous fluorescence and time-resolved fluorescence of tryptophan indicates that the state of the molecule (tertiary structure and molecular dynamics) is different in gel and in solution. The ethanol produced during gel precursor hydrolysis is not the main factor influencing the thermostability of the enzyme but more important are interactions of the protein with the gel lattice.     

Global versus local QSPR models for persistent organic pollutants: balancing between predictivity and economy

Experimentally determined data on the key physicochemical parameters for halogenated congeners of persistent organic pollutants (POPs) are available only for a limited number of compounds. In the absence of experimental data, a range of computational methods can be applied to characterize those species for which experimental data is not available. One of the techniques widely used in this context is quantitative structure–property relationships (QSPR) approach. There are two ways to develop the QSPR models: using a more complex global model or fitting a simple local model that covers a specific class of chemically related compounds. The essence of the study was to investigate, if local models have significantly better explanatory and predictive ability than global models with wider applicability domains. Based on the obtained results, we concluded that whenever global models fulfill all quality recommendations by OECD, they would be applied in practice as more efficient ones in state of more time consuming procedure of modeling the particular groups of POPs one-by-one. On the contrary, local models are applicable to solve specific problems (i.e., related to only one group of POPs), when high-quality experimental data are available for a sufficient number of training and validation compounds.     

Development of nanoscale inhomogeneities during drying of sol-gel derived amorphous lead zirconate titanate precursor thin films

The structural evolution of sol-gel derived lead zirconate titanate (PZT) precursor films during and after physical drying was investigated by transmission electron microscopy (TEM), electron energy loss spectroscopy (EELS), selected area electron diffraction (SAED), and time-resolved X-ray diffraction (XRD). Films were deposited from initial 0.3 mol/dm(3) precursor sols with varying hydrolysis ratios. Zr-rich grains of 1-10 nm size, embedded in a Pb-, Zr-, and Ti-containing amorphous matrix were found in as-dried films. The Zr-rich regions were crystalline at hydrolysis ratios [H(2)O]/[PZT] < 27.6, and amorphous at ratios > 100. X-ray diffraction analysis of PZT and zirconia sols revealed that the crystalline nanoparticles in both sols are identical and are probably composed of nanosized zirconium oxoacetate-like clusters. This study demonstrates that time-resolved X-ray diffraction combined with electron energy loss spectroscopy mapping is a powerful tool to monitor the nanoscale structural evolution of sol-gel derived thin films.     

1H, 13C, 195Pt and 15N NMR structural correlations in Pd(II) and Pt(II) chloride complexes with various alkyl and aryl derivatives of 2,2'-bipyridine and 1,10-phenanthroline

(1)H, (13)C, (195)Pt and (15)N NMR studies of platinide(II) (M = Pd, Pt) chloride complexes with such alkyl and aryl derivatives of 2,2'-bipyridine and 1,10-phenanthroline as LL = 6,6'-dimethyl-bpy, 5,5'-dimethyl-bpy, 4,4'-di-tert-butyl-bpy, 2,9-dimethyl-phen, 2,9-dimethyl-4,7-diphenyl-phen, 3,4,7,8-tetramethyl-phen, having the general [M(LL)Cl(2)] formula were performed and the respective chemical shifts (δ(1H), δ(13C), δ(195Pt), δ(15N)) reported. (1)H high-frequency coordination shifts (Δ(coord)(1H) = δ(complex)(1H)-δ(ligand)(1H)) mostly pronounced for nitrogen-adjacent protons and methyl groups in the nearest adjacency of nitrogen, as well as (15)N low-frequency coordination shifts (Δ(coord)(15H) = δ(complex)(15H)-δ(ligand)(15H)) were discussed in relation to the molecular structures.     

Catalytic residues in hydrolases: analysis of methods designed for ligand-binding site prediction

The comparison of eight tools applicable to ligand-binding site prediction is presented. The methods examined cover three types of approaches: the geometrical (CASTp, PASS, Pocket-Finder), the physicochemical (Q-SiteFinder, FOD) and the knowledge-based (ConSurf, SuMo, WebFEATURE). The accuracy of predictions was measured in reference to the catalytic residues documented in the Catalytic Site Atlas. The test was performed on a set comprising selected chains of hydrolases. The results were analysed with regard to size, polarity, secondary structure, accessible solvent area of predicted sites as well as parameters commonly used in machine learning (F-measure, MCC). The relative accuracies of predictions are presented in the ROC space, allowing determination of the optimal methods by means of the ROC convex hull. Additionally the minimum expected cost analysis was performed. Both advantages and disadvantages of the eight methods are presented. Characterization of protein chains in respect to the level of difficulty in the active site prediction is introduced. The main reasons for failures are discussed. Overall, the best performance offers SuMo followed by FOD, while Pocket-Finder is the best method among the geometrical approaches.