Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r _t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index α and the long memory parameter d of the squared returns X_t = r_t²{X_t= r_t^2} of LARCH, and of the powers X _t = |r _t | ^p of FIGARCH. We find that the X _t have infinite variance and long memory, and show how the estimates of α and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates [^(d)]{\hat d} and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.     

Highly sulfurated heterocycles via dithiiranes and trithietanes as key intermediates

2,2,4,4-Tetramethyl-3-thioxocyclobutanone (8b) easily reacts with gaseous chlorine to yield the stable alpha-chloro sulfenyl chloride 10. The same product was obtained when 8b was treated either with phosphorus pentachloride (PCl(5)) or sulfuryl chloride (SO(2)Cl(2)) in CCl(4) solution. Sulfur dichloride (SCl(2)) reacts with 8b to give the alpha-chloro thiosulfenyl chloride 12 along with an almost equimolar amount of the trisulfide 13b. The less reactive disulfur dichloride (S(2)Cl(2)) was shown to react slowly with 8b and the symmetrical tetrasulfide 15 was found as the exclusive product. The pure thiosulfenyl chloride 12 added to adamantanethione (8c) yielded the unsymmetrical trisulfide 13c. When 12 was treated with thioacetic acid, the acetylated trisulfide 17 was formed in high yield. "Unzipping" reactions with the acetylated disulfide 16 and trisulfide 17 with morpholine in THF at -40 degrees C led to the formation of mixtures of two sulfur-rich heterocycles identified as the pentathiepane 6b and the hexathiepane 7b. A mixture of analogous products was obtained when alpha-chloro sulfenyl chloride 10 was treated with sodium sulfide in anhydrous THF at -40 degrees C. The formation of 6b and 7b is believed to occur via the intermediate dithiirane 1b and/or the isomeric thiosulfine 2b. In the case of 17 the reaction starts probably with the formation of a nonisolable tetrathiane 18b as presented in Scheme 5.     

Solvent Relaxation in Phospholipid Bilayers: Principles and Recent Applications

Although there exist a number of methods, such as NMR, X-ray, e.g., which explore the hydration of phospholipid bilayers, the solvent relaxation (SR) method has the advantage of simple instrumentation, easy data treatment and possibility of measuring fully hydrated samples. The main information gained from SR by the analysis of recorded “time-resolved emission spectra” (TRES) is micro-viscosity and micro-polarity of the dye microenvironment. Based on these parameters, one can draw conclusions about water structure in the bilayer. In this review, we focus on physical background of this method, on all the procedures that are needed in order to obtain relevant parameters, and on the requirements on the fluorescence dyes. Furthermore, a few recent applications (the effect of curvature, binding of antibacterial peptides and phase transition) illustrating the versatility of this method are mentioned. Moreover, limitations and potential problems are discussed.     

Wave optics of Liesegang rings

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

Thermodynamic properties of liquid silver-antimony alloys determined from emf measurements

The thermodynamic properties of the liquid Ag-Sb alloys were determined using solid oxide galvanic cells with zirconia electrolyte. The emfs of the cells:

     

Molecular dynamics of 5-HT1A and 5-HT2A serotonin receptors with methylated buspirone analogues

In the present study experimentally determined ligand selectivity of three methylated buspirone analogues (denoted as MM2, MM5 and P55) towards 5-HT_1A and 5-HT_2A serotonin receptors was theoretically investigated on a molecular level. The relationships between the ligand structure and 5-HT_1A and 5-HT_2A receptor affinities were studied and the results were found to be in agreement with the available site-directed mutagenesis and binding affinity data. Molecular dynamics (MD) simulations of ligand-receptor complexes were performed for each investigated analogue, docked twice into the central cavity of 5-HT_1A/5-HT_2A, each time in a different orientation. Present results were compared with our previous theoretical results, obtained for buspirone and its non-methylated analogues. It was found that due to the presence of the methyl group in the piperazine ring the ligand position alters and the structure of the ligand-receptor complex is modified. Further, the positions of derivatives with pyrimidinyl aromatic moiety and quinolinyl moiety are significantly different at the 5-HT_2A receptor. Thus, methylation of such derivatives alters the 3D structures of ligand-receptor complexes in different ways. The ligand-induced changes of the receptor structures were also analysed. The obtained results suggest, that helical domains of both receptors have different dynamical behaviour. Moreover, both location and topography of putative binding sites for buspirone analogues are different at 5-HT_1A and 5-HT_2A receptors.     

Statistical Inference in a Linear Model for Spatially Located Sensors and Random Input

In the paper we consider a random linear model for observations provided by spatially located sensors measuring signals coming from one source. For this model a set of sufficient and complete statistics are found, and it is shown that the maximum likelihood estimators of unknown parameters (characteristics of the source) are functions of those statistics. The problem of nonnegative estimators of variance components of the model is shortly discussed. Comparisons of the mean squared errors of several estimators are given. Numerical example concerning hunting for defects in solar cells is considered in details.     

Conductance studies of NaBPh4, NBu4I, NaI, NaCl, NaBr, NaClO4 and the limiting ionic conductance in water + propan-1-ol mixtures at 298.15 K

The electrical conductivities of NaBPh₄, NBu₄I, NaI, NaCl, NaBr and NaClO₄ have been studied in the mixtures of propan-1-ol with water. The obtained results were analysed using the Fuoss–Justice equation. The individual limiting ionic conductivities of Na⁺, NBu₄⁺, BPh₄⁻, I⁻, Cl⁻, Br⁻, ClO₄⁻ ions have been determined using the Fuoss–Hirsch assumption. The dependencies of the limiting molar conductances Λ_o and Walden products Λ_oη versus mixed solvent composition have been discussed.     

Evaluation of semiconducting sensor materials on the basis of catalytic test reaction

Oxidative-reductive properties on the acid-base surfaces of the oxide compositions Sn-Ce-Rh-O and Zr-Mg-Y-O, active as catalysts in the ketonization of secondary alcohols were determined based on the isopropanol conversion selectivity. The kinetics of isopropanol conversion was measured in the oxygen-free atmosphere. Activation energies for both directions of conversion (dehydration to propylene and dehydrogenation to acetone) were calculated. The results were compared with the kinetics over SnO₂ and ZrO₂. Both oxide compositions, Sn-Ce-Rh-O and Zr-Mg-Y-O are oxidative-reductive catalysts containing Lewis acid centers.