Generating random correlation matrices based on vines and extended onion method

We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.G. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276–294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, Journal of Multivariate Analysis 97 (2006) 2177–2189] based on partial correlations. The latter is based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions.     

Remark on Krasnosielski’s guiding functions and Srzednicki’s periodic segments

We show that the existence of the complete set of guiding functions guarantees the existence of periodic isolating segment that carries the same information concerning periodic solutions of the non-autonomous periodic equations x^′=f(x,t)$x^{\prime }=f(x,t)$.     

Thermal [2+3]‐Cycloadditions of trans‐1‐Methyl‐2,3‐diphenylaziridine with CS and CC Dipolarophiles: An Unexpected Course with Dimethyl Dicyanofumarate

The thermal reaction of trans‐1‐methyl‐2,3‐diphenylaziridine (trans‐ 1a ) with aromatic and cycloaliphatic thioketones 2 in boiling toluene yielded the corresponding cis‐2,4‐diphenyl‐1,3‐thiazolidines cis‐ 4 via conrotatory ring opening of trans‐ 1a and a concerted [2+3]‐cycloaddition of the intermediate (E,E)‐configured azomethine ylide 3a (Scheme 1). The analogous reaction of cis‐ 1a with dimethyl acetylenedicarboxylate ( 5 ) gave dimethyl trans‐2,5‐dihydro‐1‐methyl‐2,5‐diphenylpyrrole‐3,4‐dicarboxylate (trans‐ 6 ) in accord with orbital‐symmetry‐controlled reactions (Scheme 2). On the other hand, the reactions of cis‐ 1a and trans‐ 1a with dimethyl dicyanofumarate ( 7a ), as well as that of cis‐ 1a and dimethyl dicyanomaleate ( 7b ), led to mixtures of the same two stereoisomeric dimethyl 3,4‐dicyano‐1‐methyl‐2,5‐diphenylpyrrolidine‐3,4‐dicarboxylates 8a and 8b (Scheme 3). This result has to be explained via a stepwise reaction mechanism, in which the intermediate zwitterions 11a and 11b equilibrate (Scheme 6). In contrast, cis‐1,2,3‐triphenylaziridine (cis‐ 1b ) and 7a gave only one stereoisomeric pyrrolidine‐3,4‐dicarboxylate 10 , with the configuration expected on the basis of orbital‐symmetry control, i.e., via concerted reaction steps (Scheme 10). The configuration of 8a and 10 , as well as that of a derivative of 8b , were established by X‐ray crystallography.     

Hydrophobicity‐aided potentiometric detection of catecholamines,beta‐agonists,and beta‐blockers in a mixed‐solvent capillary electrophoresis system

A series of cationic drug‐like substances with distinct basicity, hydrogen‐bonding ability, and hydrophobicity, including three catecholamines, two beta‐agonists, and thirteen beta‐blockers, was successfully detected in a capillary electrophoresis system using an end‐capillary coupled potentiometric sensor consisting of a PVC‐based liquid membrane deposited directly on a 100 μm diameter copper rod. The electrophoretic separation was performed on a 72 cm×75 μm id uncoated fused‐silica capillary with an acidic background electrolyte containing phosphoric acid in a water–acetonitrile mixture, pH* 2.8. Samples were injected electrokinetically at 5.0 kV for 10 s and a running voltage of 19.5 kV was applied. Excluding the bufuralol/practolol pair, baseline separation of all substances was achieved in the developed CE system within 9 minutes. A linear relationship (R² 0.8752) between the sensitivity of the applied potentiometric detector and the parameter log P characterising the hydrophobicity of the analytes was demonstrated. The best observable limits of detection (LODs) were obtained for the highly hydrophobic substances, i. e. bufuralol (8.10×10^–8 M injected concentration, S/N = 3), propranolol, alprenolol, and clenbuterol (ca. 1.10×10^–7 M). In the case of hydrophilic catecholamines and carbuterol their LODs with potentiometric detection were lowered by a factor of almost one thousand, reaching a value of 6.6×10^–5 M.     

Single-ion anisotropy in a four-spin system: mixing of S-states

A four-spin system with s=1 and the single-ion anisotropy, D∑ _j [s _jz ] ² , is considered. When D≠0 the Hamiltonian of the system does not commute with S ² and, therefore, S cannot be used as an additional label of energy levels. In this work we concentrate on the problem of mixing states with different total spins S. The Hamiltonian matrix is transformed to the symmetry-adapted basis (with subspaces labeled by the irreducible representations of the symmetry group) and next, after solving the eigenproblem for S ², to the basis with vectors labeled by S. Each eigenproblem is solved exactly (at least numerically) and the eigenstates are expressed as ∑ _S a _S |S〉. The coefficients a_S are analyzed, especially for their D-dependence. Even in such a small system different schemes of level mixing can be observed.      

On the power of standard information for <Emphasis Type="Italic">L</Emphasis><Subscript>∞</Subscript> approximation in the randomized setting

We study approximation of multivariate functions from a general separable reproducing kernel Hilbert space in the randomized setting with the error measured in the L _∞ norm. We consider algorithms that use standard information consisting of function values or general linear information consisting of arbitrary linear functionals. The power of standard or linear information is defined as, roughly speaking, the optimal rate of convergence of algorithms using n function values or linear functionals. We prove under certain assumptions that the power of standard information in the randomized setting is at least equal to the power of linear information in the worst case setting, and that the powers of linear and standard information in the randomized setting differ at most by 1/2. These assumptions are satisfied for spaces with weighted Korobov and Wiener reproducing kernels. For the Wiener case, the parameters in these assumptions are prohibitively large, and therefore we also present less restrictive assumptions and obtain other bounds on the power of standard information. Finally, we study tractability, which means that we want to guarantee that the errors depend at most polynomially on the number of variables and tend to zero polynomially in n ⁻¹ when n function values are used.     

Search for T, CP, and CPT violation in B0-B0 mixing with inclusive dilepton events

We report the results of a search for T, CP, CPT, and violation in B0-B0 mixing using an inclusive dilepton sample collected by the BABAR experiment at the PEP-II factory. Using a sample of 232 x 10(6) BB pairs, we measure the T and CP violation parameter |q/p| - 1 = (-0.8 +/- 2.7(stat) +/- 1.9(syst) x 10(-3), and the CPT and CP parameters Imz = (13.9 +/- 7.3(stat) +/- 3.2(syst)) x 10(-3) and Delta Gamma x Rez = (7.1 +/- 3.9(stat) +/- 2.0(stat)) x 10(-3) ps(-1). The statistical correlation between the measurements of Imz and Delta Gamma x Rez is 76%.     

Measurements of the absolute branching fractions of B+/- --> K+/-X(cc)

We study the two-body decays of B+/- mesons to K+/- and a charmonium state X(cc) in a sample of 210.5 fb(-1) of data from the BABAR experiment. We perform measurements of absolute branching fractions beta(B+/- --> K+/-X(cc)) using a missing mass technique, and report several new or improved results. In particular, the upper limit beta(B+/- --> K+/- X(3872)) < 3.2 x 10(-4) at 90% C.L. and the inferred lower limit beta(X(3872)J/psipi+ pi-) > 4.2% will help in understanding the nature of the recently discovered X(3872).     

Observation of tree-level B decays with ss production from gluon radiation

We report on our search for decays proceeding via a tree-level b-->c quark transition in which a gluon radiates into an ss[over ] pair. We present observations of the decays B;{-}-->D_{s};{+}K;{-}pi;{-} and B[over ];{0}-->D_{s};{+}K_{S};{0}pi;{-} and evidence for B;{-}-->D_{s};{+}K;{-}K;{-} and set upper limits on the branching fractions for B[over ];{0}-->D_{s};{+}K_{S};{0}pi;{-} and B;{-}-->D_{s};{+}K;{-}K;{-} using 383x10;{6} Upsilon(4S)-->BB[over ] events collected by the BABAR detector at SLAC. We present evidence that the invariant mass distributions of D_{s};{+}K;{-} pairs from B;{-}-->D_{s};{+}K;{-}pi;{-} decays are inconsistent with the phase-space model, suggesting the presence of charm resonances lying below the D_{s};{+}K;{-} threshold.     

The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market

We investigate the local fractal properties of the financial time series based on the whole history evolution (1991–2007) of the Warsaw Stock Exchange Index (WIG), connected with the largest developing financial market in Europe. Calculating the so-called local time-dependent Hurst exponent for the WIG time series we find the dependence between the behavior of the local fractal properties of the WIG time series and the crashes’ appearance on the financial market. We formulate the necessary conditions based on the behavior which have to be satisfied if the rupture or crash point is expected soon. As a result we show that the signal to sell or the signal to buy on the stock exchange market can be translated into evolution pattern. We also find a relation between the rate of the drop and the total correction the WIG index gains after the crash. The current situation on the market, particularly related to the recent Fed intervention in September ’07, is also discussed.