Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data

We consider the quickest change-point detection problem in pointwise and minimax settings for general dependent data models. Two new classes of sequential detection procedures associated with the maximal “local” probability of a false alarm within a period of some fixed length are introduced. For these classes of detection procedures, we consider two popular risks: the expected positive part of the delay to detection and the conditional delay to detection. Under very general conditions for the observations, we show that the popular Shiryaev–Roberts procedure is asymptotically optimal, as the local probability of false alarm goes to zero, with respect to both these risks pointwise (uniformly for every possible point of change) and in the minimax sense (with respect to maximal over point of change expected detection delays). The conditions are formulated in terms of the rate of convergence in the strong law of large numbers for the log-likelihood ratios between the “change” and “no-change” hypotheses, specifically as a uniform complete convergence of the normalized log-likelihood ratio to a positive and finite number. We also develop tools and a set of sufficient conditions for verification of the uniform complete convergence for a large class of Markov processes. These tools are based on concentration inequalities for functions of Markov processes and the Meyn–Tweedie geometric ergodic theory. Finally, we check these sufficient conditions for a number of challenging examples (time series) frequently arising in applications, such as autoregression, autoregressive GARCH, etc.     

Superacid mediated hydroxyalkylation reaction of 1,2,3‐indanetrione: a theoretical study

Energies of mono‐ and multiprotonation for 1,2,3‐indanetrione and ninhydrin in triflic acid (TFSA) media were estimated at PBE0/aug‐cc‐pvtz//6‐31+G** level of theory. The reactivity of formed intermediates in the reaction of aromatic electrophilic substitution has been studied at the same level of theory. It appears that the basicity of carbonyl groups in 1,2,3‐indanetrione is extremely low due to mutual influences of carbonyl groups. Carbonyl 2 is the least basic but the most reactive in accordance with experiment. Calculations demonstrated that monoprotonated intermediates are the principal reactive species in the reaction of hydroxyalkylation of 1,2,3‐indanetrione in TFSA. A new isomerization mechanism of 2,2‐diaryl‐1,3‐indanediones to 3‐(diarylmethylene)isobenzofuranones in TFSA media has been proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

An Improved Measurement of Isotopic Ratios by High Resolution Mass Spectrometry

The study of protein kinetics requires an accurate measurement of isotopic ratios of peptides. Although Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometers yield accurate mass measurements of analytes, the isotopologue ratios are consistently lower than predicted. Recently, we demonstrated that the magnitude of the spectral error in the FT-ICR mass spectrometer is proportional to the scan duration of ions. Here, we present a novel isotopic ratio extrapolation (IRE) method for obtaining accurate isotopic ratio measurements. Accuracy is achieved by performing scans with different duration and extrapolation of the data to the initial moment of the ion rotation; IRE minimizes the absolute isotopic ratio error to ≤1 %. We demonstrate the application of IRE in protein turnover studies using ²H₂O-metabolic labeling. Overall, this technique allows accurate measurements of the isotopic ratios of proteolytic peptides, a critical step for enabling routine studies of proteome dynamics.      

Complexation of Am(III) and Nd(III) by 1,10-Phenanthroline-2,9-Dicarboxylic Acid

The complexant 1,10-phenanthroline-2,9-dicarboxylic acid (PDA) is a planar tetradentate ligand that is more preorganized for metal complexation than its unconstrained analogue ethylendiiminodiacetic acid (EDDA). Furthermore, the backbone nitrogen atoms of PDA are aromatic, hence are softer than the aliphatic amines of EDDA. It has been hypothesized that PDA will selectively bond to trivalent actinides over lanthanides. In this report, the results of spectrophotometric studies of the complexation of Nd(III) and Am(III) by PDA are reported. Because the complexes are moderately stable, it was necessary to conduct these titrations using competitive equilibrium methods, competitive cation complexing between PDA and diethylenetriaminepentaacetic acid, and competition between ligand protonation and complex formation. Stability constants and ligand protonation constants were determined at 0.1 mol·L^?1 ionic strength and at 0.5 mol·L^?1 ionic strength nitrate media at 21 ± 1 °C. The stability constants are lower than those predicted from first principles and speciation calculations indicate that Am³⁺ selectivity over Nd³⁺ is less than that exhibited by 1,10-phenanthroline.     

Tuning rate of the bergman cyclization of benzannelated enediynes with ortho substituents

[reaction: see text] The Bergman cyclization of benzannelated enediynes is highly sensitive to ortho substitution. This finding opens possibilities for the rational design of conformer-specific and pH-dependent DNA-cleaving agents.     

Jacobi matrices with absolutely continuous spectrum

Let be a Jacobi matrix defined in as , where is a unilateral weighted shift with nonzero weights such that Define the seqences: If and , then has an absolutely continuous spectrum covering . Moreover, the asymptotics of the solution is also given.

     

Dynamical Analysis of Schrödinger Operators with Growing Sparse Potentials

We consider discrete half-line Schrödinger operators H with potentials of the form V(n)=S(n)+Q(n). Here Q is any compactly supported real function, if n=L_N and S(n)=0 otherwise, where (0,1) and L_N is a very fast growing sequence. We study in a rather detailed manner the time-averaged dynamics exp(–itH) for various initial states . In particular, for some we calculate explicitly the intermittency function ^–(p) which turns out to be nonconstant. The dynamical results obtained imply that the spectral measure of H has exact Hausdorff dimension for all boundary conditions, improving the result of Jitomirskaya and Last.Acknowledgement I would like to thank F. Germinet for useful discussions.     

Probing the wave function of shallow Li and Na donors in ZnO nanoparticles

Electron paramagnetic resonance and electron nuclear double resonance (ENDOR) experiments on ZnO nanoparticles reveal the presence of shallow donors related to interstitial Li and Na atoms. The shallow character of the wave function is evidenced by the multitude of 67Zn ENDOR lines and further by the hyperfine interactions with the 7Li and 23Na nuclei that are much smaller than for atomic lithium and sodium. In the case of the Li-doped nanoparticles, an increase of the hyperfine interaction with the 7Li nucleus and with the 1H nuclei in the Zn(OH)(2) capping layer is observed when reducing the size of the nanoparticles. This effect is caused by the confinement of the shallow-donor 1s-type wave function that has a Bohr radius of about 1.5 nm, i.e., comparable to the dimension of the nanoparticles.     

Overhauser effect of 67Zn nuclear spins in ZnO via cross relaxation induced by the zero-point fluctuations of the phonon field

Hole burning in and displacements of the magnetic-resonance absorption line of the electron spin of the shallow hydrogen-related donor in ZnO are observed upon resonant irradiation with microwaves at 275 GHz and at 4.5 K in a magnetic field of 10 T. These effects arise from an almost complete polarization of the many 67Zn (I=5/2) nuclear spins that have an isotropic hyperfine interaction with the electron spin of the shallow donor. It is proposed that this huge dynamic nuclear polarization is caused by a spontaneous-emission-type cross relaxation in the coupled electron-spin nuclear-spin system induced by the zero-point fluctuations of the phonon field.