The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

Donor states in tellurium-doped silicon

Hall effect and conductivity measurements are performed on Te-doped silicon in the temperature range 30KT800K. A Hall equipment suited for high temperatures up to 800 K has been constructed. The temperature dependence of the free electron concentration is analyzed for Te-doped silicon including one double-donor and several monovalent donor species. A deep level with an electrical activation energy of 200 meV is determined from the saturation of the free electron concentration at temperatures above 400 K. This level represents the first ionization stage of the Te double-donor. The second ionization stage is estimated to have an activation energy of 440 meV. The maximum electrically active Te concentration obtained is 5×10¹⁶cm^–3. Three different shallow donor states are resolved in the low-temperature range. The concentrations of these shallow donors are partially sensitive to a subsequent heat-treatment.     

Detection of Amine Impurity and Quality Assessment of the MALDI Matrix α-Cyano-4-Hydroxy-Cinnamic Acid for Peptide Analysis in the amol Range

We have studied sample preparation conditions to increase the reproducibility of positive UV-MALDI-TOF mass spectrometry of peptides in the amol range. By evaluating several α-cyano-4-hydroxy-cinnamic acid (CHCA) matrix batches and preparation protocols, it became apparent that two factors have a large influence on the reproducibility and the quality of the generated peptide mass spectra: (1) the selection of the CHCA matrix, which allows the most sensitive measurements and an easier finding of the “sweet spots,” and (2) the amount of the sample volume deposited onto the thin crystalline matrix layer. We have studied in detail the influence of a contaminant, coming from commercial CHCA matrix batches, on sensitivity of generated peptide mass spectra in the amol as well as fmol range of a tryptic peptide mixture. The structure of the contaminant, N,N-dimethylbutyl amine, was determined by applying MALDI-FT-ICR mass spectrometry experiments for elemental composition and MALDI high energy CID experiments utilizing a tandem mass spectrometer (TOF/RTOF). A recrystallization of heavily contaminated CHCA batches that reduces or eliminates the determined impurity is described. Furthermore, a fast and reliable method for the assessment of CHCA matrix batches prior to tryptic peptide MALDI mass spectrometric analyses is presented.

On‐Surface Assembly of Hydrogen‐ and Halogen‐Bonded Supramolecular Graphyne‐Like Networks

Demonstrated here is a supramolecular approach to fabricate highly ordered monolayered hydrogen‐ and halogen‐bonded graphyne‐like two‐dimensional (2D) materials from triethynyltriazine derivatives on Au(111) and Ag(111). The 2D networks are stabilized by N???H?C(sp) bonds and N???Br?C(sp) bonds to the triazine core. The structural properties and the binding energies of the supramolecular graphynes have been investigated by scanning tunneling microscopy in combination with density‐functional theory calculations. It is revealed that the N???Br?C(sp) bonds lead to significantly stronger bonded networks compared to the hydrogen‐bonded networks. A systematic analysis of the binding energies of triethynyltriazine and triethynylbenzene derivatives further demonstrates that the X₃‐synthon, which is commonly observed for bromobenzene derivatives, is weaker than the X₆‐synthon for our bromotriethynyl derivatives.     

A new mathematical procedure to evaluate peaks in complex chromatograms

Automatic peak evaluation in chromatograms and subsequent quantification of compound concentrations is still a challenge in the analysis of complex samples containing hundreds or thousands of compounds. Although a number of software packages for peak evaluation exist, baseline definition and overlapping peaks of different shapes are the main reasons which prevent reliable automatic analysis of complex chromatograms. A new mathematical procedure is presented which uses peak shapes extracted from the chromatogram itself and modified by nonlinear (in fact, hyperbolic) stretching of the peak head and tail. With this approach, the peak parameters are position, height, scale of front, scale of tail, and smoothness of transition from front to tail scaling. This approach is found to give a substantially better fit than traditional analytically defined peak shapes. Together with a good peak finding heuristic and nonlinear optimization of parameters this allows a reliable automatic analysis of chromatograms with a large number of peaks, even with large groups of overlapping peaks. The analysis matches the quality of standard interactive methods, but still permits interactive refinement. This approach has been implemented and tested on a large set of data from chromatography of hydrocarbons in ambient air samples.     

Determination of δ18O in soils: measuring conditions and a potential application

The stable oxygen isotope signature (δ¹⁸O) of soil is expected to be the result of a mixture of components within the soil with varying δ¹⁸O signatures. Thus, the δ¹⁸O of soils should provide information about the soil's substrate, especially about the relative contribution of organic matter versus minerals. As there is no standard method available for measuring soil δ¹⁸O, the method for the measurement of single components using a high‐temperature conversion elemental analyser (TC/EA) was adapted. We measured δ¹⁸O in standard materials (IAEA 601, IAEA 602, Merck cellulose) and soils (organic and mineral soils) in order to determine a suitable pyrolysis temperature for soil analysis. We consider a pyrolysis temperature suitable when the yield of signal intensity (intensity of mass 28 per 100 µg) is at a maximum and the acquired raw δ¹⁸O signature is constant for the standard materials used and when the quartz signal from the soil is still negligible. After testing several substances within the temperature range of 1075 to 1375°C we decided to use a pyrolysis temperature of 1325°C for further measurements. For the Urseren Valley we have found a sequence of increasing δ¹⁸O signatures from phyllosilicates to upland soils, wetland soils and vegetation. Our measurements show that the δ¹⁸O values of upland soil samples differ significantly from wetland soil samples. The latter can be related to the changing mixing ratio of the mineral and organic constituents of the soil. For wetlands affected by soil erosion, we have found intermediate δ¹⁸O signatures which lie between typical signatures for upland and wetland sites and give evidence for the input of upland soil material through erosion. Copyright © 2008 John Wiley & Sons, Ltd.     

Automated data reduction for hydrogen/deuterium exchange experiments,enabled by high-resolution fourier transform ion cyclotron resonance mass spectrometry

Mass analysis of proteolytic fragment peptides following hydrogen/deuterium exchange offers a general measure of solvent accessibility/hydrogen bonding (and thus conformation) of solution-phase proteins and their complexes. The primary problem in such mass analyses is reliable and rapid assignment of mass spectral peaks to the correct charge state and degree of deuteration of each fragment peptide, in the presence of substantial overlap between isotopic distributions of target peptides, autolysis products, and other interferant species. Here, we show that at sufficiently high mass resolving power (m/Δm_50% ≥ 100,000), it becomes possible to resolve enough of those overlaps so that automated data reduction becomes possible, based on the actual elemental composition of each peptide without the need to deconvolve isotopic distributions. We demonstrate automated, rapid, reliable assignment of peptide masses from H/D exchange experiments, based on electrospray ionization FT-ICR mass spectra from H/D exchange of solution-phase myoglobin. Combined with previously demonstrated automated data acquisition for such experiments, the present data reduction algorithm enhances automation (and thus expands generality and applicability) for high-resolution mass spectrometry-based analysis of H/D exchange of solution-phase proteins.     

Global analysis of the strangeness vector and axial form factors of the nucleon and their uncertainties

We have studied the strangeness contribution to the elastic vector and axial form factors of the nucleon, using all available electroweak elastic scattering data sensitive to these contributions. Specifically, we combine ??p and $\bar{\nu} p$ elastic scattering cross sections from Brookhaven E734 with parity-violating asymmetries in elastic ep scattering, and quasi-elastic ed and e ⁴He scattering, observed in the SAMPLE, HAPPEx, G0 and PVA4 experiments. We are able not only to determine these form factors at individual values of momentum-transfer (Q ²), as has been done recently, but also to fit the Q ²-dependence of these form factors using simple functional forms. We present the results of these fits using existing data.