The method of predicate least squares refinement

Parameters to be determined in a least squares refinement calculation to fit a set of observed data may sometimes usefully be `predicated' to values obtained from some independent source, such as a theoretical calculation. An algorithm for achieving this in a least squares refinement calculation is described, which leaves the operator in full control of the weight that he may wish to attach to the predicate values of the parameters.

First structural analysis of a naphthalene-based poly(ether ketone): Crystal and molecular simulation from X-ray powder data and diffraction modeling

Polycondensation of 2,6-dihydroxynaphthalene with 4,4'-bis(4"-fluorobenzoyl)biphenyl affords a novel, semicrystalline poly(ether ketone) with a melting point of 406 degreesC and glass transition temperature (onset) of 168 degreesC. Molecular modeling and diffraction-simulation studies of this polymer, coupled with data from the single-crystal structure of an oligomer model, have enabled the crystal and molecular structure of the polymer to be determined from X-ray powder data. This structure-the first for any naphthalene-containing poly(ether ketone)-is fully ordered, in monoclinic space group P2(1)/b, with two chains per unit cell. Rietveld refinement against the experimental powder data gave a final agreement factor (R-wp) of 6.7%.

Fecal water as a non-invasive biomarker in nutritional intervention: comparison of preparation methods and refinement of different endpoints

The assessment of cellular effects by the aqueous phase of human feces (fecal water, FW) is a useful biomarker approach to study cancer risks and protective activities of food. In order to refine and develop the biomarker, different protocols of preparing FW were compared. Fecal waters were prepared by 3 methods: (A) direct centrifugation; (B) extraction of feces in PBS before centrifugation; and (C) centrifugation of lyophilized and reconstituted feces. Genotoxicity was determined in colon cells using the Comet assay. Selected samples were investigated for additional parameters related to carcinogenesis. Two of 7 FWs obtained by methods A and B were similarly genotoxic. Method B, however, yielded higher volumes of FW, allowing sterile filtration for long-term culture experiments. Four of 7 samples were non-genotoxic when prepared according to all 3 methods. FW from lyophilized feces and from fresh samples were equally genotoxic. FWs modulated cytotoxicity, paracellular permeability, and invasion, independent of their genotoxicity. All 3 methods of FW preparation can be used to assess genotoxicity. The higher volumes of FWobtained by preparation method B greatly enhance the perspectives of measuring different types of biological parameters and using these to disclose activities related to cancer development.

ExtSym: a program to aid space-group determination from powder diffraction data

Once unit-cell dimensions have been determined from a powder diffraction data set and therefore the crystal system is known (e.g. orthorhombic), the method presented by Markvardsen, David, Johnson & Shankland [Acta Cryst. (2001), A57, 47-54] can be used to generate a table ranking the extinction symbols of the given crystal system according to probability. Markvardsen et al. tested a computer program (ExtSym) implementing the method against Pawley refinement outputs generated using the TF12LS program [David, Ibberson & Matthewman (1992). Report RAL-92-032. Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK]. Here, it is shown that ExtSym can be used successfully with many well known powder diffraction analysis packages, namely DASH [David, Shankland, van de Streek, Pidcock, Motherwell & Cole (2006). J. Appl. Cryst. 39, 910-915], FullProf [Rodriguez-Carvajal (1993). Physica B, 192, 55-69], GSAS [Larson & Von Dreele (1994). Report LAUR 86-748. Los Alamos National Laboratory, New Mexico, USA], PRODD [Wright (2004). Z. Kristallogr. 219, 1-11] and TOPAS [Coelho (2003). Bruker AXS GmbH, Karlsruhe, Germany]. In addition, a precise description of the optimal input for ExtSym is given to enable other software packages to interface with ExtSym and to allow the improvement/modification of existing interfacing scripts. ExtSym takes as input the powder data in the form of integrated intensities and error estimates for these intensities. The output returned by ExtSym is demonstrated to be strongly dependent on the accuracy of these error estimates and the reason for this is explained. ExtSym is tested against a wide range of data sets, confirming the algorithm to be very successful at ranking the published extinction symbol as the most likely. (C) 2008 International Union of Crystallography Printed in Singapore - all rights reserved.

Accurate molecular structures of chlorothiazide and hydrochlorothiazide by joint refinement against powder neutron and X-ray diffraction data

The compounds chlorothiazide and hydrochlorothiazide (crystalline form II) have been studied in their fully hydrogenous forms by powder neutron diffraction on the GEM diffractometer. The results of joint Rietveld refinement of the structures against multi-bank neutron and single-bank X-ray powder data are reported and show that accurate and precise structural information can be obtained from polycrystalline molecular organic materials by this route.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Experimental comparison of the comprehensibility of a Z specification and its implementation in Java

Comprehensibility is often raised as a problem with formal notations, yet formal methods practitioners dispute this. In a survey, one interviewee said 'formal specifications are no more difficult to understand than code'. Measurement of comprehension is necessarily comparative and a useful comparison for a specification is against its implementation. Practitioners have an intuitive feel for the comprehension of code. A quantified comparison will transfer this feeling to formal specifications. We performed an experiment to compare the comprehension of a Z specification with that of its implementation in Java. The results indicate there is little difference in comprehensibility between the two. (C) 2004 Elsevier B.V. All rights reserved.

Reactions of NO3 with the man-made emissions 2-methylpent-2-ene, (Z)-3-methylpent-2-ene, ethyl vinyl ether, and the stress-induced plant emission ethyl vinyl ketone

Rate coefficients for reactions of nitrate radicals (NO3) with the anthropogenic emissions 2-methylpent-2-ene, (Z)-3-methylpent-2-ene.. ethyl vinyl ether, and the stress-induced plant emission ethyl vinyl ketone (pent-1-en-3-one) were determined to be (9.3 +/- 1.1) x 10(-12), (9.3 +/- 3.2) x 10(-12), (1.7 +/- 1.3) x 10(-12) and (9.4 + 2.7) x 10(-17) cm(3) molecule(-1) s(-1). We performed kinetic experiments at room temperature and atmospheric pressure using a relative-rate technique with GC-FID analysis. Experiments with ethyl vinyl ether required a modification of our established procedure that might introduce additional uncertainties, and the errors suggested reflect these difficulties. Rate coefficients are discussed in terms of electronic and steric influences. Atmospheric lifetimes with respect to important oxidants in the troposphere were calculated. NO3-initiated oxidation is found to be the strongly dominating degradation route for 2-methylpent-2-ene, (Z)-3-methylpent-2-ene and ethyl vinyl ether. Atmospheric concentrations of the alkenes and their relative contribution to the total NMHC emissions from trucks can be expected to increase if plans for the introduction of particle filters for diesel engines are implemented on a global scale. Thus more kinetic data are required to better evaluate the impact of these emissions.

Gas-phase reactions of NO3 and N2O5 with (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol

The night-time atmospheric chemistry of the biogenic volatile organic compounds (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO3) with these stress-induced plant emissions were measured using the discharge-flow technique. We employed off-axis continuous-wave cavity-enhanced absorption spectroscopy (CEAS) for the detection of NO3, which enabled us to work in excess of the hexenol compounds over NO3. The rate coefficients determined were (2.93 +/- 0.58) x 10(-13) cm(3) molecule(-1) s(-1), (2.67 +/- 0.42) x 10(-13) cm(3) molecule(-1) s(-1), (4.43 +/- 0.91) x 10(-13) cm(3) molecule(-1) s(-1), (1.56 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1), and (1.30 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1) for (Z)-hex-4-en-1-ol, (Z)-hex-3en-1-ol, (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol. The rate coefficient for the reaction of NO3 with (Z)-hex-3-en-1-ol agrees with the single published determination of the rate coefficient using a relative method. The other rate coefficients have not been measured before and are compared to estimated values. Relative-rate studies were also performed, but required modification of the standard technique because N2O5 (used as the source of NO3) itself reacts with the hexenols. We used varying excesses of NO2 to determine simultaneously rate coefficients for reactions of NO3 and N2O5 with (E)-hex-3-en-1-ol of (5.2 +/- 1.8) x 10(-13) cm(3) molecule(-1) s(-1) and (3.1 +/- 2.3) x 10(-18) cm(3) molecule(-1) s(-1). Our new determinations suggest atmospheric lifetimes with respect to NO3-initiated oxidation of roughly 1-4 h for the hexenols, comparable with lifetimes estimated for the atmospheric degradation by OH and shorter lifetimes than for attack by O-3. Recent measurements of [N2O5] suggest that the gas-phase reactions of N2O5 with unsaturated alcohols will not be of importance under usual atmospheric conditions, but they certainly can be in laboratory systems when determining rate coefficients.

Gas-phase rate coefficients for the reactions of nitrate radicals with (Z)-pent-2-ene, (E)-pent-2-ene, (Z)-hex-2-ene, (E)-hex-2-ene, (Z)-hex-3-ene, (E)-hex-3-ene and (E)-3-methylpent-2-ene at room temperature

Rate coefficients for reactions of nitrate radicals (NO3) with (Z)-pent-2-ene, (E)-pent-2-ene, (Z)-hex-2-ene, (E)-hex-2-ene, (Z)-hex-3-ene, (E)-hex-3-ene and (E)-3-methylpent-2-ene were determined to be (6.55 +/- 0.78) x 10(-13) cm(3) molecule(-1) s(-1), (3.78 +/- 0.45) x 10(-13) cm(3) molecule(-1) s(-1), (5.30 +/- 0.73) x 10(-13) cm(3) molecule(-1) s(-1), (3.83 +/- 0.47) x 10(-13) cm(3) molecule(-1) s(-1), (4.37 +/- 0.49) x 10(-13) cm(3) molecule(-1) s(-1), (3.61 +/- 0.40) x 10(-13) cm(3) molecule(-1) s(-1) and (8.9 +/- 1.5) x 10(-12) cm(3) molecule(-1) s(-1), respectively. We performed kinetic experiments at room temperature and atmospheric pressure using a relative-rate technique with GC-FID analysis. The experimental results demonstrate a surprisingly large cis-trans (Z-E) effect, particularly in the case of the pent-2-enes, where the ratio of rate coefficients is ca. 1.7. Rate coefficients are discussed in terms of electronic and steric influences, and our results give some insight into the effects of chain length and position of the double bond on the reaction of NO3 with unsaturated hydrocarbons. Atmospheric lifetimes were calculated with respect to important oxidants in the troposphere for the alkenes studied, and NO3-initiated oxidation is found to be the dominant degradation route for (Z)-pent-2-ene, (Z)-hex-3-ene and (E)-3-methylpent-2-ene.

Refinement of the Clinical Scenario Evaluation Framework for Assessment of Competing Development Strategies with an Application to Multiple Sclerosis

When competing strategies for development programs, clinical trial designs, or data analysis methods exist, the alternatives need to be evaluated in a systematic way to facilitate informed decision making. Here we describe a refinement of the recently proposed clinical scenario evaluation framework for the assessment of competing strategies. The refinement is achieved by subdividing key elements previously proposed into new categories, distinguishing between quantities that can be estimated from preexisting data and those that cannot and between aspects under the control of the decision maker from those that are determined by external constraints. The refined framework is illustrated by an application to a design project for an adaptive seamless design for a clinical trial in progressive multiple sclerosis.

Night-time tropospheric chemistry of the unsaturated alcohols (Z)-pent-2-en-1-ol and pent-1-en-3-ol: Kinetic studies of reactions of NO3 and N2O5 with stress-induced plant emissions

The night-time tropospheric chemistry of two stress-induced volatile organic compounds (VOCs), (Z)-pent-2-en-1-ol and pent-1-en-3-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO3) with these pentenols were measured using the discharge-flow technique. Because of the relatively low volatility of these compounds, we employed off-axis continuous-wave cavity-enhanced absorption spectroscopy for detection of NO3 in order to be able to work in pseudo first-order conditions with the pentenols in large excess over NO3. The rate coefficients were determined to be (1.53 +/- 0.23) x 10(-13) and (1.39 +/- 0.19) x 10(-14) cm(3) molecule(-1) s(-1) for reactions of NO3 with (Z)-pent-2-en-1-ol and pent-1-en-3-ol. An attempt to study the kinetics of these reactions with a relative-rate technique, using N2O5 as source of NO3 resulted in significantly higher apparent rate coefficients. Performing relative-rate experiments in known excesses of NO2 allowed us to determine the rate coefficients for the N2O5 reactions to be (5.0 +/- 2.8) x 10(-19) cm(3) molecule(-1) s(-1) for (Z)-pent-2-en-1-ol, and (9.1 +/- 5.8) x 10(-19) cm(3) molecule(-1) s(-1) for pent-1-en-3-ol. We show that these relatively slow reactions can indeed interfere with rate determinations in conventional relative-rate experiments.