Note on the correction of negative measured values if the measurand is nonnegative

Often, the concentration of a substance or the activity of radionuclides in a sample is measured indirectly as the difference between signal and noise, i.e. the difference between the measured value obtained at the sample and that obtained at a sample not containing the substance or the radionuclides (blank sample). The difference can be negative, especially if the concentration or the activity is low. Since a negative measurement result for a nonnegative measurand does not make sense, measured values must be corrected to nonnegative measurement results. Weise et al. and Korun/Maver Modec use a Bayesian approach in order to obtain a nonnegative estimate of the nonnegative measurand. Their estimate is the mean of the posterior distribution. Korun and Zorko modify this estimate slightly and obtain a less biased estimate. In this paper, it is proposed to use the mode of the posterior distribution instead of the mean. The resulting estimate is equal to the measured value if it is nonnegative and 0 if it is negative. This estimate has three advantages: it is extremely easy to calculate, it is less biased than the posterior mean proposed in the other papers, and it does not use the known standard deviation, i.e. it can also be used if the standard deviation is unknown.     

Calculation of the best estimates for measurements of radioactive substances when the presence of the analyte is not assured

The best estimate and its standard deviation are calculated for the case when the a priori probability that the analyte is absent from the test sample is not zero. In the calculation, a generalization of the Bayesian prior that is used in the ISO 11929 standard is applied. The posterior probability density distribution of the true values, given the observed value and its uncertainty, is a linear combination of the Dirac delta function and the normalized, truncated, normal probability density distribution defined by the observed value and its uncertainty. The coefficients of this linear combination depend on the observed value and its uncertainty, as well as on the a priori probability. It is shown that for a priori probabilities larger than zero the lower level of the uncertainty interval of the best estimate reaches the unfeasible range (i.e., negative activities). However, for a priori probabilities in excess of 0.26 it reaches the unfeasible range even for positive observed values. The upper limit of the confidence interval covering a predefined fraction of the posterior is derived.     

Investigation of the performance of the instrument by nonlinear calibration

In the search for high reliability in chemical analysis, a straightforward method of nonlinear calibration is presented. The corresponding standard deviation (SD) was calculated by the law-of-propagation of errors that allowed the determination of uncertainties as a function of concentration within the range of concentrations defined by the lower limit of analysis (LLA) and the upper limit of analysis (ULA). The advantage of using nonlinear calibrations was demonstrated by the correspondence of average values to the peak position of the normal distribution. The concentration of cobalt in two certified reference materials (CRMs) was determined by flame absorption spectrometry (FAAS) that is recognised as an experiment of very high precision. In order to ensure the determination of a reliable value for the SD, a high number of repetitions were required for the analysis. It was thus demonstrated that results that apparently deviated significantly from the certified values, actually belonged to the overall normal distribution of results. The data of experiments were grouped according to Scott’s method, and the distribution of experiments showed a particularly high frequency of results at the peak position that exceeded the expected value predicted by the normal distribution. It also deviated from the distribution peak of experiments, which demonstrates the importance of a full investigation of the distribution of results using more than 100 repetitions. The skewness of the distribution of results was eliminated by the nonlinear calibration. Correspondence: Jens E. T. Andersen, Department of Chemistry, Technical University of Denmark, Kemitorvet building 207, DK-2800 Kgs. Lyngby, Denmark     

New approximations for calculating dispersion coefficients

Improved approaches for finding approximate values of dispersion coefficients are proposed. They are based on scaling the values of time-dependent Hartree-Fock (TDHF) dispersion coefficients by factors that use the ratio of the estimated true value and the TDHF value of static dipole polarizabilities. It is shown that for a set of 14 atoms and molecules the average absolute-value deviation of the estimated two-body isotropic dispersion coefficients with respect to the dipole oscillator strength distribution results is smaller than 1.0% for two of our approaches. For three-body isotropic dispersion coefficients the corresponding deviations are smaller than 1.2%. Our approximations work particularly well compared to approximations proposed by other researchers in cases where the TDHF results differ from the reference values by more than 10%.     

Non-linearity in the quadrupole detector system: implications for the determination of the 13C mass distribution of an ion fragment

Some biomedical (13)C tracer applications to study glucose/lactate metabolism require the determination of up to 7 mass isotopomers of glucose, generated by the (13)C-labeling. Isotopomer ratios determined by GC-Quadrupole-MS can depend on the analyte amount being measured and may differ from expected theoretical values. A calibration is necessary to correct these effects. However, the large number of different isotopomers prevents an empirical calibration, that is based on known isotopomer mixtures. Neither insufficient mass separation in the quadrupole nor proton adducts or losses of the ionized fragment can account for the observed deviation from expected values and the dependency on the sample size. We explain the deviations with a nonlinear mapping of the isotopomer amount being analyzed to the area under the elution curve for the corresponding mass channel. The nonlinear relation allows to estimate potential errors in the determination of isotopomer ratios. It also allows to define a dynamic range as the range of signal areas, for which the systematic error in the isotopomer ratio determination is below 5% of the nominal value. It is 1 : 200 and 1 : 500 for two different fragments of glucose, measured under EI and CI and is smaller than the range imposed by the measurement precision. After correcting the nonlinearities the dynamic range improved by the factor 10 in both cases.     

Paramagnet enhanced nuclear relaxation of H2 in organic solvents and in H2@C60

We have measured the bimolecular contribution (relaxivity) R1 (M(-1) s(-1)) to the spin-lattice relaxation rate for the protons of H2 and H2@C60 dissolved in organic solvents in the presence of paramagnet nitroxide radicals. It is found that the relaxation effect of the paramagnets is enhanced 5-fold in H2@C60 compared to H2 under the same conditions. 13C relaxivity in C60 induced by nitroxide has also been measured. The resulting value of R1 for 13C is substantially smaller relative to the 1H relaxation in H2@C60 than expected solely on the basis of the smaller magnetic moment of 13C. The observed values of R1 have been analyzed quantitatively using an outer-sphere model for bimolecular spin relaxation to extract an encounter distance, d, as the dependent variable. The resulting values of d for H2 and (13)C60 are similar to the sum of the van der Waals radii for the radical and the corresponding molecule. The value of d for (1)H2@C60 is substantially smaller than the corresponding van der Waals estimates, corresponding to larger than expected values of R1. A possible explanation for the enhanced relaxivity is a contribution from hyperfine coupling. Based on the results reported here, it seems that not only is the hydrogen molecule in H2@C60 not insulated from magnetic contact with the outside world but also the interaction with paramagnets is even stronger than expected based on distance alone.     

Sequential testing as an efficient screening method for interferences in routine analysis as applied to atomic-absorption spectrometry with flame and graphite furnace atomization

Reliable standardization is a serious problem for most analytical methods. In spite of extensive work on interferences, the results are not suited for prediction of gross errors in any particular case. This paper is intended to show the power of sequential testing in practical atomic-absorption spectrometric analyses for the efficient detection of interferences causing changes in sensitivity; this test is carried out by comparing the sensitivity of the standard with the sensitivity for the sample, as determined by the difference between the signals for the spiked and unspiked samples. The simple computations can be carried out instantly and experimentation is terminated as soon as a conclusion can be drawn. The major advantage over the traditional tests lies in the smaller number of independent measurements, requiring less time and sample. Three separate cases are discussed: with the mean sensitivity of the standard known and the deviation expected to occur in one direction only (single-sided alternative hypothesis); with the standard deviation of the determination known and the deviation possibly occurring in both directions (double-sided alternative hypothesis); and with the mean and the standard deviation unknown but estimated during the test (sequential t-test). It is shown that assumptions about the normal distribution of the data do not impose serious restrictions in practical AAS work.     

Trace determination of dexamethasone sodium phosphate in pharmaceutical formulations by differential pulse polarography

A simple and rapid differential pulse polarographic method has been developed for the trace determination of dexamethasone sodium phosphate. A well-defined single peak with an Ep value of -1.14 V is obtained in acetate buffer (pH 5.0). The linearity is valid in the range 0.2-1.2 mg/25 mL ( r=0.9992) with minimum detection limit of 7.6x10(-6) M. The precision of the method developed is implied from the values of relative mean deviation, standard deviation and coefficient of variation, which are 2.44%, 0.014 and 3.5% respectively. Marketed formulations of dexamethasone sodium phosphate have been analysed by calibration and standard addition methods. Recovery experiments were found to be quantitative, and analysis to determine the mass per tablet was obtained within +/-0.2% of the expected market value. The studies have shown that the method is reproducible and accurate and can be used in the analysis of marketed formulations.     

Accurate prediction of basicity in aqueous solution with COSMO-RS

The COSMO-RS method, a combination of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for realistic solvation simulations, has been used for the prediction of base pK(a) constants. For a variety of 43 organic bases the directly calculated values of the free energies of dissociation in water showed a very good correlation with experimental base pK(a) values (r2 = 0.98), corresponding to a standard deviation of 0.56 pK(a) units. Thus, we have an a priori prediction method for base pK(a) with the regression constant and the slope as only adjusted parameters. In accord with recent findings for pK(a) acidity predictions, the slope of pK(a) vs. DeltaG(diss) was significantly smaller than the theoretically expected value of 1/RTln(10). The predictivity of the presented method is general and not restricted to certain compound classes, but systematic corrections of 1 and 2 pKa units for secondary and tertiary aliphatic amines are required, respectively. The pK(a) prediction method was validated on a set of 58 complex multifunctional drug-like compounds, yielding an RMS accuracy of 0.66 pK(a) units.     

Assessment of permissible ranges for results of pH-metric acid number determinations using uncertainty calculation

 An approach to assess the permissible ranges for results of replicate determinations using uncertainty calculation is discussed. The approach is based on the known range distribution for normalized "range/standard deviation" values, which is equivalent to the distribution of the range for normalized results of replicate determinations having an average of 0 and a standard deviation of 1. It is shown that the permissible ranges can be assessed using tabulated percentiles of this distribution and calculated values of the determination (analysis) standard uncertainty. When the standard uncertainty calculation is performed before the analytical method validation, the permissible ranges can be predicted. As an example, the range is predicted for a new pH-metric method for acid number determination without titration in petroleum oils (basic, white and transformer). The results of the prediction are in good conformity with the experimental data. Received: 23 May 1999 · Accepted: 14 November 1999     

The information encrypted in accurate peptide masses-improved protein identification and assistance in glycopeptide identification and characterization

Analytically useful information from accurate mass data for peptides with an error of 相似文献   

Reporting gamma-ray spectrometric measurement results near the natural limit: primary measurement results,best estimates calculated with the Bayesian posterior and best estimates calculated with the probability density distribution resembling shifting

When reporting best estimates as measurement results, systematic influences near the natural limit are introduced that originate not only in the possible inconsistency of the analytical procedure but also in the conversion of the primary measurement results to best estimates. It has been shown that the probability density distribution resembling shifting of values observed in the unfeasible region to the limit of the feasible range (the natural limit) introduces a smaller systematic influence than the Bayesian posterior, resembling censoring with repetition of the measurements that result in observed values in the unfeasible region. The drawback that the uncertainty intervals calculated with the Bayesian posterior do not encompass the natural limit and may not encompass the observed value, although it lies within the feasible region, is avoided by using the probability density distribution resembling shifting. Therefore, such best estimates introduce a smaller systematic influence into the measurement results and are better suited as inputs for subsequent analyses.     

A study of simulated normal probability functions using Microsoft Excel

Simulations are used in many calculations and forecasting procedures, from market analysis to estimation of measurement uncertainty. Microsoft Excel offers an innate procedure to simulate a Gaussian distribution and a pseudorandom number generator (PRNG). Using the latter, five additional simulations models with a potential to simulate the normal probability distribution function (PDF) were explored and compared with the theoretical Gaussian PDF based on a defined average (location) and standard deviation (width). The simulated distributions appeared “displaced” from the Gaussian function. Simulations of the distributions by a large number of observations confirmed different properties of the six simulation procedures. The range of the distributions differed, i.e. the difference between the maximum and minimum simulated values. The innate procedure yielded an unsymmetrical distribution that was shifted to the right (higher values). A miniscule divergence from expected values was demonstrated. A systematic difference between the simulated distributions and the theoretical Gauss distribution may not be of any practical importance in applied metrology, whereas it may be devastating in other applications, e.g. encoding and market simulations. There were differences between the models which may influence their use. It is suggested that a root cause may be found in the PRNG.     

Updated Abraham model correlations for correlating solute transfer into dry butanone and dry cyclohexanone solvents

Updated Abraham solvation parameter model correlations are derived for describing the partitioning and solubility behaviour of organic nonelectrolyte solutes and inorganic gases in both anhydrous butanone and cyclohexanone solvents. The butanone and cyclohexanone correlations are based on data sets that contain 103 and 72 experimental data points, respectively. The derived correlations for butanone describe the experimental partitioning and solubility behaviour to within a standard deviation of 0.145 log units. A slightly smaller standard deviation of 0.135 was observed between the experimental and back-calculated values for the cyclohexanone solvent correlation equations.     

Detection limits and goodness-of-fit measures for the two-component model of chemical analytical error

The utility of analytical chemistry measurements in most applications is dependent on an assessment of measurement error. This paper demonstrates the use of a two-component error model in setting limits of detection and related concepts and introduces two goodness-of-fit statistics for assessing the appropriateness of the model for the data at hand. The model is applicable to analytical methods in which high concentrations are measured with approximately constant relative standard deviation. At low levels, the relative standard deviation cannot stay constant, since this implies vanishingly small absolute standard deviation. The two-component model has approximately constant standard deviation near zero concentration, and approximately constant relative standard deviation at high concentrations, a pattern that is frequently observed in practice. Here we discuss several important applications of the model to environmental monitoring and also introduce two goodness-of-fit statistics, to ascertain whether the data exhibit the error structure assumed by the model, as well as to look for problems with experimental design.     

Estimation of limits of detection and determination in X-ray fluorescence analysis by the dependence of the relative standard deviation on analyte concentration

An experimental dependence of the relative standard deviation on analyte concentration of hyperbolic type, characterizing the precision of quantitative chemical analysis, was used to estimate the limits of detection and determination in the X-ray fluorescence analysis. A method is proposed for the determination of their values using the approximation of the experimental dependence of the relative standard deviation on the analyte concentration by a power function. The choice of the values of the relative standard deviation, being criteria for the estimation of these limits, is substantiated. A concept of the limits of detection and determination of an analytical procedure is formulated, according to which the limit of detection of an analytical procedure is an objective value depending only on the precision of determinations, and the limit of determination of an analytical procedure is a subjective value depending not only on the precision of determinations but also on the requirements to their limiting (admissible) accuracy. The limits of detection and determinations of an analytical procedure found by this approach completely characterize the possibilities of an analytical procedure in determining low concentrations of analytes. The proposed approach can be used for the estimation of the limits of detection and determination of analytical procedures and in other methods of chemical analysis with the hyperbolic dependence of the relative standard deviation on the analyte concentration.     

Electron attachment to DNA and RNA nucleobases: An EOMCC investigation

We report a benchmark theoretical investigation of both vertical and adiabatic electron affinities of DNA and RNA nucleobases: adenine, guanine, cytosine, thymine, and uracil using equation of motion coupled cluster method. The vertical electron affinity (VEA) values of the first five states of the DNA and RNA nucleobases are computed. It is observed that the first electron attached state is energetically accessible in gas phase. Furthermore, an analysis of the natural orbitals exhibits that the first electron attached states of uracil and thymine are valence‐bound in nature and undergo significant structural changes on attachment of an extra electron, which reflects in the deviation of the adiabatic electron affinity (AEA) than that of the vertical ones. Conversely, the first electron attached states of cytosine, adenine, and guanine are in the category of dipole‐bound anions. Their structure, by and large, remain unaffected on attachment of an extra electron, which is evident from the observed small difference between the AEA and VEA values. VEA and AEA values of all the DNA and RNA nucleobases are found to be negative, which implies that the first electron attached states are not stable rather quasi bound. The results of all previous theoretical calculations are out of track and shows large deviation with respect to the experimentally measured values, whereas, our results are found to be in good agreement. Therefore, our computed values can be used as a reliable standard to calibrate new theoretical methods. © 2015 Wiley Periodicals, Inc.     

Reporting measurement results of activities near the natural limit: note and extension of the article “Interpretation of measurement results near the detection limit in gamma-ray spectrometry using Bayesian statistics”

When reporting activity measurement results near the natural limit for activities, (zero), care must be taken not to report observed values from the unfeasible region and not to report confidence intervals extending beyond the limit of the feasible range. This can be achieved by reporting best estimates, where the requirements that the best-estimate values remain in the feasible range and that the confidence intervals do not extend beyond its limit are taken into account. The use of the truncated and renormalized normal distribution, defined by the primary measurement result, as the posterior in the calculation of the best estimates fulfills both requirements, but suffers in that it introduces a bias into the measurement results reported, that is, the observed value may not lie within the interval, centered at the best-estimate value and having a width equal to twice its uncertainty, and that, consequently, the use of best estimates may lead to unacceptable results. Therefore, a posterior, comprising the Dirac delta function distribution δ(a) and the truncated normal distribution, is used for the calculation of the best estimate. It is shown that here the bias introduced is smaller; the observed value lies within the interval centered on the best-estimate value and has a width equal to twice its uncertainty, and that these best estimates perform better when used in calculations of the mean.     

A fluorescence study of DNS-labelled chymotrypsin and related enzymes

Various dansyl (DNS)-conjugates of chymotrypsin, chymotrypsinogen and elastase have been prepared. Excitation and emission spectra, and fluorescence depolarization measurements have been obtained in a spectrophotofluorometer, and relevant fluorescent lifetimes have been derived from fluorescence decay measurements.Free DNS-OH gave a lifetime of 13 nsec in fair agreement with other estimates, but combined DNS gave significantly lower values. In particular, ?-DNS lysine in water gave a value of 4 nsec, with higher values (up to 10 nsec) at increasing glycerol concentration. Of the various protein conjugates, specifically labelled chymotrypsin gave the lowest lifetime (6 nsec); for the others, higher values were observed, the values increasing with pH of labelling. Of the protein conjugates, only in the case of specifically labelled elastase, did 'glycerol concentration cause an increase in the measured τ value from 8 to 12 nsec.Active-site labelled chymotrypsin was unusual in that its fluorescent spectrum was dependent upon excitation wavelength and its excitation spectrum upon the selected emission wavelength. The addition of further non-specifically attached DNS-groups caused a shift towards the spectra of such DNS-groups, and saturation with indole gave spectra of such a type as well as erasing wavelength dependence. It seemed that specifically attached DNS groups were probably within the “tosyl hole” but could be dislodged by indole, a competitive inhibitor.Depolarization properties were in all cases markedly dependent upon excitation wavelength. Experiments performed with varying temperature gave relaxation times which were smaller than expected for a rigid molecule with the molecular weight of chymotrypsin but, also, considerable increases were observed with increasing excitation wavelength. It seemed that the susceptibility to temperature-activated rotation of the DNS group increased with the energy of the incident radiation. At constant temperature, apart from specifically-labelled chymotrypsin, spuriously high relaxation times were observed, for which an explanation is required. Until this is provided, depolarization measurements cannot be regarded as providing a sound method of measuring relaxation times of protein molecules in solution.