Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

Reactions of the ionized enol tautomer of acetanilide: elimination of HNCO via a novel rearrangement

The reactions of ionised acetanilide, C(6)H(5)NH(=O)CH(3)(.+), and its enol, C(6)H(5)NH(OH)=CH(2)(.+), have been studied by a combination of tandem mass spectrometric and computational methods. These two isomeric radical cations have distinct chemistries at low internal energies. The keto tautomer eliminates exclusively CH(2)=C=O to give ionised aniline. In contrast, the enol tautomer loses H-N=C=O, via an unusual skeletal rearrangement, to form predominantly ionised methylene cyclohexadiene. Hydrogen atom loss also occurs from the enol tautomer, with the formation of protonated oxindole. The mechanisms for H-N=C=O and hydrogen atom loss both involve cyclisation; the former proceeds via a spiro transition state formed by attachment of the methylene group to the ipso position, whereas the latter entails the formation of a five-membered ring by attachment to the ortho position. The behaviour of labelled analogues reveals that these two processes have different site selectivities. Hydrogen atom loss involves a reverse critical energy and is subject to an isotope effect. Surprisingly, attempts to promote the enolisation of ionised acetanilide by proton-transport catalysis were unsuccessful. In a reversal of the usual situation for ionised carbonyl compounds, ionised acetanilide is actually more stable than its enol tautomer. The enol tautomer was resistant to proton-transport catalysed ketonisation to ionised acetanilide, possibly because the favoured geometry of the encounter complex with the base molecule is inappropriate for facilitating tautomerisation.     

Simultaneous determination of arsenic, manganese, and selenium in biological materials by neutron-activation analysis

A new method was developed for the simultaneous determination of arsenic, manganese, and selenium in biological material by thermal-neutron activation analysis. The use of (81 m)Se as indicator for selenium permitted a reduction of activation time to 1 hr for a 1 g sample, and the possibility of loss of volatile compounds during irradiation could be dismissed. No pretreatment of the sample is required, and the radiochemical separation scheme is based on simple chemical operations, completed in less than 3 hr. A systematic experimental investigation of the performance characteristics of the method was carried out, including studies of the accuracy of the results. The actual precision achieved in routine application of the method in the analytical laboratory was in good agreement with the calculated precision, and the results are therefore well suited for statistical evaluation of differences at the ppM level in samples of biological tissue.     

Quality assurance and statistical control

In scientific research laboratories it is rarely possible to use quality assurance schemes, developed for large-scale analysis. Instead methods have been developed to control the quality of modest numbers of analytical results by relying on statistical control: Analysis of precision serves to detect analytical errors by comparing thea priori precision of the analytical results with the actual variability observed among replicates or duplicates. The method relies on the chi-square distribution to detect excess variability and is quite sensitive even for 5–10 results. Interference control serves to detect analytical bias by comparing results obtained by two different analytical methods, each relying on a different detection principle and therefore exhibiting different influence from matrix elements; only 5–10 sets of results are required to establish whether a regression line passes through the origo. Calibration control is an essential link in the traceability of results. Only one or two samples of pure solid or aqueous standards with accurately known content need to be analyzed. Verification is carried out by analyzing certified reference materials from BCR, NIST, or others; their limited accuracy of 5–10% make them less suitable for calibration purposes.     

Analysis of precision of activation-analysis methods

The precision of an activation-analysis method prescribes the estimation of the precision of a single analytical result. The adequacy of these estimates to account for the observed variation between duplicate results from the analysis of different samples and materials, is tested by the statistic T, which is shown to be approximated by a chi(2) distribution. Application of this test to the results of determinations of manganese in human serum by a method of established precision, led to the detection of airborne pollution of the serum during the sampling process. The subsequent improvement in sampling conditions was shown to give not only increased precision, but also improved accuracy of the results.     

Analysis of proteins from a glioma cell line by using micro-scale solution isoelectric focusing in combination with liquid chromatography/tandem mass spectrometry

In this study we have investigated whether micro-solution isoelectric focusing (microsol-IEF) can be used as a pre-fractionation step prior to liquid chromatography/tandem mass spectrometry (LC/MS/MS) and if extensive sample purification of the different fractions is required. We found that, in spite of the high concentrations of buffer and detergents, no clean up of the digested microsol-IEF fractions was necessary before analysis by LC/MS/MS. We also concluded that it is possible to identify at least twice as many proteins in a glioma cell lysate with the combination of microsol-IEF and LC/MS/MS than with LC/MS/MS alone. Furthermore, most of the proteins that were identified from one microsol-IEF fraction by using analytical narrow-range two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) and peptide mass fingerprinting with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) were also identified by LC/MS/MS. Finally, we used the combination of microsol-IEF and LC/MS/MS to compare two sample preparation methods for glioma cells and found that several nuclear, mitochondria, and endoplasmic reticulum proteins were only present in the sample that had been subjected to lipid extraction by incubating the homogenized cells in chloroform/methanol/water.     

Sampling and metrology

The result of a measurement refers in principle only to the amount of substance actually contributing to the analytical signal. However, an appropriate definition of the measurand must include a specification of the system for which the result of the measurement should apply. All systems being inherently heterogeneous, representativity assumes importance for the metrological quality of a measurement, and the process needed to ascertain representativity is sampling. The contribution from this characteristic must be included when expressing the uncertainty of the reported value of the measurand. Representative sampling of systems that are infinite or non-uniform was developed by Pierre Gy in his Theory of Sampling. Finite systems can achieve uniformity by mechanical treatment and mixing; the heterogeneity of these systems can be characterized by a sampling constant, expressed in units of weight, for each particular species being determined. Examples of the contribution of sampling to the uncertainty of analytical results are discussed for some biological materials. Presented at the 2nd International Conference on Metrology – Trends and Applications in Calibration and Testing Laboratories, November 4–6, 2003, Eilat, Israel.     

Indirect determination of soluble trace elements in certified reference materials by neutron activation analysis

Since 1983 we have analyzedaqua regia extracts from environmental reference materials of 5 different soils and 4 different sludges by neutron activation analysis. Aqua regia as such is not accepted for irradiation in a nuclear reactor, and therefore the solution has to be evaporated to dryness, mixed and dried to constant weight before an aliquot can be taken and subjected to instrumental neutron activation analysis (INAA). Results for leachable Cr and Zn were found to display greater variability than results for total contents of these elements, and the reasons for this will be discussed.For the 1994 certification campaign for one soil and two sludges we have chosen to determine the total content of trace elements in these reference materials by INAA before and afteraqua regia leaching. The leachable contents are then found indirectly as a difference between the two results; in this way we eliminate the sources of uncertainty associated with the drying and handling of theaqua regia extracts, and we reduce the contributions from counting statistics.     

Determination of magnesium in botanical reference materials by instrumental neutron activation analysis

Instrumental neutron activation analysis (INAA) was applied to the rapid determination of magnesium in the botanical reference materials Beech Leaves-100 and Spruce Needles-101. The magnesium content was quantitatively determined by measuring the gamma-ray photopeak at 1014 keV of the short-lived radionuclide²⁷Mg (9.46 m). The magnesium concentrations in the two materials were found to be 834.6±50.2 g·g^–1 dry weight and 618.6±36.2 g·g^–1, respectively. When assaying a 0.1 g sample under the same experimental conditions the limit of detection is 30 g of Mg.Work carried out at Risø National Laboratory, Isotopes Division, DK-4000 Roskilde, Denmark.