Applications of accurate, high-precision Pb isotope ratio measurement by multi-collector ICP-MS

The isotope composition of Ph is difficult to determine accurately due to the lack of a stable normalisation ratio. Double and triple-spike addition techniques provide one solution and presently yield the most accurate measurements. A number of recent studies have claimed that improved accuracy and precision could also be achieved by multi-collector ICP-MS (MC-ICP-MS) Pb-isotope analysis using the addition of Tl of known isotope composition to Pb samples. In this paper, we verify whether the known isotope composition of Tl can be used for correction of mass discrimination of Pb with an extensive dataset for the NIST standard SRM 981, comparison of MC-ICP-MS with TIMS data, and comparison with three isochrons from different geological environments. When all our NIST SRM 981 data are normalised with one constant Tl-205/Tl-203 of 2.38869, the following averages and reproducibilities were obtained: Pb-207/Pb-206=0.91461+/-18; Pb-208/Ph-206 = 2.1674+/-7; and (PbPh)-Pb-206-Ph-204 = 16.941+/-6. These two sigma standard deviations of the mean correspond to 149, 330, and 374 ppm, respectively. Accuracies relative to triple-spike values are 149, 157, and 52 ppm, respectively, and thus well within uncertainties. The largest component of the uncertainties stems from the Ph data alone and is not caused by differential mass discrimination behaviour of Ph and Tl. In routine operation, variation of sample introduction memory and production of isobaric molecular interferences in the spectrometer's collision cell currently appear to be the ultimate limitation to better reproducibility. Comparative study of five different datasets from actual samples (bullets, international rock standards, carbonates, metamorphic minerals, and sulphide minerals) demonstrates that in most cases geological scatter of the sample exceeds the achieved analytical reproducibility. We observe good agreement between TIMS and MC-ICP-MS data for international rock standards but find that such comparison does not constitute the ultimate. test for the validity of the MC-ICP-MS technique. Two attempted isochrons resulted in geological scatter (in one case small) in excess of analytical reproducibility. However, in one case (leached Great Dyke sulphides) we obtained a true isochron (MSWD = 0.63) age of 2578.3 +/- 0.9 Ma, which is identical to and more precise than a recently published U-Pb zircon age (2579 3 Ma) for a Great Dyke websterite [Earth Planet. Sci. Lett. 180 (2000) 1-12]. Reproducibility of this age by means of an isochron we regard as a robust test of accuracy over a wide dynamic range. We show that reliable and accurate Pb-isotope data can be obtained by careful operation of second-generation MC-ICP magnetic sector mass spectrometers. (C) 2002 Elsevier Science B.V. All rights reserved.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Rates of gene rearrangement and nucleotide substitution are correlated in the mitochondrial genomes of insects

A number of studies indicated that lineages of animals with high rates of mitochondrial (mt) gene rearrangement might have high rates of mt nucleotide substitution. We chose the hemipteroid assemblage and the Insecta to test the idea that rates of mt gene rearrangement and mt nucleotide substitution are correlated. For this purpose, we sequenced the mt genome of a lepidopsocid from the Psocoptera, the only order of hemipteroid insects for which an entire mtDNA sequence is not available. The mt genome of this lepidopsocid is circular, 16,924 bp long, and contains 37 genes and a putative control region; seven tRNA genes and a protein-coding gene in this genome have changed positions relative to the ancestral arrangement of mt genes of insects. We then compared the relative rates of nucleotide substitution among species from each of the four orders of hemipteroid insects and among the 20 insects whose mt genomes have been sequenced entirely. All comparisons among the hernipteroid insects showed that species with higher rates of gene rearrangement also had significantly higher rates of nucleotide substitution statistically than did species with lower rates of gene rearrangement. In comparisons among the 20 insects, where the mt genomes of the two species differed by more than five breakpoints, the more rearranged species always had a significantly higher rate of nucleotide substitution than the less rearranged species. However, in comparisons where the mt genomes of two species differed by five or less breakpoints, the more rearranged species did not always have a significantly higher rate of nucleotide substitution than the less rearranged species. We tested the statistical significance of the correlation between the rates of mt gene rearrangement and mt nucleotide substitution with nine pairs of insects that were phylogenetically independent from one 2 another. We found that the correlation was positive and statistically significant (R-2 = 0.73, P = 0.01; R-s = 0.67, P < 0.05). We propose that increased rates of nucleotide substitution may lead to increased rates of gene rearrangement in the mt genomes of insects.