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.     

Dilute and concentrated solutions of polystyrene in trans-decalin close to and far from the θ-temperature—II. Osmotic pressure measurements

Osmotic pressure measurements on polystyrene ($\text{M}{}_{\mathrm{n}}\text{= 396. 000}$) in trans-decalin for concentrations up to 140 kg m^?3 and from 20 to 40 are reported. The θ-temperature is 20.8 . The ratio

where c⁺ is the concentration at which a homogeneous segment distribution is assumed to prevail, increases with temperature up to the plateau value of 0.7. From the temperature dependence of the osmotic pressure, the partial molar enthalpy. Δh₁, and entropy, Δs₁. of mixing are found to be positive. The solvent-solute interaction parameter increases linearly with concentration at all temperatures.     

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 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.     

Anomalous curie response of impurities in quantum-critical spin-1/2 Heisenberg antiferromagnets

We consider a magnetic impurity in two different S=1/2 Heisenberg bilayer antiferromagnets at their respective critical interlayer couplings separating Néel and disordered ground states. We calculate the impurity susceptibility using a quantum Monte Carlo method. With intralayer couplings in only one of the layers (Kondo lattice), we observe an anomalous Curie constant C*, as predicted on the basis of field-theoretical work [S. Sachdev, Science 286, 2479 (1999)10.1126/science.286.5449.2479]. The value C* = 0.262 +/- 0.002 is larger than the normal Curie constant C=S(S+1)/3. Our low-temperature results for a symmetric bilayer are consistent with a universal C*.