An ideal point method for the design of compromise experiments to simultaneously estimate the parameters of rival mathematical models

When several rival mathematical models are proposed for one and the same process, experimental design techniques are available to design optimal discriminatory experiments. Because these techniques are model-based, it is important that the model predictions are not too uncertain. Therefore, model discrimination may become more efficient and effective if this uncertainty is reduced first. This can be achieved by performing experiments designed to increase the accuracy of the parameter estimates and, thus, the model predictions. However, performing such an additional experiment for each rival model may undermine the overall goal of optimal experimental design, which is to minimize the experimental effort. This paper deals with the design of a so-called compromise experiment, which is an experiment that is not optimal for each of the rival models, but sufficiently informative to improve the overall accuracy of the parameters of all rival models. For this purpose, the problem is approached as a multi-objective optimization problem and the ideal point method is proposed to design the compromise experiment. This method searches for the experiment that is as close as possible to the optimal experiments of the individual rival models. The method is applied to a case study where nine rival models are competing to describe the kinetics of an enzymatic reaction, and the obtained results show that the ideal method is capable of designing a compromise experiment.     

Variational density matrix optimization using semidefinite programming

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N-representable density matrix leads to matrix-positivity constraints on the density matrix. We then formulate this in a standard semidefinite programming form, after which two interior point methods are discussed to solve the SDP. As an example we show the results of an application of the method on the isoelectronic series of Beryllium.     

Opal

Abstract

Calcite collectors often ask, “How many kinds of calcite twins are there?” The answer is hard to give because the word kinds is ambiguous. The question can be given an unambiguous answer, however, if the question is rephrased: “How many twin laws are there for calcite?” In this case, the answer is “four.” I will go further and assert that there are four, and only four, twin laws for calcite. The rest of this article will be spent explaining my answer and providing enough information that an observant collector should be able to tell whether a calcite crystal is twinned or not and to determine which of the four twin laws is represented. The basics of calcite crystallography are well covered in the excellent article by Brock (1993), and basic aspects of twinning are covered by Werner Lieber elsewhere in this issue.     

Antioxidant phytochemical and fruit quality changes in mango (Mangifera indica L.) following hot water immersion and controlled atmosphere storage

Tropical fruits such as mangoes destined for import into the United States are commonly required to have a thermal treatment against invasive pests, which could be combined with controlled atmosphere (CA) storage to prolong shelf life and preserve fruit quality. Changes in antioxidant phytochemicals and resultant quality during storage and ripening were investigated in fresh mangoes, as influenced by application of CA in combination with a hot water immersion quarantine treatment (46 °C for 75 min). Mature-green mangoes with or without a hot water treatment, were held in air, 3% O₂ + 97% N₂, or 3% O₂ + 10% CO₂ + 87% N₂ and evaluated for external quality and phytochemical differences after storage for 2 weeks at 10 °C and after subsequent ripening in air at 25 °C. Visible appearance of anthracnose during ripening was effectively inhibited by the hot water treatments combined with CA. Concentrations of gallic acid and numerous hydrolysable tannins and their resultant antioxidant capacity were unaffected by the hot water treatment, while total polyphenolics naturally decreased throughout fruit ripening, regardless of hot water treatment or storage atmosphere. However, the overall decline in polyphenolic concentration was inhibited by the CA treatments, as a result of delayed ripening. Quality parameters such as flesh colour and titratable acidity provided supporting evidence that the CA conditions helped to delay fruit ripening.     

Crystal structures of MgyTi100−y thin film alloys in the as-deposited and hydrogenated state

In situ X-ray diffraction was used to identify the crystal structures of as-deposited and hydrogenated Mg_yTi_100-y thin film alloys containing 70, 80 and 90 at.% Mg. The preferred crystallographic orientation of the films in both the as-prepared and hydrogenated state made it difficult to unambiguously identify the crystal structure up to now. In this work, identification of the unit cells was achieved by in situ recording diffraction patterns at various tilt angles. The results reveal a hexagonal closed packed structure for all alloys in the as-deposited state. Hydrogenating the layers under 10⁵ Pa H₂ transforms the unit cell into face-centered cubic for the Mg₇₀Ti₃₀ and Mg₈₀Ti₂₀ compounds, whereas the unit cell of hydrogenated Mg₉₀Ti₁₀ has a body-centered tetragonal symmetry. The (de)hydrogenation kinetics changes along with the crystal structure of the metal hydrides from rapid for fcc-structured hydrides to sluggish for hydrides with a bct symmetry and emphasizes the influence of the crystal structure on the hydrogen transport kinetics.     

Health effects of methyl tertiary butyl ether (MTBE) in gasoline in Alaska

OBJECTIVES: This ecologic study assessed whether there was a change in health status in Alaska in the winter of 1992-93 after the introduction of MTBE in gasoline. Methyl tertiary butyl ether(MTBE) is used as a fuel oxygenate in the United States and in Europe. In the winter of 1992-93 MTBE was added to gasoline in the cities of Fairbanks and Anchorage, Alaska. The program was discontinued in Fairbanks in December, 1992, but continued in Anchorage until February 28, 1993. METHODS: Outpatient visits for state employees and dependents (n = approximately 28,000) living in Alaska were compared over three winters by analyzing health insurance claims. RESULTS: Odds ratios were calculated. The odds ratios indicated that the winter of 92-93 was not statistically different from previous winters in numbers of claims for upper respiratory illness, bronchitis, headache, or asthma in either Anchorage or Fairbanks. CONCLUSION: There was no increase in claims for respiratory illness in either city after introduction of MTBE.     

Characterization of spin polarized dilute3He-4He solutions below 500 mK

We have prepared a large sample of spin polarized liquid ³ He- ⁴ He at 500 mK. Polarization is obtained by laser optical pumping, and studied by pulsed NMR. We have observed a nuclear magnetization lifetime T ₁ longer than 1 hour, and an anomalously long, non linear decay of tranverse magnetization.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associé au CNRS (URA 18).     

High-performance liquid chromatography-fluorescence assay of pyruvic acid to determine cysteine conjugate beta-lyase activity: application to S-1,2-dichlorovinyl-L-cysteine and S-2-benzothiazolyl-L-cysteine

An HPLC-fluorescence assay has been developed for the determination of the activity of rat renal cytosolic cysteine conjugate beta-lyase. The method is based on isocratic HPLC separation and fluorescence detection of pyruvic acid, derivatized with o-phenylenediamine (OPD), and is shown to be rapid, specific, and very sensitive. The assay has been evaluated with two model substrates for rat renal cytosolic beta-lyase, notably S-1,2-dichorovinyl-L-cysteine (DCVC) and S-2-benzothiazolyl-L-cysteine (BTC). Equimolar formation of pyruvic acid and 2-mercaptobenzothiazole, a chromophoric thiol, indicated that pyruvic acid formation actually reflects the beta-elimination activity of beta-lyase during the beta-elimination of BTC. From this it follows that the pyruvic acid assay can be applied to the measurement of the beta-elimination activity of this enzyme, independent of the presence of chromophoric groups or radiolabels in substrates. Due to the large linear range and the very high sensitivity of the present HPLC-fluorescence assay (detection limit, 7.5 pmol of pyruvic acid), both good and poor substrates of beta-lyase can be measured. Enzyme kinetic data are presented for the model substrates BTC and DCVC and for four structurally related S-2,2-difluoroethyl-L-cysteine conjugates.