A fast ‘Monte-Carlo cross-validation’ procedure for large least squares problems with noisy data

Summary We propose a fast Monte-Carlo algorithm for calculating reliable estimates of the trace of the influence matrixA involved in regularization of linear equations or data smoothing problems, where is the regularization or smoothing parameter. This general algorithm is simply as follows: i) generaten pseudo-random valuesw ₁, ...,w _n , from the standard normal distribution (wheren is the number of data points) and letw=(w ₁, ...,w _n ) ^T , ii) compute the residual vectorw–A w, iii) take the normalized inner-product (w ^T (w–A w))/(w ^T w) as an approximation to (1/n)tr(I–A ). We show, both by theoretical bounds and by numerical simulations on some typical problems, that the expected relative precision of these estimates is very good whenn is large enough, and that they can be used in practice for the minimization with respect to of the well known Generalized Cross-Validation (GCV) function. This permits the use of the GCV method for choosing in any particular large-scale application, with only a similar amount of work as the standard residual method. Numerical applications of this procedure to optimal spline smoothing in one or two dimensions show its efficiency.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

Fe(CO)5 thin films adsorbed on Au(111) and on self-assembled organic monolayers: I. Structure

The adsorption of Fe(CO)(5) onto Au(111)/mica and C(4), C(8), C(12), and C(16) SAMs/Au(111)/mica surfaces has been studied using infrared spectroscopy to elucidate the coverage-dependent structures of these films and the intermolecular couplings that determine the form of the spectra. For all substrates, the first layer is composed of molecules physisorbed with one axial and two equatorial carbonyl groups directed toward the substrate; subsequent layers are preferentially oriented with the C(3) molecular axis aligned perpendicular to the substrate (i.e., one axial carbonyl group directed toward the substrate). The axial vibrational band systematically shifts to higher frequencies with increasing surface coverage because of the effects of intermolecular coupling of the quasiparallel transition dipole moments. The strong effects of dipolar coupling are also witnessed by the trends of the band positions when the distance to the image plane is systematically varied using highly organized self-assembled organic substrates; no band shifts are observed when dilute Fe(CO)(5) is embedded in Xe matrixes under identical experimental conditions. The as-deposited films are structurally stable below 125 K on Au(111)/mica surfaces and below 100 K on the organic self-assembled monolayers. The instability of the films above these temperatures demonstrates that the as-adsorbed films do not form thermodynamically well-defined phases but are structurally metastable. The results presented herein and in the companion paper provide a consistent framework to interpret the spectroscopy of these systems that resolves outstanding issues concerning these films and provides a structural model that explains the dynamic properties of these films during exposure to low-energy electron beams.     

Synthesis of some substituted 3-alkenyl-1-phenylpyrazoles

The regioselective synthesis of new 3-alkenyl-1-phenylpyrazoles 4 from the reaction of phenylhydrazine with 2,3-dihydro-4H-pyran-4-ones 1 is described.     

Synthetic applications of 2-chlorooxiranes: preparation of thiazoles,dihydrothiazoles and selenazoles

The reaction of 2-chlorooxiranes 1 with thioamides and thioureas provides access to thiazoles, 4-hydroxy-4,5-dihydrothiazoles and 2-imino-2,3-dihydrothiazoles under mild conditions and with excellent yields. With 1 and selenourea, near quantitative yields of selenazoles are obtained.     

Determination of zearalenone and ochratoxin A in soil

Mycotoxins are secondary metabolites, formed by the action of fungi on agricultural crops in the field or during storage. These metabolites are highly toxic to animals and humans and high levels have been measured in agricultural crops. In order to evaluate human risks due to ingestion of mycotoxin-contaminated food different methods have been developed for analysis of mycotoxins in cereals and maize. In this project the focus was on mycotoxins in agricultural soil and the fate of these toxins in the soil-water-plant system. Two different mycotoxins were selected in the study: zearalenone (ZON) produced by species of Fusariumor Aspergillusand ochratoxin A (OTA) produced by species of Penicillium. We developed a method for analysis of these toxins in soil. Soil samples were extracted with methanol-water (9:1) and purified by solid-phase extraction (SPE, C8-columns). The final extract was analysed using high-pressure liquid chromatography (HPLC) with fluorescence detection. A Phenyl Hexyl column was used to separate the toxins. The detection limits obtained were 0.1 and 1.0 microg kg(-1) dry weight (dw) for OTA and ZON, respectively. The developed method has been used for analysis of different soils in connection with growth chamber experiments. The soil types used in the growth chamber experiments were a sandy soil, a sandy clay soil, and a soil with high content of organic matter. The recovery was determined as 85.8 and 93.4% and the repeatability to 5.1 and 12.8% for OTA and ZON, respectively. The reproducibility obtained was 8.5 and 15.0% for soil samples, representing concentration levels from 0.2-30 microg kg(-1) dw (OTA) and from 1.0-100 microg kg(-1) dw (ZON).     

Platinum metallodrug-protein binding studies by capillary electrophoresis-inductively coupled plasma-mass spectrometry: characterization of interactions between Pt(II) complexes and human serum albumin

Characterizing how platinum metallocomplexes bind to human serum albumin (HSA) is essential in evaluating anticancer drug candidates. Using cisplatin as a reference complex, the application of capillary electrophoresis (CE) to reliably assess drug/HSA interactions was validated. Since this complex is small compared to the size of the protein, the binding response could only be recognized when applying CE coupled to a (platinum) metal-specific mode of detection, namely inductively coupled plasma-mass spectrometry (ICP-MS). This coupling allowed for confirmation of a specific affinity of cisplatin and novel Pt complexes to HSA, measurement of the kinetics of binding reactions, and determination of the number of drug molecules attached to the protein. As the cisplatin/HSA molar ratio increased, the reaction rate became faster with a maximum on the kinetic curve appearing at about 50 h of incubation at 20 times excess of cisplatin. The reaction was characterized as a pseudo-first order reaction with the rate constant k = 0.003 min(-1) at 37 degrees C. When incubated with a 20-fold excess of cisplatin, HSA bound up to 10 mol of Pt per mol of the protein. This is indicative for a strong metal-protein coordination occurring at several HSA sites other than the only protein cysteine residue. Structural analogs of cisplatin, bearing aminoalcohol ligands, showed comparable protein binding reactivity and stoichiometry but a common equilibrium was not reached even after one week of incubation. Also apparent was a two-step mechanism of the binding reaction. Results demonstrated the suitability of CE-ICP-MS as a rapid assay for high-throughput studying of drug/HSA interactions.     

31P solid state NMR studies of metal selenophosphates containing [P2Se6]4-, [P4Se10]4-, [PSe4]3-, [P2Se7]4-, and [P2Se9]4- ligands

31P solid-state nuclear magnetic resonance (NMR) spectra of 12 metal-containing selenophosphates have been examined to distinguish between the [P(2)Se(6)](4-), [PSe(4)](3-), [P(4)Se(10)](4-), [P(2)Se(7)](4-), and [P(2)Se(9)](4-) anions. There is a general correlation between the chemical shifts (CSs) of anions and the presence of a P[bond]P. The [P(2)Se(6)](4-) and [P(4)Se(10)](4-) anions both contain a P[bond]P and resonate between 25 and 95 ppm whereas the [PSe(4)](3-), [P(2)Se(7)](4-), and [P(2)Se(9)](4-) anions do not contain a P[bond]P and resonate between -115 and -30 ppm. The chemical shift anisotropies (CSAs) of compounds containing [PSe(4)](3-) anions are less than 80 ppm, which is significantly smaller than the CSAs of any of the other anions (range: 135-275 ppm). The smaller CSAs of the [PSe(4)](3-) anion are likely due to the unique local tetrahedral symmetry of this anion. Spin-lattice relaxation times (T(1)) have been determined for the solid compounds and vary between 20 and 3000 s. Unlike the CS, T(1) does not appear to correlate with P-P bonding. (31)P NMR is also shown to be a good method for impurity detection and identification in the solid compounds. The results of this study suggest that (31)P NMR will be a useful tool for anion identification and quantitation in high-temperature melts.     

The optimal amount of isotopic spike solution for ultratrace analysis by isotope dilution mass spectrometry

 Inductively coupled plasma mass spectrometry (ICP-MS) and high resolution inductively coupled plasma mass spectrometry (HR-ICP-MS) are powerful methods of determining metallic impurities in the low- and sub-ppt level in process media such as ultra-pure water used in semiconductor and wafer manufacturing. By using mass spectrometers for analysis, an isotope dilution analysis (IDMS) is possible. The reproducibility of an IDMS is unmatched. For concentration levels near the instrument detection limit a novel method is reported to find the optimal amount of isotopic spike solution. This optimal value can be derived by the law of propagation of uncertainty combined with the Poisson statistics of the measured number of counts. Generally, an excess of isotopic spike solution should be used to provide results of lowest possible uncertainty. The results are presented in a diagram for easy practical use. Received: 14 October 1997 · Accepted: 13 February 1998