Criteria to define the standard deviation for proficiency assessment for the determination of essential trace elements in serum: comparison of Z-scores based on the Horwitz function or on biological variability

A critical issue in the organisation of Proficiency Testing/External Quality Assessment Schemes is the definition of the criteria against which the performance of individual laboratories should be evaluated. Organisers of EQAS in Occupational and Environmental Laboratory Medicine (http://www.occupational-environmental-laboratory.com) collaborate to define common acceptable levels of performance. The aim of this study was to compare the Horwitz function to the Fraser’s approach. Sets of results obtained from the distribution of test materials in the Network schemes (for the measurands: copper, selenium or zinc in serum) were used to calculate Z-scores according to both approaches. Quality specifications derived from both approaches were also compared to the standard deviations obtained. Except for selenium, Horwitz criteria suggests a more stringent evaluation than Fraser criteria, the latter being very stringent as regard the participant analytical variability.     

Some local approximation properties of simple point processes

For simple point processes ξ on a Borel space S, we prove some approximations involving conditional distributions, given that ξ hits a small set B. Beginning with general versions of some classical limit theorems, going back to the pioneering work of Palm and Khinchin, we proceed to prove that, under suitable regularity conditions, the contributions to B and B ^c are asymptotically conditionally independent. We further derive approximations in total variation of reduced Palm distributions and show that, when ξ hits some small sets B ₁,..., B _n , the corresponding restrictions are asymptotically independent. Next we give general versions of the asymptotic relations P{ξ B > 0} ~ Eξ B and prove some ratio limit theorems for conditional expectations E[η | ξ B > 0], valid even when Eξ is not σ-finite and the Palm distributions may fail to exist.     

Kohnen’s limit process for real-analytic Siegel modular forms

Kohnen introduced a limit process for Siegel modular forms that produces Jacobi forms. He asked if there is a space of real-analytic Siegel modular forms such that skew-holomorphic Jacobi forms arise via this limit process. In this paper, we initiate the study of harmonic skew-Maass–Jacobi forms and harmonic Siegel–Maass forms. We improve a result of Maass on the Fourier coefficients of harmonic Siegel–Maass forms, which allows us to establish a connection to harmonic skew-Maass–Jacobi forms. In particular, we answer Kohnen’s question in the affirmative.     

Minimization of side reactions during Lys Tag derivatization of C-terminal lysine peptides

Several issues need to be considered concerning chemical labeling strategies in proteomics. Some of these are labeling specificity, possible side reactions, completeness of reaction, recovery rate, conserving integrity of sample, hydrolysis of peptide bonds at high pH, and signal suppression in mass spectrometry (MS). We tested the effects of different reaction conditions for 2-methoxy-4,5-dihydro-1H-imidazole (Lys Tag) derivatization of the ?-amine group of lysine (K) residues. By using nanoflow LC–electrospray ionization-MS (LC–ESI-MS) and MS/MS in combination with MSight 2-D image analysis, we found that standard Lys Tag derivatization processes and conditions induce side reactions such as (i) Lys Tag labeling of the N-terminus, (ii) methylation of internal aspartic acid (D), glutamic acid (E) and C- and N-peptide termini and (iii) deamidation of asparagine (N) and glutamine (Q). We found temperature and pH to be the main variables to control side reactions. Lowering the reaction temperature from 55 °C to room temperature reduced deamidation from 22.8 ± 1.4% (SEM) to 7.7 ± 5.5% (SEM) and almost totally blocked methylation (7.0 ± 1.2% (SEM) to 0.4 ± 0.4% (SEM) of the internal acidic amino acids (D and E) at high pH. We conclude that lowering the reaction temperature minimizes undesired side reactions during Lys Tag derivatization in solution.     

Some Problems of Local Hitting, Scaling, and Conditioning

The aim of this paper is to convey the basic ideas regarding some local hitting and conditioning properties of random measures. Some very general results are obtainable in the special case of simple point processes. Though much of this theory has no counterpart for general random measures, similar results do exist in two cases of special interest—for local time random measures and for Dawson–Watanabe superprocesses. This is an informal account of some of the basic hitting and conditioning properties common to all three cases. Precise statements and proofs will be provided elsewhere.     

Visualizing information in multivariate data: Applications to petroleum geochemistry : Part 1. Projection methods

General procedures are developed for revealing and comparing the information carried by experimental data obtained for different petroleum fractions. Oblique rotation of principal components is used to obtain projections amenable to geochemical interpretation. A systematic method is given for selecting markers, i.e., compounds related to specific geochemical factors. By projecting samples onto axes defined by markers, their potential for describing a petroleum fraction can be evaluated. The similarity between samples or groups (classes) of samples is revealed by projecting samples onto “geochemicalrdquo; axes and by comparing their residual distances to class models. In class modelling, projections on markers are proposed as a method for eliminating differences induced by alteration processes not related directly to the source of the oils, e.g., maturity.     

An Elementary Approach to the Daniell-Kolmogorov Theorem and Some Related Results

We give a short elementary proof of the Daniell-Kolmogorov existence theorem for probability measures on product spaces, assuming nothing but the existence of Lebesgue measure on the unit interval. Related approaches are used to prove the existence of regular conditional distributions directly on Polish spaces, and to establish the existence of random measures and sets with given finite-dimensional distributions or hitting probabilities, respectively.     

The computation of orthogonal rational functions and their interpolating properties

We shall consider nested spacesl _n ,n = 0, 1, 21... of rational functions withn prescribed poles outside the unit disk of the complex plane. We study orthogonal basis functions of these spaces for a general positive measure on the unit circle. In the special case where all poles are placed at infinity,l _n = _n , the polynomials of degree at mostn. Thus the present paper is a study of orthogonal rational functions, which generalize the orthogonal Szegö polynomials. In this paper we shall concentrate on the functions of the second kind which are natural generalizations of the corresponding polynomials.The work of the first author is partially supported by a research grant from the Belgian National Fund for Scientific Research     

Asymptotics for Szegö polynomial zeros

The Wiener-Levinson method and algorithm, formulated here in terms of Szegö polynomials _n ( _N,I ;z) orthogonal on the unit circle, is used to find unknown frequencies _j from anN-sample of a discrete time signal consisting of the superposition of sinusoidal waves with frequencies ₁,...,₁. In a recent paper the authors (and W.J. Thron) have shown that zerosz(j, n, N, I) of _n ( _N,I ;z) converge asN to the critical points ,j=1, 2,...,I, providednn ₀ (I)=2I+L, whereL is 0 or 1. The present paper gives results on the convergence of zerosz(j, n, N, I) to some of the for the case in whichnn ₀ (I), wheren is the degree of _n ( _N,I ;z).Research supported in part by the United States Educational Foundation in Norway (Fulbright Grant), the Norwegian Research Council (NAVF) and the US National Science Foundation under Grant No. DMS-9103141.     

Solvent effects on optically detected magnetic resonance in triplet spin labels

We have calculated solvent effects on the zero-field splitting (ZFS) constants induced by electron spin–spin coupling (SSC) in the low-lying triplet states of azaaromatic molecules in solutions using multiconfiguration self-consistent-field wave functions and the polarizable continuum model. The second-order spin–orbit coupling (SOC) contribution to the splitting of the ^3* states is found to be almost negligible, and the calculations therefore provide a good estimate of the ZFS parameters and their solvent dependence based only on the electron spin–spin coupling expectation values. The correlation between the shift in the ZFS and the phosphorescence frequency that has been observed in optically detected magnetic resonance experiments in low-temperature glasses is supported by our direct SSC calculations without taking SOC into account. This makes it possible to distinguish between the two theories that earlier were proposed to explain the inhomogeneous broadening of triplet state spectra, and discard the one that is exclusively based on the SOC-induced mixing of the singlet and triplet states.Contribution to the Jacopo Tomasi Honorary IssueAcknowledgments. This work was supported (B. M.) by the Swedish Royal Academy of Science (KVA). This work was also supported by the Norwegian Research Council through a grant of computer time from the Program for Supercomputing. We are grateful to B. Schimmelpfenning for his valuable assistance in the computations.