Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.     

Imaginary vibrational modes in polycyclic aromatic hydrocarbons: a challenging test for the hardness profiles.

In a very recent article (J. Am. Chem. Soc. 2006, 128, 9342-9343) Moran et al. found that electron-correlated methodologies using popular Pople basis sets lead to spurious nonplanar polycyclic aromatic hydrocarbon (PAH) equilibrium structures. Furthermore, some of the present authors have shown that the hardness profiles along a reaction path can be a useful tool to find spurious stationary points in the potential energy surface. Herein, we test the performance of the hardness profiles to detect shortcomings in energy profiles for the challenging case of nonplanar PAHs. The results obtained show that in 41 of the 42 imaginary vibrational modes studied, the hardness profiles indicate the wrong number and type of the potential energy surface stationary points.     

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

This paper studies a generalized version of multi-class cost-constrained random-coding ensemble with multiple auxiliary costs for the transmission of N correlated sources over an N-user multiple-access channel. For each user, the set of messages is partitioned into classes and codebooks are generated according to a distribution depending on the class index of the source message and under the constraint that the codewords satisfy a set of cost functions. Proper choices of the cost functions recover different coding schemes including message-dependent and message-independent versions of independent and identically distributed, independent conditionally distributed, constant-composition and conditional constant composition ensembles. The transmissibility region of the scheme is related to the Cover-El Gamal-Salehi region. A related family of correlated-source Gallager source exponent functions is also studied. The achievable exponents are compared for correlated and independent sources, both numerically and analytically.     

Vibrational spectroscopy differentiates between multipotent and pluripotent stem cells

Over the last few years, there has been an increased interest in the study of stem cells in biomedicine for therapeutic use and as a source for healing diseased or injured organs/tissues. More recently, vibrational spectroscopy has been applied to study stem cell differentiation. In this study, we have used both synchrotron based FTIR and Raman microspectroscopies to assess possible differences between human pluripotent (embryonic) and multipotent (adult mesenchymal) stem cells, and how O(2) concentration in cell culture could affect the spectral signatures of these cells. Our work shows that infrared spectroscopy of embryonic (pluripotent) and adult mesenchymal (multipotent) stem cells have different spectral signatures based on the amount of lipids in their cytoplasm (confirmed with cytological staining). Furthermore, O(2) concentration in cell culture causes changes in both the FTIR and Raman spectra of embryonic stem cells. These results show that embryonic stem cells might be more sensitive to O(2) concentration when compared to mesenchymal stem cells. While vibrational spectroscopy could therefore be of potential use in identifying different populations of stem cells further work is required to better understand these differences.     

Assembly of titanium embedded polyoxometalates with unprecedented structural features

Two titanium embedded polyoxometalates with unprecedented structural features are presented: a monotitanium containing tungstoantimonate Na(13)H(3)[TiO(SbW(9)O(33))(2)]·33 H(2)O featuring a {Ti=O}(2+) moiety (1) and a hexatitanium containing tungstoarsenate K(6)[Ti(4)(H(2)O)(10)(AsTiW(8)O(33))(2)]·30 H(2)O containing a {Ti(4)(H(2)O)(10)}(16+) moiety (2). Both compounds have been fully characterised by single crystal X-ray diffraction, elemental analysis, IR and TGA. 1 is constructed from two α-B-{Sb(III)W(9)O(33)} fragments linked by five sodium cations and an unprecedented square pyramidal Ti(O)O(4) group with a terminal Ti=O bond, and 2 exhibits a Krebs-type structure composed of two {AsTiW(8)O(33)} fragments, where one W(VI) centre has been substituted for a Ti(IV) centre in each, fused together via a belt of four additional Ti(IV) centres. This system represents the tungsten Ti-incorporated polyoxoanion with one of the highest Ti:W ratios so far reported. Additionally, 2 could also be isolated as an n-tetrabutylammonium salt and has been further characterised by electrochemistry and electrospray ionisation (ESI) MS studies. Due to the unique nature of these systems, both have been fully investigated using DFT calculations yielding highly interesting results. Structure 1 has been optimised with five sodium atoms in the belt position, which in addition to reducing the high charge of the cluster influence a stabilisation of the antimony lone pairs. Electrostatic potential calculations highlight the high electronegativity of the terminal oxygen on the titanium centre, enhancing real potentiality as a reactive site for catalysis.     

Determination of antibacterials in animal feed by pressurized liquid extraction followed by online purification and liquid chromatography-electrospray tandem mass spectrometry

A fully automated method has been developed for analysis of eighteen antibacterial compounds, including penicillins, cephalosporins and sulfonamides, in animal feed with limits of quantification in the range 0.25–5.79 μg kg⁻¹. The method is based on pressurized liquid extraction of 3 g homogenized feed with water and online clean-up of 500 μL of the extract with C₁₈HD cartridges. The purified sample was directly analysed by liquid chromatography–electrospray tandem mass spectrometry (SPE–LC–ESI-MS–MS). Chromatographic separation was achieved within 10 min by use of a C₁₂ Phenomenex Hydro-RP reversed-phase analytical column and a mobile phase gradient (water + 0.1% formic acid–methanol + 0.1% formic acid). The method was validated, revealing capability for detection of concentrations as low as 0.09 μg kg⁻¹, decision limits (CCα) and detection capabilities (CCβ) in the range 10–174 μg kg⁻¹ and 22–182 μg kg⁻¹, respectively, and inter-day precision ranging from 0.7 to 8.3%. Recovery, with internal standard correction, was in the range 93–134% for all analytes. The method was then applied to analysis of fifteen feed samples, nine of which contained at least one antimicrobial at concentrations between 0.006 and 1.526 mg kg⁻¹. The performance data and results from the method were compared with those from a previous method developed by our group, using offline SPE, by analyzing the same set of samples by both methods. The online SPE approach resulted in slightly improved sensitivity, with LODs of 0.09–2.12 μg kg⁻¹ compared with 0.12–3.94 μg kg⁻¹ by the offline approach. In general, better recovery was achieved by use of online purification (for 72% of the analytes) and the correlation between the two methods was good. The main advantages of the new online method are rapid and automated sample pre-treatment, and reduction of sample manipulation, enabling high-throughput analysis and highly accurate results. Because of all these characteristics, the proposed method is applicable and could be deemed necessary within the field of food control and safety.     

Testosterone metabolism revisited: discovery of new metabolites

The metabolism of testosterone is revisited. Four previously unreported metabolites were detected in urine after hydrolysis with KOH using a liquid chromatography–tandem mass spectrometry method and precursor ion scan mode. The metabolites were characterized by a product ion scan obtained with accurate mass measurements. Androsta-4,6-dien-3,17-dione, androsta-1,4-dien-3,17-dione, 17-hydroxy-androsta-4,6-dien-3-one and 15-androsten-3,17-dione were proposed as feasible structures for these metabolites on the basis of the mass spectrometry data. The proposed structures were confirmed by analysis of synthetic reference compounds. Only 15-androsten-3,17-dione could not be confirmed, owing to the lack of a commercially available standard. That all four compounds are testosterone metabolites was confirmed by the qualitative analysis of several urine samples collected before and after administration of testosterone undecanoate. The metabolite androsta-1,4-dien-3,17-dione has a structure analogous to that of the exogenous anabolic steroid boldenone. Specific transitions for boldenone and its metabolite 17β-hydroxy-5β-androst-1-en-3-one were also monitored. Both compounds were also detected after KOH treatment, suggesting that this metabolic pathway is involved in the endogenous detection of boldenone previously reported by several authors.     

Application of the new electroanalytical technique AGNES for the determination of free Zn concentration in river water

Absence of gradients and Nernstian equilibrium stripping (AGNES) is a recently developed electroanalytical technique specifically designed for the direct determination of free concentrations of metal ions. AGNES is applied here to the determination of free Zn concentration in a river water sample. The method has been validated with synthetic solutions of low ionic strengths containing Zn and 2,6-pyridinedicarboxylic acid and then applied to synthetic river waters and to a natural sample collected from Besòs River in Montcada i Reixac (Catalonia, North-Eastern Spain). In the river sample, an average free Zn concentration of 12.8(4) nM was obtained, while the total dissolved Zn concentration was 0.51(8)?μM. To control and maintain pH and pCO₂ constant during AGNES measurements, a novel device for N₂/CO₂ mixed purging has been developed.     

Towards the Accurate Calculation of 183W NMR Chemical Shifts in Polyoxometalates: The Relevance of the Structure

DFT calculations were carried out to study ¹⁸³W NMR chemical shifts in the family of the Keggin anions with formula α‐[XW₁₂O₄₀]^q? (X=B, Al, Si, P, Ga, Ge, As, Zn), in the β‐ and γ‐[SiW₁₂O₄₀]^4? geometric isomers, in the derivative Dawson anion [P₂W₁₈O₆₂]^6?, and in the most symmetrical Lindqvist [W₆O₁₉]^2? anion and its derivative [W₁₀O₃₂]^4?. In this article, we show that the geometry employed in the calculation of NMR chemical shifts in polyoxotungstates is extremely important if we want to be quantitative. Using very large basis sets of QZ4P quality and taking into account the conductor‐like screening model (COSMO) to account for solvent effects (aqueous and organic solutions), good geometries were found for the polyoxoanions. From these optimal geometries the ¹⁸³W NMR chemical shifts were computed with the more standard basis sets of TZP quality and including spin–orbit corrections inside the zero‐order regular approximation (ZORA) to describe the relativistic effects of the internal electrons. With this strategy the mean absolute error between experimental and theoretical values was found to be less than 10 ppm, which is similar to the experimental error. We also discuss how the geometry of the polyoxoanion influences on the shielding.