Free Wreath Product by the Quantum Permutation Group

Let A be a compact quantum group, let nN ^* and let A _aut(X _n ) be the quantum permutation group on n letters. A free wreath product construction A*_w A _aut(X _n ) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.     

Quantum automorphism groups of finite graphs

A quantum analogue of the automorphism group of a finite graph is introduced. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group .

     

Quantum automorphism groups of vertex-transitive graphs of order ≤ 11

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups , symmetric groups S _n and quantum symmetric groups , by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.     

Detection of 20‐hydroxyecdysone in calf urine by comparative liquid chromatography/high‐resolution mass spectrometry and liquid chromatography/tandem mass spectrometry measurements: application to the control of the potential misuse of ecdysteroids in cattle

Ecdysteroids, which are steroid hormones in invertebrates, but which are also present in plants, could potentially be used as anabolic agents in food‐producing animals. The control of ecdysteroid misuse in cattle relies on the development of an efficient method for their detection in biological matrices at trace levels (µg L⁻¹). In order to propose an analytical procedure dedicated to the identification of excreted 20‐hydroxyecdysone (20E) in urine and faecal samples of breeding animals, a comparative study of the spectrometric behaviour of these compounds was carried out both by LC/(ESI‐)/HRMSⁿ (hybrid linear ion trap – orbital trap) and by LC/(ESI+)/MS/MS (triple quadrupole). This study revealed the formation of a large number of product ions both in positive and negative ion mode, corresponding to losses of water molecules and specific cleavages on the side chain. The sample preparation consisted of sequential purification on two solid‐phase extraction cartridges (SPE octadecylsilyl and SPE silica). The detection limits were around 0.5 µg L⁻¹ in the selected reaction monitoring (SRM) mode and recoveries above 60% were obtained. The method was successfully applied to the analysis of real samples collected from calves treated with 60 mg 20E over 4 days. Analysis of the samples allowed the investigation of the kinetics of elimination of 20E in calf urine and determination of the time‐frame for the control of potential abuse. Copyright © 2008 John Wiley & Sons, Ltd.     

Representations of quantum permutation algebras

We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π:A_s(n)→B(H). We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can be performed up to n=6.     

Galois Reconstruction of Finite Quantum Groups

Let be a (small) category and let F:  →  alg_f be a functor, where alg_f is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra A_aut(F) such that F factorizes through a functor :  →  coalg_f(A_aut(F)), where coalg_f(A_aut(F)) is the category of finite-dimensional measured A_aut(F)-comodule algebras. This general reconstruction result allows us to recapture a finite-dimensional Hopf algebra A from the category coalg_f(A) and the forgetful functor ω: coalg_f(A) →  alg_f: we have A  A_aut(ω). Our universal construction is also done in a C*-algebra framework, and we get compact quantum groups in the sense of Woronowicz.     

Targeted phase II metabolites profiling as new screening strategy to investigate natural steroid abuse in animal breeding

The use of steroid hormones as growth promoters in cattle is banned within the European Union since 1988 but can still be fraudulently employed in animal breeding farms for anabolic purposes. While efficient targeted confirmatory methods have been implemented in control laboratories for many years, fast and reliable screening methods are still required, especially in the case of natural hormones abuse, but more globally for new "fishing" strategies allowing to reveal the use of even unknown anabolic agents. The development of focused profiling or untargeted metabolomic approaches is thus emerging in this context. The present study was a focused profiling study using steroids phase II metabolites, with the aim to get a better understanding of the steroid metabolism disruptions after exogenous administration of androstenedione and finally reveal potential biomarkers signing its administration. A sample preparation procedure was first developed, based on a separation of 31 glucuronide and sulphate conjugate compounds using an anion exchange SPE system. Each fraction was then analysed by UPLC-MS/MS in MRM mode showing a rapid (between 4h and 4 days after treatment) and huge excretion of several direct metabolites of androstenedione such as etiocholanolone-glucuronide or epiandrosterone-sulphate.     

Multi-residue method for the determination of thyreostats in urine samples using liquid chromatography coupled to tandem mass spectrometry after derivatisation with 3-iodobenzylbromide

Thyreostats are banned compounds in Europe since 1981 (directive 81/602/EC) because of their carcinogenic and teratogenic properties. The control of their illegal use in breeding animals is amongst the most difficult because of their low molecular weight, high polarity and the existence of tautomeric forms. The analytical procedure described in this paper involves, after a derivatisation step with 3-iodobenzylbromide, the detection and identification at low level (microg/L) by LC-ESI(-)-MS/MS of eight thyreostats in various biological matrices (urine, muscle, liver, thyroid, animal feed, faeces and hair). The urine method has been validated according to the EU criteria (2002/657/EC decision): CCalpha and CCbeta were found in the range (0.1-5.2 microg/L) and (2.6-23.2 microg/L), respectively. The performances fulfil the requirements of the EU regarding the provisional minimum required performance limit (MRPL) fixed at 100 microg/L in urine.