Berezinians, Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of \GL(V). They are expressed by vanishing of certain Hankel determinants of order $q+1$ in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to explicitly express the Berezinian of an operator as a rational function of traces. We analyze the Cayley--Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and expanded, new results include

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

Impacts of the mycotoxin zearalenone on growth and photosynthetic responses in laboratory populations of freshwater macrophytes (Lemna minor) and microalgae (Pseudokirchneriella subcapitata).

Mycotoxins are an important class of chemicals of emerging concern, recently detected in aquatic environments, potentially reflecting the influence of fungicide resistance and climatic factors on fungal diseases in agricultural crops. Zearalenone (ZON) is a mycotoxin formed by Fusarium spp. and is known for its biological activity in animal tissues; both in vitro and in vivo. ZON has been reported in US and Polish surface waters at 0.7 - 96 ng/L, with agricultural run-off and wastewater treatment plants being the likely sources of mycotoxins. As some mycotoxins can induce phytotoxicity, laboratory studies were conducted to evaluate the toxicity of ZON (as measured concentrations) to freshwater algae (Pseudokirchneriella subcapitata) and macrophytes (Lemna minor) following OECD test guidelines 201 and 221, respectively. Zinc sulphate was used as a positive control. In the OECD 201 algal static study (72 h at 24 ± 1 °C), exposure to ZON gave average specific growth rate (cell density) EC50 and yield (cell density) EC50 values of > 3.1 and 0.92 (0.74 - 1.8) mg/L, respectively. ZON was less toxic in the OECD 221 static study and after 7 d at 24 ± 1 °C. L. minor growth was significantly reduced based on frond number and frond area at 11.4 mg ZON/L, showing a higher tolerance than reported for other mycotoxins with Lemna spp. Chlorophyll fluorescence parameters were used as biomarkers of impacts on photosystem II efficiency, with no effect seen in algae but, with responses being observed in L. minor between 5.2 - 14.4 mg ZON/L. ZON toxicity seen here is not of immediate concern in context with environmental levels, but this study highlights that other freshwater organisms including algae are more sensitive to mycotoxins than Lemna sp., the only current source of toxicity data for freshwater plants

Confirmation of low genetic diversity and multiple breeding females in a social group of Eurasian badgers from microsatellite and field data

The Eurasian badger ( Meles meles ) is a facultatively social carnivore that shows only rudimentary co-operative behaviour and a poorly defined social hierarchy. Behavioural evidence and limited genetic data have suggested that more than one female may breed in a social group. We combine pregnancy detection by ultrasound and microsatellite locus scores from a well-studied badger population from Wytham Woods, Oxfordshire, UK, to demonstrate that multiple females reproduce within a social group. We found that at least three of seven potential mothers reproduced in a group that contained 11 reproductive age females and nine offspring. Twelve primers showed variability across the species range and only five of these were variable in Wytham. The microsatellites showed a reduced repeat number, a significantly higher number of nonperfect repeats, and moderate heterozygosity levels in Wytham. The high frequency of imperfect repeats and demographic phenomena might be responsible for the reduced levels of variability observed in the badger

Persistent spin splitting of a two-dimensional electron gas in tilted magnetic fields

By varying the orientation of the applied magnetic field with respect to the normal of a two-dimensional electron gas, the chemical potential and the specific heat reveal persistent spin splitting in all field ranges. The corresponding shape of the thermodynamic quantities distinguishes whether the Rashba spin-orbit interaction RSOI, the Zeeman term or both dominate the splitting. The interplay of the tilting of the magnetic field and RSOI resulted to an amplified splitting in weak fields. The effects of changing the RSOI strength and the Landau level broadening are also investigated.Comment: 10 pages, 5 figure

Analysis of host responses to Mycobacterium tuberculosis antigens in a multi-site study of subjects with different TB and HIV infection states in sub-Saharan Africa.

BACKGROUND: Tuberculosis (TB) remains a global health threat with 9 million new cases and 1.4 million deaths per year. In order to develop a protective vaccine, we need to define the antigens expressed by Mycobacterium tuberculosis (Mtb), which are relevant to protective immunity in high-endemic areas. METHODS: We analysed responses to 23 Mtb antigens in a total of 1247 subjects with different HIV and TB status across 5 geographically diverse sites in Africa (South Africa, The Gambia, Ethiopia, Malawi and Uganda). We used a 7-day whole blood assay followed by IFN-γ ELISA on the supernatants. Antigens included PPD, ESAT-6 and Ag85B (dominant antigens) together with novel resuscitation-promoting factors (rpf), reactivation proteins, latency (Mtb DosR regulon-encoded) antigens, starvation-induced antigens and secreted antigens. RESULTS: There was variation between sites in responses to the antigens, presumably due to underlying genetic and environmental differences. When results from all sites were combined, HIV- subjects with active TB showed significantly lower responses compared to both TST(-) and TST(+) contacts to latency antigens (Rv0569, Rv1733, Rv1735, Rv1737) and the rpf Rv0867; whilst responses to ESAT-6/CFP-10 fusion protein (EC), PPD, Rv2029, TB10.3, and TB10.4 were significantly higher in TST(+) contacts (LTBI) compared to TB and TST(-) contacts fewer differences were seen in subjects with HIV co-infection, with responses to the mitogen PHA significantly lower in subjects with active TB compared to those with LTBI and no difference with any antigen. CONCLUSIONS: Our multi-site study design for testing novel Mtb antigens revealed promising antigens for future vaccine development. The IFN-γ ELISA is a cheap and useful tool for screening potential antigenicity in subjects with different ethnic backgrounds and across a spectrum of TB and HIV infection states. Analysis of cytokines other than IFN-γ is currently on-going to determine correlates of protection, which may be useful for vaccine efficacy trials

Relaxation dynamics and ionic conductivity in a fragile plastic crystal

We report a thorough characterization of the dielectric relaxation behavior and the ionic conductivity in the plastic-crystalline mixture of 60% succinonitrile and 40% glutaronitrile. The plastic phase can be easily supercooled and the relaxational behavior is investigated by broadband dielectric spectroscopy in the liquid, plastic crystalline, and glassy crystal phases. The very pronounced alpha-relaxation found in the spectra is characterized in detail. From the temperature dependence of the alpha-relaxation time, a fragility parameter of 62 was determined making this material one of the most fragile plastic-crystalline glass formers. A well-pronounced secondary and faint indications for a third relaxation process were found, the latter most likely being of Johari-Goldstein type. In addition, relatively strong conductivity contributions were detected in the spectra exhibiting the typical features of ionic charge transport.Comment: 8 pages, 7 figure

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Social preferences, accountability, and wage bargaining

We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect