Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

Giant microwave photoresistivity in a high-mobility quantum Hall system

We report the observation of a remarkably strong microwave photoresistivity effect in a high-mobility two-dimensional electron system subject to a weak magnetic field and low temperature. The effect manifests itself as a giant microwave-induced resistivity peak which, in contrast to microwave-induced resistance oscillations, appears only near the second harmonic of the cyclotron resonance and only at sufficiently high microwave frequencies. Appearing in the regime linear in microwave intensity, the peak can be more than an order of magnitude stronger than the microwave-induced resistance oscillations and cannot be explained by existing theories.Comment: 4 pages, 4 figure

HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web

When users interact with the Web today, they leave sequential digital trails on a massive scale. Examples of such human trails include Web navigation, sequences of online restaurant reviews, or online music play lists. Understanding the factors that drive the production of these trails can be useful for e.g., improving underlying network structures, predicting user clicks or enhancing recommendations. In this work, we present a general approach called HypTrails for comparing a set of hypotheses about human trails on the Web, where hypotheses represent beliefs about transitions between states. Our approach utilizes Markov chain models with Bayesian inference. The main idea is to incorporate hypotheses as informative Dirichlet priors and to leverage the sensitivity of Bayes factors on the prior for comparing hypotheses with each other. For eliciting Dirichlet priors from hypotheses, we present an adaption of the so-called (trial) roulette method. We demonstrate the general mechanics and applicability of HypTrails by performing experiments with (i) synthetic trails for which we control the mechanisms that have produced them and (ii) empirical trails stemming from different domains including website navigation, business reviews and online music played. Our work expands the repertoire of methods available for studying human trails on the Web.Comment: Published in the proceedings of WWW'1

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

Gradient Representations and Affine Structures in AE(n)

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.Comment: 43 page

E_{11} origin of Brane charges and U-duality multiplets

We derive general equations which determine the decomposition of the G^{+++} multiplet of brane charges into the sub-algebras that arise when the non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We apply this to calculate the low level E_8 multiplets of brane charges that arise when the E_{8}^{+++}, or E_{11}, non-linearly realised theory is dimensionally reduced to three dimensions on an eight dimensional torus. We find precise agreement with the U-duality multiplet of brane charges previously calculated, thus providing a natural eleven dimensional origin for the "mysterious" brane charges found that do not occur as central charges in the supersymmetry algebra. We also discuss the brane charges in nine dimensions and how they arise from the IIA and IIB theories.Comment: 30 pages, plain te

Armillaria mellea can infect the perennial weed, Rumex obtusifolius , in the UK

Armillaria mellea is a common pathogen of trees, woody shrubs and some herbaceous plants, causing root, root-collar and butt rot (Fox, 2000). On examination of a wilted broad-leaved dock (Rumex obtusifolius), growing on the edge of woodland, near Reading, UK, in 1994, the main root and root-collar region was found to be colonised with mycelial fans, typical of Armillaria mellea. Rhizomorphs were found in the soil adjacent to the plant. The mycelium was isolated onto Malt Extract Agar and its identity was confirmed to be Armillaria mellea. To fulfil Koch's postulates, ten potted dock plants were each inoculated with an isolate of Armillaria mellea by placing colonised sections of hazel (Corylus avellana) branch (≈6cm long by 2.5cm in diameter; West, 2000) adjacent to the tap root of the plants. Additionally an isolate of Armillaria ostoyae, which is a serious pathogen of coniferous trees, was tested against ten similar plants. After 7 months, the foliage of most plants (7 out of ten, for both isolates) was observed to be wilted or senesced. Examination of the roots and collar region of these plants showed extensive rotting and fans of white mycelium confirming infection by Armillaria. All other plants also had infected roots, but as the infection had not yet reached the root collar, the foliage had not been affected. A. mellea and A. ostoyae were also found to infect artificially inoculated docks in field conditions. Broad-leaved dock is a common perennial weed of short-term leys and permanent pastureland. Salmon (1923) had noticed that "Armillaria mellea" (at that time "sensu lato" - which in Britain was a complex of several species) spread from an apple tree to brambles (Rubus sp.) and docks (Rumex sp.) but the species of dock was unknown and it was not reported whether the docks were killed. Our study confirms that there is potential for docks to assist the vegetative spread of both Armillaria mellea and Armillaria ostoyae across pasture or other treeless habitats and into woodlands in a similar way to that proposed for Epilobium angustifolium by Klein-Gebbinck et al. (1993)

A Completely Invariant SUSY Transform of Supersymmetric QED

We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and observe that this corresponds to a breaking of the Lorentz gauge condition by SUSY. Reasoning by analogy with SUSY's violation of the Wess-Zumino gauge, we argue that the SUSY transformation, already modified to preserve Wess-Zumino gauge, should be further modified by another gauge transformation which restores the Lorentz gauge condition. We derive this modification and use the resulting transformation to derive a Ward identitiy relating the photon and photino propagators without using ghost fields. Our transformation also fulfills the SUSY algebra, modulo terms that vanish in Lorentz gauge

Non-linear magnetotransport in microwave-illuminated two-dimensional electron systems

We study magnetoresistivity oscillations in a high-mobility two-dimensional electron system subject to both microwave and dc electric fields. First, we observe that the oscillation amplitude is a periodic function of the inverse magnetic field and is strongly suppressed at microwave frequencies near half-integers of the cyclotron frequency. Second, we obtain a complete set of conditions for the differential resistivity extrema and saddle points. These findings indicate the importance of scattering without microwave absorption and a special role played by microwave-induced scattering events antiparallel to the electric field.Comment: 4 pages, 4 figure