Counting supersymmetric branes

Maximal supergravity solutions are revisited and classified, with particular emphasis on objects of co-dimension at most two. This class of solutions includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We present a group theory derivation of the counting of these objects based on the corresponding tensor hierarchies derived from E11 and discrete T- and U-duality transformations. This provides a rationale for the wrapping rules that were recently discussed for \sigma<4 in the literature and extends them. Explicit supergravity solutions that give rise to co-dimension two branes are constructed and analysed.Comment: 1+33 pages. To the memory of Laurent Houart. v2: Published version with added reference

IIA/IIB Supergravity and Ten-forms

We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as "top-forms", require a careful analysis since in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear supersymmetry algebra can be introduced. We give a superspace explanation of our work. All of our results are precisely in line with the predictions of the E(11) algebra.Comment: 17 page

Generalised geometry, eleven dimensions and E11

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial note added which gives the equation of motion relating the gravity field to its dua

Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

By dimensionally reducing the higher derivative corrections of ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1} automorphic forms that occur in d=10-n dimensions. In particular we argue that these automorphic forms involve the representation of E_{n+1} with fundamental weight \lambda^{n+1}, which is also the representation to which the string charges in d dimensions belong. We also consider a similar calculation for the reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE

Higher derivative type II string effective actions, automorphic forms and E11

By dimensionally reducing the ten-dimensional higher derivative type IIA string theory effective action we place constraints on the automorphic forms that appear in the effective action in lower dimensions. We propose a number of properties of such automorphic forms and consider the prospects that E11 can play a role in the formulation of the higher derivative string theory effective action.Comment: 34 page

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

E11, generalised space-time and equations of motion in four dimensions

We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time

Standardizing estimates of the Plasmodium falciparum parasite rate

<p>Abstract</p> <p>Background</p> <p>The <it>Plasmodium falciparum </it>parasite rate (PfPR) is a commonly reported index of malaria transmission intensity. PfPR rises after birth to a plateau before declining in older children and adults. Studies of populations with different age ranges generally report average PfPR, so age is an important source of heterogeneity in reported PfPR data. This confounds simple comparisons of PfPR surveys conducted at different times or places.</p> <p>Methods</p> <p>Several algorithms for standardizing PfPR were developed using 21 studies that stratify in detail PfPR by age. An additional 121 studies were found that recorded PfPR from the same population over at least two different age ranges; these paired estimates were used to evaluate these algorithms. The best algorithm was judged to be the one that described most of the variance when converting the PfPR pairs from one age-range to another.</p> <p>Results</p> <p>The analysis suggests that the relationship between PfPR and age is predictable across the observed range of malaria endemicity. PfPR reaches a peak after about two years and remains fairly constant in older children until age ten before declining throughout adolescence and adulthood. The PfPR pairs were poorly correlated; using one to predict the other would explain only 5% of the total variance. By contrast, the PfPR predicted by the best algorithm explained 72% of the variance.</p> <p>Conclusion</p> <p>The PfPR in older children is useful for standardization because it has good biological, epidemiological and statistical properties. It is also historically consistent with the classical categories of hypoendemic, mesoendemic and hyperendemic malaria. This algorithm provides a reliable method for standardizing PfPR for the purposes of comparing studies and mapping malaria endemicity. The scripts for doing so are freely available to all.</p

Bound States of String Theory and Beyond

All bound states of fundamental strings, D-branes and NS-branes of string theory, both type-IIA and type-IIB, which may be described by a null geodesic motion on the coset G/K(G) where G is a group of type A, D or E embedded within E(11) are presented.Comment: 54+1 pages, 6 figures, 3 data files; typos corrected, added extended discussion of the temporal involutio

Three Distinct Domains Contribute to Nuclear Transport of Murine Foxp3

Foxp3, a 47-kDa transcription factor, is necessary for the function of CD4+CD25+ regulatory T cells (Tregs), with an essential role in the control of self-reactive T cells and in preventing autoimmunity. Activation of Tregs by TCR engagement results in upregulation of Foxp3 expression, followed by its rapid nuclear transport and binding to chromatin. Here, we identify three distinct Foxp3 domains that contribute to nuclear transport. The first domain (Domain 1) comprises the C-terminal 12 amino acids. The second domain (Domain 2) is located immediately N-terminal to the forkhead domain (FHD), recently reported to be a binding site for the runt-related transcription factor 1/acute myeloid leukemia 1 (Runx1/AML1). The third domain (Domain 3) is located within the N-terminal first 51 amino acids. Unlike the known nuclear localization signals (NLSs), none of these three regions are rich in basic residues and do not bear any similarity to known monopartite or bipartite NLSs that have one or more clusters of basic amino acids. The basic arginine-lysine-lysine-arginine (RKKR) sequence, located 12-aa from the C-terminal end of Foxp3 was previously reported to be a nuclear localization signal (NLS) for several proteins, including for a GFP-Foxp3 hybrid. Evidence is provided here that in the full-length native Foxp3 RKKR does not function as an NLS. The data reported in this study indicates that Foxp3 achieves nuclear transport by binding to other nuclear factors and co-transporting with them to the nucleus