Generalised BPS conditions

We write down two E11 invariant conditions which at low levels reproduce the known half BPS conditions for type II theories. These new conditions contain, in addition to the familiar central charges, an infinite number of further charges which are required in an underlying theory of strings and branes. We comment on the application of this work to higher derivative string corrections

Generalised Space-time and Gauge Transformations

We consider the generalised space-time introduced by the author in 2003 in the context of the non-linear realisation of the semi-direct product of E11 and its first fundamental representation. For all the fields we propose gauge transformations which are compatible with the underlying E11 structure. A crucial role is played by the generalised vielbein that the generalised space-time possess. We work out the explicit form of the gauge transformations, at low levels, in four, five and eleven dimensions.Comment: 33 page

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

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

Chiral Green's Functions in Superconformal Field Theory

By solving the Ward identities in a superconformal field theory we find the unique three-point Green's functions composed of chiral superfields for N = 1,2,3,4 supersymmetry. We show that the N=1 four-point function with R-charge equal to one is uniquely determined by the Ward identities up to the specification of four constants. We discuss why chiral Green's functions above three-points, with total R-charge greater than N, are not uniquely determined.Comment: 32 pages, no figures, LaTeX2e forma

Fractional Calculus as a Macroscopic Manifestation of Randomness

We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus.Comment: 20 pages, 1 figur

E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories

In view of the newly conjectured Kac-Moody symmetries of supergravity theories placed in eleven and ten dimensions, the relation between these symmetry groups and possible compactifications are examined. In particular, we identify the relevant group cosets that parametrise the vacuum solutions of AdS x S type.Comment: discussion improve

Remarks on E11 approach

We consider a few topics in $E_{11}$ approach to superstring/M-theory: even subgroups ($Z_2$ orbifolds) of $E_{n}$, n=11,10,9 and their connection to Kac-Moody algebras; $EE_{11}$ subgroup of $E_{11}$ and coincidence of one of its weights with the $l_1$ weight of $E_{11}$, known to contain brane charges; possible form of supersymmetry relation in $E_{11}$; decomposition of $l_1$ w.r.t. the $SO(10,10)$ and its square root at first few levels; particle orbit of $l_1 \ltimes E_{11}$. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in $E_{11}$.Comment: Two references adde

E_11 and M Theory

We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde

Mining Missing Hyperlinks from Human Navigation Traces: A Case Study of Wikipedia

Hyperlinks are an essential feature of the World Wide Web. They are especially important for online encyclopedias such as Wikipedia: an article can often only be understood in the context of related articles, and hyperlinks make it easy to explore this context. But important links are often missing, and several methods have been proposed to alleviate this problem by learning a linking model based on the structure of the existing links. Here we propose a novel approach to identifying missing links in Wikipedia. We build on the fact that the ultimate purpose of Wikipedia links is to aid navigation. Rather than merely suggesting new links that are in tune with the structure of existing links, our method finds missing links that would immediately enhance Wikipedia's navigability. We leverage data sets of navigation paths collected through a Wikipedia-based human-computation game in which users must find a short path from a start to a target article by only clicking links encountered along the way. We harness human navigational traces to identify a set of candidates for missing links and then rank these candidates. Experiments show that our procedure identifies missing links of high quality