The gauge structure of generalised diffeomorphisms

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.Comment: 24 pp., plain tex, 1 figure. v2: minor changes, including a few added ref

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

Synopsis of aeronautic radiator investigations for years 1917 and 1918

Extensive series of experiments have been conducted at the Bureau of Standards to determine the properties of cooling radiator cores manufactured for airplanes and to develop improvements in design. The analysis of the problem on which this work was based, and consequently the experimental method employed, is different from that commonly used. Instead of attempting to test complete radiators, either full size or in model, uniform sections representing different types of core construction have been tested and an analysis of the results made with a view to determining independently the various factors which influence its performance. This report describes referenced method of analysis in predicting the performance of radiators designed for aeronautic use

K(E10), Supergravity and Fermions

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility of supersymmetry with local K(E10) is investigated. We find that all structures involving A9 levels 0,1 and 2 nicely agree with expectations, and provide many non-trivial consistency checks of the existence of a supersymmetric extension of the E10/K(E10) coset model, as well as a new derivation of the `bosonic dictionary' between supergravity and coset variables. However, there are also definite discrepancies in some terms involving level 3, which suggest the need for an extension of the model to infinite-dimensional faithful representations of the fermionic degrees of freedom.Comment: 50 page

Supersymmetric quantum cosmological billiards

D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.Comment: 4 pages. v2: Added ref. Version to be published in PR

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

Modelling the effect of malaria endemicity on spatial variations in childhood fever, diarrhoea and pneumonia in Malawi

BACKGROUND: Co-morbidity with conditions such as fever, diarrhoea and pneumonia is a common phenomenon in tropical Africa. However, little is known about geographical overlaps in these illnesses. Spatial modelling may improve our understanding of the epidemiology of the diseases for efficient and cost-effective control. METHODS: This study assessed subdistrict-specific spatial associations of the three conditions (fever, diarrhoea and pneumonia) in relation to malaria endemicity. We used data from the 2000 Malawi demographic and health survey which captured the history of childhood morbidities 2 weeks prior to the survey date. The disease status of each child in each area was the outcome of interest and was modelled using a trivariate logistic regression model, and incorporated random effects to measure spatial correlation. RESULTS: The risk of fever was positively associated with high and medium malaria endemicity levels relative to low endemicity level, while for diarrhoea and pneumonia we observed marginal positive association at high endemicity level relative to low endemicity level, controlling for confounding covariates and heterogeneity. A positive spatial correlation was found between fever and diarrhoea (r = 0.29); while weak associations were estimated between fever and pneumonia (r = 0.01); and between diarrhoea and pneumonia (r = 0.05). The proportion of structured spatial variation compared to unstructured variation was 0.67 (95% credible interval (CI): 0.31-0.91) for fever, 0.67 (95 % CI: 0.27-0.93) for diarrhoea, and 0.87 (95% CI: 0.62-0.96) for pneumonia. CONCLUSION: The analysis suggests some similarities in subdistrict-specific spatial variation of childhood morbidities of fever, diarrhoea and pneumonia, and might be a result of shared and overlapping risk factors, one of which is malaria endemicity

Results of Tests on Radiators for Aircraft Engines

Part 1 is to present the results of tests on 56 types of core in a form convenient for use in the study of the performance of and possible improvements in existing designs. Working rules are given by which the data contained in the report may be used, and the most obvious conclusions as to the behavior of cores are summarized. Part 2 presents the results of tests made to determine the pressure necessary to produce water flows up to 50 gallons per minute through an 8-inch square section of radiator core. These data are of special value in evaluating the hydraulic head against which the circulating pump is required to operate