G-Structures and Wrapped NS5-Branes

We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R^{1,9-n} x M_n with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d=7, preserving two or four supersymmetries, corresponding to branes wrapped on associative or SLAG three-cycles. Given the existence of Killing spinors, we show that M_7 admits a G_2-structure or an SU(3)-structure, respectively, of specific type. We also prove the converse result. We use the existence of these geometric structures as a new technique to derive some known and new explicit solutions, as well as a simple theorem implying that we have vanishing NS three-form and constant dilaton whenever M_7 is compact with no boundary. The analysis extends simply to other type II examples and also to type I supergravity.Comment: 29 pages. v2: typos fixed, references added, and Discussion expande

All supersymmetric solutions of minimal supergravity in five dimensions

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the G\"odel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.Comment: 63 pages; substantial additions to the analysis of maximally supersymmetric solutions. Typos corrected and references adde

M-Theory solutions with AdS factors

Solutions of D=7 maximal gauged supergravity are constructed with metrics that are a product of a n-dimensional anti-de Sitter (AdS) space, with n=2,3,4,5, and certain Einstein manifolds. The gauge fields have the same form as in the recently constructed solutions describing the near-horizon limits of M5-branes wrapping supersymmetric cycles. The new solutions do not preserve any supersymmetry and can be uplifted to obtain new solutions of D=11 supergravity, which are warped and twisted products of the D=7 metric with a squashed four-sphere. Some aspects of the stability of the solutions are discussed.Comment: 30 pages. References adde

The Geometry of D=11 Null Killing Spinors

We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.Comment: 30 pages, typos corrected, reference added, new solution included in section 5.1; uses JHEP3.cl

Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger operators -\Delta -V, with V being either the critical borderline potential V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Scr\"odinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a serier of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a byproduct of our technique we are able to answer positively to a conjecture of E.B.Davies.Comment: 40 page

The Geometry of D=11 Killing Spinors

We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the former case we determine what kind of local SU(5) structure is present and show that almost all of the form of the geometry is determined by the structure. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D=11 Godel solution.Comment: 36 pages. Typos corrected and discussion on G-structures improved. Final version to appear in JHE

Producing Enactable Protocols in Artificial Agent Societies

This paper draws upon our previous work [7, 16] in which we proposed the organisation of services around the concept of artificial agent societies and presented a framework for representing roles and protocols using LTSs. The agent would apply for a role in the society, which would result in its participation in a number of protocols. We advocated the use of the games-based metaphor for describing the protocols and presented a framework for assessing the admission of the agent to the society on the basis of its competence. In this work we look at the subsequent question: what information should the agent receive upon entry?. We can not provide it with the full protocol because of security and overload issues. Therefore, we choose to only provide the actions pertinent to the protocols that the role the agent applied for participates in the society. We employ branching bisimulation for producing a protocol equivalent to the original one with all actions not involving the role translated into silent (τ) actions. However, this approach sometimes results in non-enactable protocols. In this case, we need to repair the protocol by adding the role in question as a recipient to certain protocol messages that were causing the problems. We present three different approaches for repairing protocols, depending on the number of messages from the original protocol they modify. The modified protocol is adopted as the final one and the agent is given the role automaton that is derived from the branching bisimulation process

GameUp: Exergames for mobility – a project to keep elderly active

A big challenge for Europe is the demographic shift towards an aging population. Resources in the health care sector are limited, so it is important that the seniors of tomorrow will be able to stay healthy and manage themselves as long as possible, preferably also with a good quality of life. Physical activity is very important both for mobility and for the general well-being, but it can be hard to find motivation to exercise alone at home. Also in rehabilitation there is a need for a more engaging approach than a sheet of paper describing exercises that should be performed. In the GameUp project we developed fun and motivational exergames particularly targeting elderly in a user centred approach. Physiotherapists ensured that the movements and exercises were good for flexibility, leg strength and balance. In addition to seven Kinect games, a walking app and a professional portal were developed. The Kinect games can be played in several levels, and those who are at risk of falling are able to play while seated. The professional portal ensures that the results of the project also can be used as a tool in rehabilitation. Test results from 20 elderly aged 65-95 as well as clinical trials of adherence to the exercises are encouraging, and the international and multidisciplinary team behind the project is now looking for ways to commercialize the project outcomes