Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

Calculations for Mirror Symmetry with D-branes

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D-branes. A 4-d domain wall which is obtained in one region of closed string moduli space from wrapping a four-chain interpolating between two Lagrangian submanifolds is, for other values of the parameters, represented by a disk ending on a single Lagrangian.Comment: 42 page

Matrix Factorizations and Homological Mirror Symmetry on the Torus

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.Comment: 41 pages, 9 figures, v2: reference added, minor corrections and clarifications, version published in JHE

Systematic techniques for assisting recruitment to trials (START): study protocol for embedded, randomized controlled trials

BACKGROUND: Randomized controlled trials play a central role in evidence-based practice, but recruitment of participants, and retention of them once in the trial, is challenging. Moreover, there is a dearth of evidence that research teams can use to inform the development of their recruitment and retention strategies. As with other healthcare initiatives, the fairest test of the effectiveness of a recruitment strategy is a trial comparing alternatives, which for recruitment would mean embedding a recruitment trial within an ongoing host trial. Systematic reviews indicate that such studies are rare. Embedded trials are largely delivered in an ad hoc way, with interventions almost always developed in isolation and tested in the context of a single host trial, limiting their ability to contribute to a body of evidence with regard to a single recruitment intervention and to researchers working in different contexts. METHODS/DESIGN: The Systematic Techniques for Assisting Recruitment to Trials (START) program is funded by the United Kingdom Medical Research Council (MRC) Methodology Research Programme to support the routine adoption of embedded trials to test standardized recruitment interventions across ongoing host trials. To achieve this aim, the program involves three interrelated work packages: (1) methodology - to develop guidelines for the design, analysis and reporting of embedded recruitment studies; (2) interventions - to develop effective and useful recruitment interventions; and (3) implementation - to recruit host trials and test interventions through embedded studies. DISCUSSION: Successful completion of the START program will provide a model for a platform for the wider trials community to use to evaluate recruitment interventions or, potentially, other types of intervention linked to trial conduct. It will also increase the evidence base for two types of recruitment intervention. TRIAL REGISTRATION: The START protocol covers the methodology for embedded trials. Each embedded trial is registered separately or as a substudy of the host trial

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure

A Hybrid Global Minimization Scheme for Accurate Source Localization in Sensor Networks

We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves the space for unavailability of an accurate signal attenuation model in the environment by considering the model as an unknown function with reasonable prior assumptions about its functional space. Such approach is capable of enhancing the localization performance compared to only utilizing the signal attenuation information or the time delays. In this paper, the localization problem is modeled as a cost function in terms of the source locations, attenuation model parameters and the multi-path parameters. To globally perform the minimization, we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm. Besides the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided. Finally, the validity of the proposed method is examined in several localization scenarios, taking into account the noise in the environment, the multi-path phenomenon and considering the sensors not being synchronized