Rotational Perturbations of Friedmann-Robertson-Walker Type Brane-World Cosmological Models

First order rotational perturbations of the Friedmann-Robertson-Walker metric are considered in the framework of the brane-world cosmological models. A rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane is derived under the assumption of slow rotation. The mathematical structure of the rotation equation imposes strong restrictions on the temporal and spatial dependence of the brane matter angular velocity. The study of the integrable cases of the rotation equation leads to three distinct models, which are considered in detail. As a general result we find that, similarly to the general relativistic case, the rotational perturbations decay due to the expansion of the matter on the brane. One of the obtained consistency conditions leads to a particular, purely inflationary brane-world cosmological model, with the cosmological fluid obeying a non-linear barotropic equation of state.Comment: 14 pages, 5 figures, REVTEX

Update on the management of parkinson's disease

Parkinson's disease is a chronic disabling condition with specific histopathological findings. No cure is yet available although treatment response can be remarkable. Family physicians are often faced with problematic issues on diagnosis and therapy when managing patients with Parkinson's disease. Levodopa is still the mainstay of treatment but its long-term use can be associated with considerable side-effects. We advocate the use of dopamine agonists as de novo therapy in younger onset patients. The application of stereotactic functional surgery has great potential in the treatment of Parkinson's disease.published_or_final_versio

The impact of molecular biology on clinical neurology.

Advances in molecular biology have increased our understanding of both inherited and sporadic forms of neurological disease. In this review, the impact of these advances is discussed in relation to specific neurological conditions. These include the hereditary neuropathies and ataxias, Huntington's disease, and the muscular dystrophies, as well as Alzheimer's disease, Parkinson's disease, and motor neuron disease. Genetic channelopathies, such as familial hemiplegic migraine, are also described. Although knowledge in this area overall is still relatively scant, current advances in molecular biology have helped in the reclassification of some neurological disorders, thereby providing a further step towards the development of rational therapies to treat these conditions.published_or_final_versio

Dehn twists and Lagrangian spherical manifolds

Abstract We study Dehn twists along Lagrangian submanifolds that are finite free quotients of spheres. We describe the induced auto-equivalences to the derived Fukaya category and explain their relations to mirror symmetry.National Science Foundation under agreement No. DMS- 1128155, EPSRC (Establish Career Fellowship EP/N01815X/1), Simons Collaboration Grant 52442

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline