Relaxation of optimal control problems to equivalent convex programs

AbstractRelaxed controls induce convexity of the velocity sets in optimal control problems, permitting a general existence theory. Here we obtain complete convexity, of the set of control-trajectory pairs, by relaxing the problem constraints to admit certain measures on the product of the control and trajectory spaces. It is proved that these measures are just unit mixtures of control-trajectory pairs and that admitting them does not alter the minimum value of the control problems. This can be used to derive necessary and sufficient conditions for optimality of dynamic programming type

Enhancing spaceflight safety with UOS3 cubesat

Earth orbits are becoming increasingly congested. This will not only impact future space operations but also become a concern for the population on the ground; with more spacecraft being flown, more objects will re-enter the atmosphere in an uncontrolled fashion. Parts of these satellites can reach Earth surface and endanger the ground population (e.g. ROSAT or UARS satellites). A student-run project from the University of Southampton aims to build a 1U cubesat (approx. 10 by 10 by 10 cm satellite), which will gather data that will improve the accuracy of re-entry predictions. The cubesat will record and deliver its position and attitude during the orbital decay, thus providing validation data for re-entry prediction tools. This will reduce the risk to the ground population because more accurate prognoses will allow mitigation measures to be implemented in the areas at risk. The mission could also allow the risk of collision between spacecraft to be estimated more accurately thanks to improvement of the atmospheric models. This would give the decision makers more complete information to use, for instance, in collision avoidance manoeuvre plannin

A peroxisome proliferator-activated receptor-δ agonist provides neuroprotection in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine model of Parkinson's disease

Copyright © 2013 IBRO. Published by Elsevier Ltd. All rights reserved.Peer reviewedPublisher PD

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Constraints on early dark energy from CMB lensing and weak lensing tomography

Dark energy can be studied by its influence on the expansion of the Universe as well as on the growth history of the large-scale structure. In this paper, we follow the growth of the cosmic density field in early dark energy cosmologies by combining observations of the primary CMB temperature and polarisation power spectra at high redshift, of the CMB lensing deflection field at intermediate redshift and of weak cosmic shear at low redshifts for constraining the allowed amount of early dark energy. We present these forecasts using the Fisher-matrix formalism and consider the combination of Planck-data with the weak lensing survey of Euclid. We find that combining these data sets gives powerful constraints on early dark energy and is able to break degeneracies in the parameter set inherent to the various observational channels. The derived statistical 1-sigma-bound on the early dark energy density parameter is sigma(Omega_d^e)=0.0022 which suggests that early dark energy models can be well examined in our approach. In addition, we derive the dark energy figure of merit for the considered dark energy parameterisation and comment on the applicability of the growth index to early dark energy cosmologies.Comment: 25 pages, 14 figures, 3 tables; v2: very minor additions, updated to match version to be published in JCA

Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.Comment: 12 pages, 9 figures; calculation of exact exchange potential for n=1,2,3 included, energies of electron-solid phases now calculated with the help of the exact potential, and discussion of approximation include

The History of Galaxy Formation in Groups: An Observational Perspective

We present a pedagogical review on the formation and evolution of galaxies in groups, utilizing observational information from the Local Group to galaxies at z~6. The majority of galaxies in the nearby universe are found in groups, and galaxies at all redshifts up to z~6 tend to cluster on the scale of nearby groups (~1 Mpc). This suggests that the group environment may play a role in the formation of most galaxies. The Local Group, and other nearby groups, display a diversity in star formation and morphological properties that puts limits on how, and when, galaxies in groups formed. Effects that depend on an intragroup medium, such as ram-pressure and strangulation, are likely not major mechanisms driving group galaxy evolution. Simple dynamical friction arguments however show that galaxy mergers should be common, and a dominant process for driving evolution. While mergers between L_* galaxies are observed to be rare at z < 1, they are much more common at earlier times. This is due to the increased density of the universe, and to the fact that high mass galaxies are highly clustered on the scale of groups. We furthermore discus why the local number density environment of galaxies strongly correlates with galaxy properties, and why the group environment may be the preferred method for establishing the relationship between properties of galaxies and their local density.Comment: Invited review, 16 pages, to be published in ESO Astrophysics Symposia: "Groups of Galaxies in the Nearby Universe", eds. I. Saviane, V. Ivanov, J. Borissov

Task specific influences of Parkinson’s disease on the striato-thalamo-cortical and cerebello-thalamo-cortical motor circuitries

The motor deficits in Parkinson’s disease (PD) have been primarily associated with internally guided (IG), but not externally guided (EG), tasks. This study investigated the functional mechanisms underlying this phenomenon using genetically-matched twins. Functional magnetic resonance images were obtained from a monozygotic twin pair discordant for clinical PD. Single-photon emission computed tomography neuroimaging using [123I](−)-2-β-carboxymethoxy-3-β-(4-iodophenyl)tropane confirmed their disease-discordant status by demonstrating a severe loss of transporter binding in the PD-twin, whereas the non-PD-twin was normal. Six runs of fMRI data were acquired from each twin performing EG and IG right-hand finger sequential tasks. The percentage of voxels activated in each of several regions of interest (ROI) was calculated. Multiple analysis of variance was used to compare each twin’s activity in ROIs constituting the striato-thalamo-cortical motor circuits [basal ganglia (BG)-cortical circuitry, but including the globus pallidus/putamen, thalamus, supplementary motor area, and primary motor cortex] and cerebello-thalamo-cortical circuits (referred to as the cerebellar–cortical circuitry, including the cerebellum, thalamus, somatosensory cortex, and lateral premotor cortex). During the EG task, there were no significant differences between the twins in bilateral BG-cortical pathways, either basally or after levodopa, whereas the PD-twin had relatively increased activity in the cerebellar-cortical pathways basally that was normalized by levodopa. During the IG task, the PD-twin had less activation than the non-PD-twin in ROIs of the bilateral BG-cortical and cerebellar-cortical pathways. Levodopa normalized the hypoactivation in the contralateral BG-cortical pathway, but “over-corrected” the activation in the ipsilateral BG-cortical and bilateral cerebellar-cortical pathways. In this first fMRI study of twins discordant for PD, the data support the hypothesis that BG-cortical and cerebellar-cortical pathways are task-specifically influenced by PD. The levodopa-induced “over-activation” of BG-cortical and cerebellar-cortical pathways, and its relevance to both compensatory changes in PD and the long-term effects of levodopa in PD, merit further exploration

Telecommunication wavelength GaAsBi light emitting diodes

GaAsBi light emitting diodes containing ∼6% Bi are grown on GaAs substrates. Good room-temperature electroluminescence spectra are obtained at current densities as low as 8 Acm − 2. Measurements of the integrated emitted luminescence suggest that there is a continuum of localised Bi states extending up to 75 meV into the bandgap, which is in good agreement with previous photoluminescence studies. X-ray diffraction analysis shows that strain relaxation has probably occurred in the thicker samples grown in this study