Additional symmetries of constrained CKP and BKP hierarchies

The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly. Furthermore, we show that acting on the space of the wave operator, $\partial_k^*$ forms new centerless $W^{cC}_{1+\infty}$ and $W^{cB}_{1+\infty}$-subalgebra of centerless $W_{1+\infty}$ respectively. In order to define above symmetry flows $\partial_k^*$ of the cCKP and cBKP hierarchies, two vital operators $Y_k$ are introduced to revise the additional symmetry flows of the CKP and BKP hierarchies.Comment: 14 pages, accepted by SCIENCE CHINA Mathematics(2010

On the performance of algorithms for the minimization of ℓ1\ell_1-penalized functionals

The problem of assessing the performance of algorithms used for the minimization of an $\ell_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation isochrones' is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.Comment: 18 pages, 10 figures; v3: expanded version with an additional synthetic test problem

CH 3 GHz Observations of the Galactic Center

A 3 $\times$ 3 map of the Galactic Center was made at 9\arcmin resolution and 10\arcmin spacing in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz. The CH emission shows a velocity extent that is nearly that of the CO(1-0) line, but the CH line profiles differ markedly from the CO. The 3335 MHz CH transition primarily traces low-density molecular gas and our observations indicate that the mass of this component within $\sim$ 30 pc of the Galactic Center is $\sim$ 9 $\times$ 10$^6$ M$_\odot$. The CO-H$_2$ conversion factor obtained for the low-density gas in the mapped region is greater than that thought to apply to the dense molecular gas at the Galactic Center. In addition to tracing the low-density molecular gas at the Galactic Center, the CH spectra show evidence of emission from molecular clouds along the line of sight both in the foreground and background. The scale height of these clouds ranges from 27 - 109 pc, consistent with previous work based on observations of molecular clouds in the inner Galaxy.Comment: 29 pages, 12 figure

Iterative algorithms for total variation-like reconstructions in seismic tomography

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.Comment: 28 pages, 8 figures. Corrected sign errors in formula (25

Do alpine skiers and snowboarders wear protective equipment more often after an accident?

Questions under study/principles: Analysis of changes in the behaviour of wearing protective equipment by alpine skiers and snowboarders after injury, performed at a level I trauma centre in Switzerland. Methods: We present a study, using a standardised questionnaire, assessing behaviour on ski slopes by adult patients admitted between Oct 2007 and April 2008. Patients were re-interviewed after the 2008/2009 season. McNemar tests were used to analyse differences in protective clothing wearing rates between the two seasons. Multiple logistic regression with age, gender and injury severity score (ISS) as predictors, was used to compare findings in those who started wearing protective equipment and those who did not. Results: A total of 104/132 patients from the 2007/2008 season were questioned about wearing protective equipment in 2008/2009. 20 patients could not be reassessed (7 declined, 13 had abandoned winter sports). A total of 84 patients were reassessed (61 alpine skiers and 23 snowboarders). The median age of participants was 39 years and 70.2% were male. Helmet and back protector wearing rates increased from 40.5% to 78.6% (p <0.001) and from 14.3% to 23.8% (p = 0.021), respectively. Snowboarders more than doubled their helmet wearing rate (39.1% to 82.6%, p = 0.002). Skiers showed a trend towards doubling their back protector wearing rate (6.6% to 14.8%, p = 0.063). Younger skiers started wearing back protectors more often than older skiers. Conclusions: Sustained injury might provide skiers and snowboards with a potent trigger to change their attitude towards the use of protective equipment. The psychological processes influencing the use of protective equipment require further investigation

CH 3 GHz Observations of Molecular Clouds Along the Galactic Plane

Spectra in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz were obtained in three 5-point crosses centered on the Galactic plane at $\ell =$ 50\arcdeg, 100\arcdeg, and 110\arcdeg. The lines of sight traverse both Giant Molecular Clouds (GMCs) and local, smaller entities. This transition is a good tracer of low-density molecular gas and the line profiles are very similar to CO(1-0) data at nearly the same resolution. In addition, the CH 3335 MHz line can be used to calibrate the CO-H$_2$ conversion factor (X$_{\rm CO}$) in low-density molecular gas. Although this technique underestimates X$_{\rm CO}$ in GMCs, our results are within a factor of two of X$_{\rm CO}$ values calibrated for GMCs by other techniques. The similarity of CH and CO line profiles, and that of X$_{\rm CO}$ values derived from CH and more traditional techniques, implies that most of the molecular gas along the observed lines of sight is at relatively low densities ($n \le$ 10$^3$ cm$^{-3}$).Comment: 26 pages, 12 figures, submitted to the AJ, revised after referee repor

Dark Matter and Dark Energy from a single scalar field and CMB data

Axions are likely to be the Dark Matter (DM) that cosmological data require. They arise in the Peccei Quinn solution of the strong CP problem. In a previous work we showed that their model has a simple and natural generalization which yields also Dark Energy (DE), in fair proportions, without tuning any parameter: DM and DE arise from a single scalar field and are weakly coupled in the present era. In this paper we extend the analysis of this dual-axion cosmology and fit it to WMAP data, by using a Markov chain technique. We find that LCDM, dynamical DE with a SUGRA potential, DE with a SUGRA potential and a constant DE-DM coupling, as well as the dual-axion model with a SUGRA potential, fit data with a similar accuracy. The best-fit parameters are however fairly different, although consistency is mostly recovered at the 2-sigma level. A peculiarity of the dual-axion model with SUGRA potential is to cause more stringent constraints on most parameters and to favor high values of the Hubble parameter.Comment: 34 pages, 15 figures, replaced with accepted versio

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5

MOVING/ROTATING ANTENNAS FOR WIRELESS ACCESS POINTS

Conventionally, the position and orientation of antennas for wireless access points depends on the position in which a wireless access point is oriented during installation and typically does not change unless the positioning of the wireless access point is changed. Thus, wireless antenna position/orientation typically remains static once an access point is installed. Techniques proposed herein introduce a sensor fusion approach for controlling the direction/orientation of wireless access point antennas in order to improve wireless communications for wireless networks

Home parenteral nutrition with an omega-3-fatty-acid-enriched MCT/LCT lipid emulsion in patients with chronic intestinal failure (the HOME study):study protocol for a randomized, controlled, multicenter, international clinical trial

BACKGROUND: Home parenteral nutrition (HPN) is a life-preserving therapy for patients with chronic intestinal failure (CIF) indicated for patients who cannot achieve their nutritional requirements by enteral intake. Intravenously administered lipid emulsions (ILEs) are an essential component of HPN, providing energy and essential fatty acids, but can become a risk factor for intestinal-failure-associated liver disease (IFALD). In HPN patients, major effort is taken in the prevention of IFALD. Novel ILEs containing a proportion of omega-3 polyunsaturated fatty acids (n-3 PUFA) could be of benefit, but the data on the use of n-3 PUFA in HPN patients are still limited. METHODS/DESIGN: The HOME study is a prospective, randomized, controlled, double-blind, multicenter, international clinical trial conducted in European hospitals that treat HPN patients. A total of 160 patients (80 per group) will be randomly assigned to receive the n-3 PUFA-enriched medium/long-chain triglyceride (MCT/LCT) ILE (Lipidem/Lipoplus® 200 mg/ml, B. Braun Melsungen AG) or the MCT/LCT ILE (Lipofundin® MCT/LCT/Medialipide® 20%, B. Braun Melsungen AG) for a projected period of 8 weeks. The primary endpoint is the combined change of liver function parameters (total bilirubin, aspartate transaminase and alanine transaminase) from baseline to final visit. Secondary objectives are the further evaluation of the safety and tolerability as well as the efficacy of the ILEs. DISCUSSION: Currently, there are only very few randomized controlled trials (RCTs) investigating the use of ILEs in HPN, and there are very few data at all on the use of n-3 PUFAs. The working hypothesis is that n-3 PUFA-enriched ILE is safe and well-tolerated especially with regard to liver function in patients requiring HPN. The expected outcome is to provide reliable data to support this thesis thanks to a considerable number of CIF patients, consequently to broaden the present evidence on the use of ILEs in HPN. TRIAL REGISTRATION: ClinicalTrials.gov, ID: NCT03282955. Registered on 14 September 2017