Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism

Autoregression as a means of assessing the strength of seasonality in a time series

BACKGROUND: The study of the seasonal variation of disease is receiving increasing attention from health researchers. Available statistical tests for seasonality typically indicate the presence or absence of statistically significant seasonality but do not provide a meaningful measure of its strength. METHODS: We propose the coefficient of determination of the autoregressive regression model fitted to the data ([Image: see text]) as a measure for quantifying the strength of the seasonality. The performance of the proposed statistic is assessed through a simulation study and using two data sets known to demonstrate statistically significant seasonality: atrial fibrillation and asthma hospitalizations in Ontario, Canada. RESULTS: The simulation results showed the power of the [Image: see text] in adequately quantifying the strength of the seasonality of the simulated observations for all models. In the atrial fibrillation and asthma datasets, while the statistical tests such as Bartlett's Kolmogorov-Smirnov (BKS) and Fisher's Kappa support statistical evidence of seasonality for both, the [Image: see text] quantifies the strength of that seasonality. Corroborating the visual evidence that asthma is more conspicuously seasonal than atrial fibrillation, the calculated [Image: see text] for atrial fibrillation indicates a weak to moderate seasonality ([Image: see text] = 0.44, 0.28 and 0.45 for both genders, males and females respectively), whereas for asthma, it indicates a strong seasonality ([Image: see text] = 0.82, 0.78 and 0.82 for both genders, male and female respectively). CONCLUSIONS: For the purposes of health services research, evidence of the statistical presence of seasonality is insufficient to determine the etiologic, clinical and policy relevance of findings. Measurement of the strength of the seasonal effect, as can be determined using the [Image: see text] technique, is also important in order to provide a robust sense of seasonality

SWIRP (Submm-Wave and Long Wave InfraRed Polarimeter); Development and Characterization of a Sub-Mm Polarimeter for Ice Cloud Investigations

A major source of uncertainty in climate models is the presence, shape and distribution of ice particles in the uppermost layers of the clouds. The effects of this component are poorly constrained, turning ice particles into an almost-free variable in many climate models.NASA-GSFC is developing a new instrument aimed at measuring the size and shape of ice particles. The instrument consists of two sub-mm polarimeters (at 220 and 670 GHz) coupled with a long-wave infrared polarimeter at 10 micron. Each polarimeter has identical V-pol and H-pol channels; the axes of polarization are defined geometrically by the orientation of the waveguide elements, and the purity has been measured in the lab. The instrument is configured as a conical scanner, suitable for deployment as a payload on a small satellite or on a high-altitude sub-orbital platform. From a 400 km orbit, the instrument has a 3dB spatial resolution of 20 (10) km at 220 (670) GHz and a swath of 600 km over 180 degrees of view.The BAPTA (Bearing And Power Transfer Assembly) carries heritage from the SSMIS design, now in its 22nd year of on-orbit operation, but with a much reduced SWaP (Size Weight and Power) footprint, suitable for a small satellite.The main components of the instrument have been fabricated and are undergoing final testing prior to their integration as a single unit. The sub-mm channels have dedicated secondary reflectors which illuminate a shared primary reflector. The receiving units are placed behind the focal point of the optical arrangement, so that all beams equally illuminate the primary reflector and are almost co-located on the ground (within a single 220 GHz footprint). Primary and secondary beam patterns have been measured and verified to match the as-designed expectations. A Zytex (TM) window is deployed to protect the secondary reflectors and the feed horns from debris and other contaminants, and to reduce the heat load from the active (hot) IR calibration unit. The insertion loss of Zytex has been measured and is accounted in the calibration equation of the sub-mm channels.The radiometric performance of the sub-mm receivers has been characterized in the lab and under operational conditions of temperature and pressure.This paper discusses the design constraints on the sub-mm components, details of the scientific goals and their flowdown, and describes the characterization of the polarimeters. Options to optimize the layout and distribution of the masses within the assembly, with the goal of making the instrument even more compact and fully-compatible with cubesat-class satellites will be presented

Life history of an anticyclonic eddy

19 pages, 11 figures, 1 table, supporting information https://doi.org/10.1029/2004JC002526We use the trajectory of three buoys dragged below the surface mixed layer, together with sea surface temperature imagery, to examine the evolution of an anticyclonic warm-core eddy since its generation by the Canary Islands. Two buoys remain within the eddy during some 100 days, and the third one remains almost 200 days, while drifting southwestward up to 500 km with the mean Canary Current. The eddy merges with several younger anticyclonic and cyclonic eddies, in each occasion, suffering substantial changes. The eddy core, defined as a region with near-solid-body-type rotation and radial convergence, initially occupies the whole eddy. After interacting with another vortex the inner core markedly slows down, although it continues displaying radial convergence and relatively small radial oscillations, and an uncoupled outer ring is formed or enhanced, which revolves even more slowly and displays large radial fluctuations. The vortex extensive life is consistent with its inertially stable character and observations of radial convergence. A very simple model of vortex merging, where cylinders fuse conserving mass and angular momentum, gives fair results. The observations suggest that the eddy changes, as the result of its own slow evolution and sporadic mixing events, from a young stage, where the core retains its vorticity and occupies most of the eddy, through a mature stage, where the eddy has a reduced inner core and a slowly revolving outer ring, to a decay stage, where the vorticity maximum is substantially reducedThis work has been supported by the Spanish government through projects FRENTES (AMB95-0731), COCA (REN2000-1471-C02-02MAR), and BREDDIES (REN2001-2650/ANT) and the special action MAR1999-1489-E and by the European Union through projects CANIGO (MAS3-CT96-0060) and OASIS (EVK3-CT-2002-00073-OASIS)Peer Reviewe

The Tulczyjew triple for classical fields

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important feature of our approach is that we do not postulate {\it ad hoc} the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of Field Theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps $\alpha$ and $\beta$ which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We discuss also the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theor

Elevated Blood Lead Concentrations and Vitamin D Deficiency in Winter and Summer in Young Urban Children

BACKGROUND: It is widely recognized that blood lead concentrations are higher in the summer than in winter. Although the effects of some environmental factors such as lead in dust on this phenomenon have been studied, relationships to sunlight-induced vitamin D synthesis have not been adequately investigated. Vitamin D status is influenced by the diet, sunlight exposure, age, skin pigmentation, and other factors, and may modify gastrointestinal lead absorption or release of lead stored in bones into the bloodstream. OBJECTIVE AND METHODS: We collected paired blood samples from 142 young, urban African-American and Hispanic children in the winter and summer to study the seasonal increase in blood lead and its relationships to vitamin D nutrition, age, and race. RESULTS: A winter/summer (W/S) increase in blood lead concentrations of 32.4% was found for children 1–3 years of age. There was a smaller W/S increase of 13.0% in children 4–8 years of age. None of the 51 Hispanic children had an elevated blood lead concentration (≥ 10 μg/dL) during the winter, and only one had an elevated summertime concentration. In contrast, elevated blood lead concentrations were frequent in the 91 African-American children, especially those 1–3 years of age. For the latter, the percentage with elevated blood lead levels increased from 12.2% in winter to 22.5% in summer. A 1.2% W/S increase in serum 25-hydroxy-vitamin D (serum 25-OH-D) concentrations was found for children 1–3 years of age. However, in children 4–8 years of age the W/S increase in serum 25-OH-D was much larger—33.6%. The percentages of children with low (< 16 μg/L) serum 25-OH-D concentrations were 12.0% in winter and 0.7% in summer and were consistently greater in African-American than in Hispanic children. The seasonal increases in blood lead and serum 25-OH-D in children 4–8 years of age were significantly associated. CONCLUSION: The higher summertime serum 25-OH-D concentrations for the 4- to 8-year-old children are likely caused by increased sunlight-induced vitamin D synthesis and may contribute to the seasonal increase in blood lead. Age and race are key factors that affect blood lead and vitamin D nutrition, as well as their interactions, in young urban children

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Web: A Wireless Experiment Box for the Dextre Pointing Package ELC Payload

The Wireless Experiment Box (WEB) was proposed to work with the International Space Station (ISS) External Wireless Communication (EWC) system to support high-definition video from the Dextre Pointing Package (DPP). DPP/WEB was a NASA GSFC proposed ExPRESS Logistics Carrier (ELC) payload designed to flight test an integrated suite of Autonomous Rendezvous and Docking (AR&D) technologies to enable a wide spectrum of future missions across NASA and other US Government agencies. The ISS EWC uses COTS Wireless Access Points (WAPs) to provide high-rate bi-directional communications to ISS. In this paper, we discuss WEB s packaging, operation, antenna development, and performance testing

Elevated Depression Symptoms, Antidepressant Medicine Use, and Risk of Developing Diabetes During the Diabetes Prevention Program

OBJECTIVE—To assess the association between elevated depression symptoms or antidepressant medicine use on entry to the Diabetes Prevention Program (DPP) and during the study and the risk of developing diabetes during the study. RESEARCH DESIGN AND METHODS—DPP participants (n = 3,187) in three treatment arms (intensive lifestyle [ILS], metformin [MET], and placebo [PLB]) completed the Beck Depression Inventory (BDI) and reported their use of antidepressant medication at randomization and throughout the study (average duration in study 3.2 years). RESULTS—When other factors associated with the risk of developing diabetes were controlled, elevated BDI scores at baseline or during the study were not associated with diabetes risk in any arm. Baseline antidepressant use was associated with diabetes risk in the PLB (hazard ratio 2.25 [95% CI 1.38–3.66]) and ILS (3.48 [1.93–6.28]) arms. Continuous antidepressant use during the study (compared with no use) was also associated with diabetes risk in the same arms (PLB 2.60 [1.37–4.94]; ILS 3.39 [1.61–7.13]), as was intermittent antidepressant use during the study in the ILS arm (2.07 [1.18–3.62]). Among MET arm participants, antidepressant use was not associated with developing diabetes. CONCLUSIONS—A strong and statistically significant association between antidepressant use and diabetes risk in the PLB and ILS arms was not accounted for by measured confounders or mediators. If future research finds that antidepressant use independently predicts diabetes risk, efforts to minimize the negative effects of antidepressant agents on glycemic control should be pursued