Extending the first-order post-Newtonian scheme in multiple systems to the second-order contributions to light propagation

In this paper, we extend the first-order post-Newtonian scheme in multiple systems presented by Damour-Soffel-Xu to the second-order contribution to light propagation without changing the virtueof the scheme on the linear partial differential equations of the potential and vector potential. The spatial components of the metric are extended to second order level both in a global coordinates ($q_{ij}/ c^4$) and a local coordinates ($Q_{ab}/ c^4$). The equations of $q_{ij}$ (or $Q_{ab}$) are obtained from the field equations.The relationship between $q_{ij}$ and $Q_{ab}$ are presented in this paper also. In special case of the solar system (isotropic condition is applied ($q_{ij} = \delta_{ij} q$)), we obtain the solution of $q$. Finally, a further extension of the second-order contributions in the parametrized post-Newtonian formalism is discussed.Comment: Latex2e; 6 pages PS fil

Super-ASTROD: Probing primordial gravitational waves and mapping the outer solar system

Super-ASTROD (Super Astrodynamical Space Test of Relativity using Optical Devices or ASTROD III) is a mission concept with 3-5 spacecraft in 5 AU orbits together with an Earth-Sun L1/L2 spacecraft ranging optically with one another to probe primordial gravitational-waves with frequencies 0.1 microHz - 1 mHz, to test fundamental laws of spacetime and to map the outer solar system. In this paper we address to its scientific goals, orbit and payload selection, and sensitivity to gravitational waves.Comment: 7 pages, 1 figure, presented to 7th International LISA Symposium, 16-20 June 2008, Barcelona; submitted to Classical and Quantum Gravity; presentation improve

Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitation Wave detection) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared to that of LISA. The mission orbits of the 3 spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecraft range interferometrically with one another with arm length about 260 million kilometers. In order to attain the requisite sensitivity for ASTROD-GW, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. For suppressing laser frequency noise, we need to use time delay interferometry (TDI) to match the two different optical paths (times of travel). Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the (TDI), we simulate the time delay numerically using CGC 2.7 ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the residual optical path differences in the first and second generation TDI for one-detector case. In our optimized mission orbits for 20 years, changes of arm length are less than 0.0003 AU; the relative Doppler velocities are less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.Comment: 17 pages, 7 figures, 1 tabl

Simulation of the White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes and present the corresponding generalized spectral method needed to characterize such process. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 14 pages and 6 figures. Submitted to Classical and Quantum Gravity (Proceedings of GWDAW9

Progress in Interferometry for LISA at JPL

Recent advances at JPL in experimentation and design for LISA interferometry include the demonstration of Time Delay Interferometry using electronically separated end stations, a new arm-locking design with improved gain and stability, and progress in flight readiness of digital and analog electronics for phase measurements.Comment: 11 pages, 9 figures, LISA 8 Symposium, Stanford University, 201

Numerical simulation of time delay interferometry for eLISA/NGO

eLISA/NGO is a new gravitational wave detection proposal with arm length of 10^6 km and one interferometer down-scaled from LISA. Just like LISA and ASTROD-GW, in order to attain the requisite sensitivity for eLISA/NGO, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for LISA and ASTROD-GW with one arm dysfunctional by using the CGC 2.7 ephemeris. The results are well below their respective limits which the laser frequency noise is required to be suppressed. In this paper, we follow the same procedure to simulate the time delay interferometry numerically. To do this, we work out a set of 1000-day optimized mission orbits of the eLISA/NGO spacecraft starting at January 1st, 2021 using the CGC 2.7 ephemeris framework. We then use the numerical method to calculate the residual optical path differences in the second-generation TDI solutions as in our previous papers. The maximum path length difference, for all configurations calculated, is below 13 mm (43 ps). It is well below the limit which the laser frequency noise is required to be suppressed for eLISA/NGO. We compare and discuss the resulting differences due to the different arm lengths for various mission proposals -- eLISA/NGO, an NGO-LISA-type mission with a nominal arm length of 2 x 10^6 km, LISA and ASTROD-GW.Comment: 17 pages, 13 figures, 3 tables, minor changes in description to match the accepted version of Classical and Quantum Gravity. arXiv admin note: text overlap with arXiv:1102.496

I-MOVE multicentre case–control study 2010/11 to 2014/15 : is there within-season waning of influenza type/subtype vaccine effectiveness with increasing time since vaccination?

Influenza vaccines are currently the best method available to prevent seasonal influenza infection. In most European countries one dose (or two doses for children) of seasonal vaccine is given from September to December to the elderly and other target groups for vaccination. In Europe, influenza seasons can last until mid-May (1), and it is expected that vaccination conveys protection on the individual for the duration of the season. In 13/15 reviewed studies on the length of vaccine-induced protection among the elderly, using anti-haemagglutination antibody titres as a proxy for seroprotection levels, seroprotection rates lasted at least >4 months after vaccination (2). However in the 2011-12 influenza season various studies in Europe reported a decrease in influenza vaccine effectiveness (VE) against A(H3N2) over time within the season (3–5). In the United States, a decrease in VE against A(H3N2) with time since vaccination was suggested in the 2007-8 influenza season (6). The observed decrease of VE over time can be explained by viral change (notably antigenic drift) occurring in the season. Drift in B viruses may be slower than in A viruses (7), and A(H3N2) viruses undergo antigenic drift more frequently than A(H1N1)pdm09 viruses (8). The decrease of VE over time can also be explained by a waning of the immunity conferred by the vaccine independently from viral changes. If vaccine-induced protection wanes more rapidly during the season, then depending on the start and duration of the influenza season, the decline of VE may cause increases in overall incidence, hospitalisations and deaths. Changes to vaccination strategies (timing and boosters) may be needed. As anti-haemagglutination antibody titres are not well defined as a correlate of protection (9,10), vaccine efficacy (as measured in trials) or vaccine effectiveness observational studies may be one way to measure vaccine-induced protection. These studies require a large sample size to model VE by time since vaccination and currently, most of the seasonal observational studies lack the precision required to provide evidence for waning immunity. In this study we pooled data across five post-pandemic seasons (2010/11-2014/15) from the I-MOVE (Influenza - Monitoring Vaccine Effectiveness) multicentre case control studies (1,3,11,12), to obtain a greater sample size to study the effects of time since vaccination on influenza type/subtype-specific VE. We measure influenza type/subtype-specific VE by time since vaccination for the overall season, but also in the early influenza phase; under the hypothesis that virological changes are fewer in the early season, but waning of the vaccine effect should be present regardless of time within the influenza phase

Longitudinal trajectories and reference centiles for the impact of health conditions on daily activities of children with cerebral palsy.

AIM: First, to describe the impact of health conditions on daily activities over time in children with cerebral palsy (CP) and to create age-specific reference centiles. Second, to determine the amount of change typical over a 1-year period, across Gross Motor Function Classification System (GMFCS) levels. METHOD: A prospective, cohort design, with five assessments over 2 years, involved 708 children with a confirmed diagnosis of CP participating in the On Track Study (396 males, 312 females; mean age 6y [SD 2y 7mo]; range 18mo-12y at first assessment; 32.1% in GMFCS level I, 22.7% in GMFCS level II, 11.2% in GMFCS level III, 18.2% in GMFCS level IV, 15.7% in GMFCS level V). The impact of health conditions on daily activities was assessed using the Child Health Conditions Questionnaire. Data were analyzed using mixed-effects models and quantile regression. RESULTS: Linear longitudinal trajectories describe the relatively stable impact of health conditions over time for each functional level for children aged 2 years to 12 years, with the lowest scores (least impact) in GMFCS level I and the highest scores (highest impact) in GMFCS level V. Centiles were created for children in each GMFCS level. A system to interpret the magnitude of change over time in centiles was developed. INTERPRETATION: Longitudinal trajectories of co-occurring health conditions assist with understanding children\u27s prognoses. Centiles assist in understanding a child\u27s experience relative to children in similar GMFCS levels. Guidelines are provided to determine if children are progressing \u27as expected\u27, \u27better than expected\u27 or \u27more poorly than expected\u27 in regard to the impact of health conditions on daily activities. WHAT THIS PAPER ADDS: For children with cerebral palsy, the mean impact of health conditions on daily activities is relatively stable. Significant intraindividual and interindividual variability for the impact of health conditions exists, which complicates prognosis. Centiles enable interpretation of the impact of health conditions relative to Gross Motor Function Classification System level