"Hey, that's not an ODE": Faster ODE Adjoints with 12 Lines of Code

Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is accepted if its error, \emph{relative to some norm}, is sufficiently small; else it is rejected, the step is shrunk, and the process is repeated. Here, we demonstrate that the particular structure of the adjoint equations makes the usual choices of norm (such as $L^2$) unnecessarily stringent. By replacing it with a more appropriate (semi)norm, fewer steps are unnecessarily rejected and the backpropagation is made faster. This requires only minor code modifications. Experiments on a wide range of tasks---including time series, generative modeling, and physical control---demonstrate a median improvement of 40% fewer function evaluations. On some problems we see as much as 62% fewer function evaluations, so that the overall training time is roughly halved

Comet C/2013 A1 (Siding Spring) as seen with the Herschel Space Observatory

The thermal emission of comet C/2013 A1 (Siding Spring) was observed on March 31, 2013, at a heliocentric distance of 6.48 au using the PACS photometer camera of the Herschel Space Observatory. The comet was clearly active, showing a coma that could be traced to a distance of 10", i.e. 50000 km. Analysis of the radial intensity profiles of the coma provided dust mass and dust production rate; the derived grain size distribution characteristics indicate an overabundance of large grains in the thermal emission. We estimate that activity started about 6 months before these observations, at a heliocentric distance of 8 au.Comment: 4 pages, 3 figures + a one-page Appendix with 2 figures, accepted for publication in Astronomy & Astrophysics (Letter

Physical Properties of Asteroid (308635) 2005 YU55 derived from multi-instrument infrared observations during a very close Earth-Approach

The near-Earth asteroid (308635) 2005 YU55 is a potentially hazardous asteroid which was discovered in 2005 and passed Earth on November 8th 2011 at 0.85 lunar distances. This was the closest known approach by an asteroid of several hundred metre diameter since 1976 when a similar size object passed at 0.5 lunar distances. We observed 2005 YU55 from ground with a recently developed mid-IR camera (miniTAO/MAX38) in N- and Q-band and with the Submillimeter Array (SMA) at 1.3 mm. In addition, we obtained space observations with Herschel/PACS at 70, 100, and 160 micron. Our thermal measurements cover a wide range of wavelengths from 8.9 micron to 1.3 mm and were taken after opposition at phase angles between -97 deg and -18 deg. We performed a radiometric analysis via a thermophysical model and combined our derived properties with results from radar, adaptive optics, lightcurve observations, speckle and auxiliary thermal data. We find that (308635) 2005 YU55 has an almost spherical shape with an effective diameter of 300 to 312 m and a geometric albedo pV of 0.055 to 0.075. Its spin-axis is oriented towards celestial directions (lam_ecl, beta_ecl) = (60 deg +/- 30deg, -60 deg +/- 15 deg), which means it has a retrograde sense of rotation. The analysis of all available data combined revealed a discrepancy with the radar-derived size. Our radiometric analysis of the thermal data together with the problem to find a unique rotation period might be connected to a non-principal axis rotation. A low to intermediate level of surface roughness (r.m.s. of surface slopes in the range 0.1 - 0.3) is required to explain the available thermal measurements. We found a thermal inertia in the range 350-800 Jm^-2s^-0.5K^-1, very similar to the rubble-pile asteroid (25143) Itokawa and indicating a mixture of low conductivity fine regolith with larger rocks and boulders of high thermal inertia on the surface.Comment: Accepted for publication in Astronomy & Astrophysics, 12 pages, 10 figure

Participatory Action Research on School Culture and Student Mental Health: A Study Protocol

Background: Young people spend a large proportion of their time in school, which presents both risk and protective factors for their mental health. A supportive school culture can promote and protect good mental health by creating experiences of safety and belonging amongst staff and students. In this qualitative study, we seek to explore whether a participatory action research (PAR) approach is an effective way to promote and improve student mental health. Methods: Participatory action research is an approach in which people collaboratively research their own experience: the researched communities become co-researchers of their own experiences in a specific context. We will work with four secondary schools in the UK to develop PAR projects. In each school, a group of 2–4 staff and 6–8 students will work together to develop a shared understanding of their school culture and to introduce activities or changes to make the culture more supportive of student mental health. We will evaluate the effectiveness of the PAR approach through i) a review of school documents pertaining to mental health (e.g., policies and Ofsted reports), ii) interviews with staff members ( n = 40), parents ( n = 8) and students ( n = 24–40) before and after the PAR intervention, iii) observations and reports of the PAR group meetings and iv) interviews with members of the PAR groups after the PAR intervention. Discussion: We anticipate that our research findings will advance knowledge on effective methods to develop a positive school culture that will contribute to the improvement of young people’s mental health and well-being. We will seek to identify the mechanisms through which school culture can have a positive impact on mental health and develop a logic model and a school culture toolkit that can be utilised as a resource to inform public health interventions to promote mental health in a range of educational settings.National Institute for Health Research (NIHR) School for Public Health Research (Grant Reference Number PD–SPH–2015)

Historic Light Curve and Long-term Optical Variation of BL Lacertae 2200+420

In this paper, historical optical(UBVRI) data and newly observed data from the Yunnan Observatory of China(about100 years) are presented for BL Lacertae. Maximum variations in UBVRI: 5.12, 5.31, 4.73, 2.59, and 2.54 and color indices of U-B = -0.11 +/- 0.20, B-V= 1.0 +/- 0.11, V-R= 0.73 +/- 0.19, V-I= 1.42 +/- 0.25, R-I= 0.82 +/- 0.11, and B-I= 2.44 +/- 0.29 have been obtained from the literature; The Jurkevich method is used to investigate the existence of periods in the B band light curve, and a long-term period of 14 years is found. The 0.6 and 0.88 year periods reported by Webb et al.(1988) are confirmed. In addition, a close relation between B-I and B is found, suggesting that the spectra flattens when the source brightens.Comment: 21 pages, 6 figures, 2 table, aasms4.sty, to be published in ApJ, Vol. 507, 199

A search for periodicity in the light curves of selected blazars

We present an analysis of multifrequency light curves of the sources 2223-052 (3C 446), 2230+114 (CTA 102), and 2251+158 (3C 454.3), which had shown evidence of quasi-periodic activity. The analysis made use of data from the University of Michican Radio Astronomy Observatory (USA) at 4.8, 8, and 14.5 GHz, as well as the Metsahovi Radio Astronomy Observatory (Finland) at 22 and 37 GHz. Application of two different methods (the discrete autocorrelation function and the method of Jurkevich) both revealed evidence for periodicity in the flux variations of these sources at essentially all frequencies. The periods derived for at least two of the sources -- 2223-052 and 2251+158-- are in good agreement with the time interval between the appearance of successive VLBI components. The derived periods for 2251+158 (P = 12.4 yr and 2223-052 (P = 5.8 yr) coincide with the periods found earlier by other authors based on optical light curves.Comment: 27 pages, 11 figures, accepted for publication in Astronomy Report

Optical and Radio monitoring of S5 1803+74

The optical (BVRI) and radio (8.4 GHz) light curves of S5 1803+784 on a time span of nearly 6 years are presented and discussed. The optical light curve showed an overall variation greater than 3 mag, and the largest changes occured in three strong flares. No periodicity was found in the light curve on time scales up to a year. The variability in the radio band is very different, and shows moderate oscillations around an average constant flux density rather than relevant flares, with a maximum amplitude of $\sim$30%, without a simultaneous correspondence between optical and radio luminosity. The optical spectral energy distribution was always well fitted by a power law. The spectral index shows small variations and there is indication of a positive correlation with the source luminosity. Possible explanations of the source behaviour are discussed in the framework of current models.Comment: 25 pages, 12 figure

Radio and optical intra-day variability observations of five blazars

We carried out a pilot campaign of radio and optical band intra-day variability (IDV) observations of five blazars (3C66A, S5 0716+714, OJ287, B0925+504, and BL Lacertae) on December 18--21, 2015 by using the radio telescope in Effelsberg (Germany) and several optical telescopes in Asia, Europe, and America. After calibration, the light curves from both 5 GHz radio band and the optical R band were obtained, although the data were not smoothly sampled over the sampling period of about four days. We tentatively analyse the amplitudes and time scales of the variabilities, and any possible periodicity. The blazars vary significantly in the radio (except 3C66A and BL Lacertae with only marginal variations) and optical bands on intra- and inter-day time scales, and the source B0925+504 exhibits a strong quasi-periodic radio variability. No significant correlation between the radio- and optical-band variability appears in the five sources, which we attribute to the radio IDV being dominated by interstellar scintillation whereas the optical variability comes from the source itself. However, the radio- and optical-band variations appear to be weakly correlated in some sources and should be investigated based on well-sampled data from future observations.Comment: 6 pages, 6 figures, accepted by MNRA

Searches for HCl and HF in comets 103P/Hartley 2 and C/2009 P1 (Garradd) with the Herschel space observatory

HCl and HF are expected to be the main reservoirs of fluorine and chlorine wherever hydrogen is predominantly molecular. They are found to be strongly depleted in dense molecular clouds, suggesting freeze-out onto grains in such cold environments. We can then expect that HCl and HF were also the major carriers of Cl and F in the gas and icy phases of the outer solar nebula, and were incorporated into comets. We aimed to measure the HCl and HF abundances in cometary ices as they can provide insights on the halogen chemistry in the early solar nebula. We searched for the J(1-0) lines of HCl and HF at 626 and 1232 GHz, respectively, using the HIFI instrument on board the Herschel Space Observatory. HCl was searched for in comets 103P/Hartley 2 and C/2009 P1 (Garradd), whereas observations of HF were conducted in comet C/2009 P1. In addition, observations of H$_2$O and H$_2^{18}$O lines were performed in C/2009 P1 to measure the H$_2$O production rate. Three lines of CH$_3$OH were serendipitously observed in the HCl receiver setting. HCl is not detected, whereas a marginal (3.6-$\sigma$) detection of HF is obtained. The upper limits for the HCl abundance relative to water are 0.011% and 0.022%, for 103P and C/2009 P1, respectively, showing that HCl is depleted with respect to the solar Cl/O abundance by a factor more than 6$^{+6}_{-3}$ in 103P, where the error is related to the uncertainty in the chlorine solar abundance. The marginal HF detection obtained in C/2009 P1 corresponds to an HF abundance relative to water of (1.8$\pm$0.5) $\times$ 10$^{-4}$, which is approximately consistent with a solar photospheric F/O abundance. The observed depletion of HCl suggests that HCl was not the main reservoir of chlorine in the regions of the solar nebula where these comets formed. HF was possibly the main fluorine compound in the gas phase of the outer solar nebula.Comment: Accepted for publication in Astronomy & Astrophysic

The Dust Trail of Comet 67P/Churyumov-Gerasimenko between 2004 and 2006

We report on observations of the dust trail of comet 67P/Churyumov-Gerasimenko (CG) in visible light with the Wide Field Imager at the ESO/MPG 2.2m telescope at 4.7 AU before aphelion, and at 24 micron with the MIPS instrument on board the Spitzer Space Telescope at 5.7 AU both before and after aphelion. The comet did not appear to be active during our observations. Our images probe large dust grains emitted from the comet that have a radiation pressure parameter beta<0.01. We compare our observations with simulated images generated with a dynamical model of the cometary dust and constrain the emission speeds, size distribution, production rate and geometric albedo of the dust. We achieve the best fit to our data with a differential size distribution exponent of -4.1, and emission speeds for a beta=0.01 particle of 25 m/s at perihelion and 2 m/s at 3 AU. The dust production rate in our model is on the order of 1000 kg/s at perihelion and 1 kg/s at 3 AU, and we require a dust geometric albedo between 0.022 and 0.044. The production rates of large (>10 micron) particles required to reproduce the brightness of the trail are sufficient to also account for the coma brightness observed while the comet was inside 3 AU, and we infer that the cross-section in the coma of CG may be dominated by grains of the order of 60-600 micron.Comment: 79 pages, 13 figures, 6 tables. Accepted for publication in Icaru