Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Precipitable Water Comparisons Over Ghana using PPP Techniques and Reanalysis Data

Atmospheric Water vapor is an important greenhouse gas and contributes greatly in maintaining the Earth’s energy balance. This critical meteorological parameter is not being sensed by any of the 22 synoptic weather stations in Ghana. This study presents a highly precise tool for water vapor sensing based on the concept Global Navigation Satellite Systems (GNSS) meteorology and tests the computed results against global reanalysis data. Conventional approaches used to sense the atmospheric water vapor or Precipitable Water (PW) such as radiosondes, hygrometers, microwave radiometers or sun photometers are expensive and have coverage and temporal limitations. Whereas GNSS meteorological concept offers an easier, inexpensive and all-weather technique to retrieve PW or Integrated Water Vapor (IWV) from zenith tropospheric delays (ZTD) over a reference station. This study employed precise point positioning (PPP) techniques to quantify the extend of delays on the signal due to the troposphere and stratosphere where atmospheric water vapor resides. Stringent processing criteria were set using an elevation cut-off of 5 degrees, precise orbital and clock products were used as well as nominal tropospheric corrections and mapping functions implemented. The delays which are originally slanted are mapped unto the zenith direction and integrated with surface meteorological parameters to retrieve PW or IWV. The gLAB software, Canadian Spatial Reference System (CSRS) and Automatic Precise Positioning Service (APPS) online PPP services were the approaches used to compute ZTD. PW values obtained were compared with Japanese Metro Agency Reanalysis (JRA), European Centre for Medium-Range Weather Forecasts Reanalysis (ERA-interim) and National Center for Environmental Prediction (NCEP) global reanalysis data. Correlation analysis were run on the logged station data using the three approaches and global reanalysis data. The obtained results show stronger correlation between the retrieved PW values and those provided by the ERA-interim. Finally, the study results indicate that with a more densified network of GNSS base stations the retrieved PW or IWV will greatly improve numerical weather predictions in Ghana.Keywords: GNSS Signals, PPP, Integrated Water vapour, Precipitable Water, Reanalysis Model

Implementing machine ethics: using machine learning to raise ethical machines

As more decisions and tasks are delegated to the artificially intelligent machines of the 21st century, we must ensure that these machines are, on their own, able to engage in ethical decision-making and behaviour. This dissertation makes the case that bottom-up reinforcement learning methods are the best suited for implementing machine ethics by raising ethical machines. This is one of three main theses in this dissertation, that we must seriously consider how machines themselves, as moral agents that can impact human well-being and flourishing, might make ethically preferable decisions and take ethically preferable actions. The second thesis is that artificially intelligent machines are different in kind from all previous machines. The conjunction of autonomy and intelligence, among other unique features like the ability to learn and their general-purpose nature, is what sets artificially intelligent machines apart from all previous machines and tools. The third thesis concerns the limitations of artificially intelligent machines. As impressive as these machines are, their abilities are still derived from humans and as such lack the sort of normative commitments humans have. In short, we ought to care deeply about artificially intelligent machines, especially those used in times and places when considered human judgment is required, because we risk lapsing into a state of moral complacency otherwise

ISOCAM observations of the L1551 star formation region

The results of a deep mid-IR ISOCAM survey of the L1551 dark molecular cloud are presented. The aim of this survey is a search for new YSO (Young Stellar Object) candidates, using two broad-band filters centred at 6.7 and 14.3 micron. Although two regions close to the centre of L1551 had to be avoided due to saturation problems, 96 sources were detected in total (76 sources at 6.7 micron and 44 sources at 14.3 micron). Using the 24 sources detected in both filters, 14 were found to have intrinsic mid-IR excess at 14.3 micron and were therefore classified as YSO candidates. Using additional observations in B, V, I, J, H and K obtained from the ground, most candidates detected at these wavelengths were confirmed to have mid-IR excess at 6.7 micron as well, and three additional YSO candidates were found. Prior to this survey only three YSOs were known in the observed region (avoiding L1551 IRS5/NE and HL/XZ Tau). This survey reveals 15 new YSO candidates, although several of these are uncertain due to their extended nature either in the mid-IR or in the optical/near-IR observations. Two of the sources with mid-IR excess are previously known YSOs, one is a brown dwarf MHO 5 and the other is the well known T Tauri star HH30, consisting of an outflow and an optically thick disk seen edge on.Comment: 14 Pages, 8 Figure

ISOCAM observations of the rho Ophiuchi cloud: Luminosity and mass functions of the pre-main sequence embedded cluster

We present the results of the first extensive mid-infrared (IR) imaging survey of the rho Ophiuchi embedded cluster, performed with the ISOCAM camera on board the ISO satellite. The main molecular cloud L1688, as well as L1689N and L1689S, have been completely surveyed for point sources at 6.7 and 14.3 micron. A total of 425 sources are detected including 16 Class I, 123 Class II, and 77 Class III young stellar objects (YSOs). Essentially all of the mid-IR sources coincide with near-IR sources, but a large proportion of them are recognized for the first time as YSOs. Our dual-wavelength survey allows us to identify essentially all the YSOs with IR excess in the embedded cluster down to Fnu ~ 10 - 15 mJy. It more than doubles the known population of Class II YSOs and represents the most complete census to date of newly formed stars in the rho Ophiuchi central region. The stellar luminosity function of the complete sample of Class II YSOs is derived with a good accuracy down to L= 0.03 Lsun. A modeling of this lumino- sity function, using available pre-main sequence tracks and plausible star for- mation histories, allows us to derive the mass distribution of the Class II YSOs which arguably reflects the IMF of the embedded cluster. We estimate that the IMF in rho Ophiuchi is well described by a two-component power law with a low- mass index of -0.35+/-0.25, a high-mass index of -1.7 (to be compared with the Salpeter value of -1.35), and a break occurring at M = 0.55+/-0.25 Msun. This IMF is flat with no evidence for a low-mass cutoff down to at least 0.06 Msun.Comment: A&A Document Class -- version 5.01, 27 pages, 10 figures v2: typos added including few changes in source numberin

A deep optical/near-infrared catalog of Serpens

We present a deep optical/near-infrared imaging survey of the Serpens molecular cloud. This survey constitutes the complementary optical data to the Spitzer "Core To Disk" (c2d) Legacy survey in this cloud. The survey was conducted using the Wide Field Camera at the Isaac Newton Telescope. About 0.96 square degrees were imaged in the R and Z filters, covering the entire region where most of the young stellar objects identified by the c2d survey are located. 26524 point-like sources were detected in both R and Z bands down to R=24.5 mag and Z=23 mag with a signal-to-noise ratio better than 3. The 95% completeness limit of our catalog corresponds to 0.04 solar masses for members of the Serpens star forming region (age 2 Myr and distance 260 pc) in the absence of extinction. Adopting the typical extinction of the observed area (Av=7 mag), we estimate a 95% completeness level down to 0.1 solar masses. The astrometric accuracy of our catalog is 0.4 arcsec with respect to the 2MASS catalog. Our final catalog contains J2000 celestial coordinates, magnitudes in the R and Z bands calibrated to the SDSS photometric system and, where possible, JHK magnitudes from 2MASS for sources in 0.96 square degrees in the direction of Serpens. This data product has been already used within the frame of the c2d Spitzer Legacy Project analysis in Serpens to study the star/disk formation and evolution in this cloud; here we use it to obtain new indications of the disk-less population in Serpens.Comment: 7 page, 5 figure

The time delay of the quadruple quasar RX J0911.4+0551

We present optical lightcurves of the gravitationally lensed components A (=A1+A2+A3) and B of the quadruple quasar RX J0911.4+0551 (z = 2.80). The observations were primarily obtained at the Nordic Optical Telescope between 1997 March and 2001 April and consist of 74 I-band data points for each component. The data allow the measurement of a time delay of 146 +- 8 days (2 sigma) between A and B, with B as the leading component. This value is significantly shorter than that predicted from simple models and indicates a very large external shear. Mass models including the main lens galaxy and the surrounding massive cluster of galaxies at z = 0.77, responsible for the external shear, yield H_0 = 71 +- 4 (random, 2 sigma) +- 8 (systematic) km/s/Mpc. The systematic model uncertainty is governed by the surface-mass density (convergence) at the location of the multiple images.Comment: 12 pages, 3 figures, ApJL, in press (June 20, 2002