Children and their Families: Function of the Community

Hogg Foundation for Mental Healt

Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

Operational LANDSAT remote sensing system development

The reduction of $121.6 million dollars from NOAA's LANDSAT development program for FY 1982, and the shortened time period for transferring remote sensing technology to the private sector resulted in changes in the Agency's plans for managing the operational system. Proposed legislation for congressional consideration or enactment to establish conditions under which this private sector transfer will occur, and the expected gradual rise in the price of data products are discussed. No money exists for capital investment and none is projected for investing in an operational data handling system for the LANDSAT D satellite. Candidates knowledgeable of various aspects of the needs and uses of remote sensing are urged to consider participation in NOAA's advisory committee

Uncovering the physics behind the blazar sequence using a realistic model for jet emission

Blazar spectra are one of the most important windows into the physical processes occurring along jets. The spectrum, composed from the different emitting regions along the jet, allows us to constrain the physical conditions in the jet. I present my work modelling blazar spectra using an extended inhomogeneous jet model with an accelerating, magnetically dominated, parabolic base transitioning to a slowly decelerating, conical section motivated by observations, simulations and theory. We set the inner geometry of our multi-zone model using observations of the jet in M87 which transitions from parabolic to conical at 10^5 Schwarzschild radii. This model is able to reproduce quiescent blazar spectra very well across all wavelengths (including radio observations) for a sample of 42 BL Lacs and FSRQs. Using this inhomogeneous model we are able to constrain the location at which the synchrotron emission is brightest in these jets by fitting to the optically thick to thin synchrotron break. We find that the radius of the jet at which the synchrotron emission is brightest (where the jet first approaches equipartition) scales approximately linearly with the jet power. We also find a correlation between the length of the accelerating, parabolic section of the jet and the maximum bulk Lorentz factor. In agreement with previous work we find that BL Lacs are low power blazars whereas FSRQs are high power blazars. Together with our simple jet power-radius relation this leads us to a deeper understanding of the physics underlying the blazar sequence.Comment: 5 pages, 5 figures, to appear in "The Innermost Regions of Relativistic Jets and Their Magnetic Fields" conference proceedings; includes minor change

Synchrotron and inverse-Compton emission from blazar jets - III. Compton-dominant blazars

In this paper we develop the extended jet model of Potter & Cotter to model the simultaneous multi-wavelength spectra of six Compton-dominant blazars. We include an accelerating parabolic base transitioning to a slowly decelerating conical jet with a geometry set by observations of M87 and consistent with simulations and theory. We investigate several jet models and find that the optically thick to thin synchrotron break in the radio spectrum requires the jet to first come into equipartition at large distances along the jet (10^5 Schwarzschild radii), consistent with the observed transition from parabolic to conical in the jet of M87. We confirm this result analytically and calculate the expected frequency core-shift relations for the models under consideration. We find that a parabolic jet transitioning to a ballistic conical jet, which starts in equipartition and becomes more particle dominated at larger distances, fits the multiwavelength data of the six blazars well, whilst an adiabatic equipartition conical section requires very large bulk Lorentz factors to reproduce the Compton-dominance of the blazars. We find that all these blazars require high power, high bulk Lorentz factor jets observed close to the line of sight as we expect from the blazar sequence and consistent with the results from Paper II. The inverse-Compton emission in our fits is due to inverse-Compton scattering of high-redshift CMB photons at large distances along the jet due to the high bulk Lorentz factors of the jets. We postulate a new interpretation of the blazar sequence based on the radius of the transition region of the jet (where the jet is brightest in synchrotron emission) scaling linearly with black hole mass.Comment: 13 pages, 5 figures, accepted for publication in MNRA