3,269 research outputs found
Stochastic Development Regression on Non-Linear Manifolds
We introduce a regression model for data on non-linear manifolds. The model
describes the relation between a set of manifold valued observations, such as
shapes of anatomical objects, and Euclidean explanatory variables. The approach
is based on stochastic development of Euclidean diffusion processes to the
manifold. Defining the data distribution as the transition distribution of the
mapped stochastic process, parameters of the model, the non-linear analogue of
design matrix and intercept, are found via maximum likelihood. The model is
intrinsically related to the geometry encoded in the connection of the
manifold. We propose an estimation procedure which applies the Laplace
approximation of the likelihood function. A simulation study of the performance
of the model is performed and the model is applied to a real dataset of Corpus
Callosum shapes
XMM-Newton view of Swift J1834.9-0846 and its Magnetar Wind Nebula
We report on the analysis of two XMM-Newton observations of the recently
discovered soft gamma repeater Swift J1834.9-0846, taken in September 2005 and
one month after the source went into outburst on 2011 August 7. We performed
timing and spectral analyses on the point source as well as on the extended
emission. We find that the source period is consistent with an extrapolation of
the Chandra ephemeris reported earlier and the spectral properties remained
constant. The source luminosity decreased to a level of 1.6x10^34 erg s^-1
following a decay trend of . Our spatial analysis of the
source environment revealed the presence of two extended emission regions
around the source. The first (Region A) is a symmetric ring around the point
source, starting at 25arcsec and extending to ~50arcsec. We argue that Region A
is a dust scattering halo. The second (Region B) has an asymmetrical shape
extending between 50arcsec and 150arcsec, and is detected both in the pre- and
post-outburst data. We argue that this region is a possible magnetar wind
nebula (MWN). The X-ray efficiency of the MWN with respect to the rotation
energy loss is substantially higher than those of rotation powered pulsars:
. The
higher efficiency points to a different energy source for the MWN of Swift
J1834.9-0846, most likely bursting activity of the magnetar, powered by its
high magnetic field, B=1.4x10^14 G.Comment: 10 pages, 10 figures, accepted for publication in Ap
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