21,413 research outputs found
Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging
Locally adaptive differential frames (gauge frames) are a well-known
effective tool in image analysis, used in differential invariants and
PDE-flows. However, at complex structures such as crossings or junctions, these
frames are not well-defined. Therefore, we generalize the notion of gauge
frames on images to gauge frames on data representations defined on the extended space of positions and
orientations, which we relate to data on the roto-translation group ,
. This allows to define multiple frames per position, one per
orientation. We compute these frames via exponential curve fits in the extended
data representations in . These curve fits minimize first or second
order variational problems which are solved by spectral decomposition of,
respectively, a structure tensor or Hessian of data on . We include
these gauge frames in differential invariants and crossing preserving PDE-flows
acting on extended data representation and we show their advantage compared
to the standard left-invariant frame on . Applications include
crossing-preserving filtering and improved segmentations of the vascular tree
in retinal images, and new 3D extensions of coherence-enhancing diffusion via
invertible orientation scores
Finite-size scaling of directed percolation above the upper critical dimension
We consider analytically as well as numerically the finite-size scaling
behavior in the stationary state near the non-equilibrium phase transition of
directed percolation within the mean field regime, i.e., above the upper
critical dimension. Analogous to equilibrium, usual finite-size scaling is
valid below the upper critical dimension, whereas it fails above. Performing a
momentum analysis of associated path integrals we derive modified finite-size
scaling forms of the order parameter and its higher moments. The results are
confirmed by numerical simulations of corresponding high-dimensional lattice
models.Comment: 4 pages, one figur
The optimal schedule for pulsar timing array observations
In order to maximize the sensitivity of pulsar timing arrays to a stochastic
gravitational wave background, we present computational techniques to optimize
observing schedules. The techniques are applicable to both single and
multi-telescope experiments. The observing schedule is optimized for each
telescope by adjusting the observing time allocated to each pulsar while
keeping the total amount of observing time constant. The optimized schedule
depends on the timing noise characteristics of each individual pulsar as well
as the performance of instrumentation. Several examples are given to illustrate
the effects of different types of noise. A method to select the most suitable
pulsars to be included in a pulsar timing array project is also presented.Comment: 16 pages, 6 figures, accepted by MNRA
Very Long Baseline Interferometry Measured Proper Motion and Parallax of the -ray Millisecond Pulsar PSR J0218+4232
PSR J02184232 is a millisecond pulsar (MSP) with a flux density 0.9
mJy at 1.4 GHz. It is very bright in the high-energy X-ray and -ray
domains. We conducted an astrometric program using the European VLBI Network
(EVN) at 1.6 GHz to measure its proper motion and parallax. A model-independent
distance would also help constrain its -ray luminosity. We achieved a
detection of signal-to-noise ratio S/N > 37 for the weak pulsar in all five
epochs. Using an extragalactic radio source lying 20 arcmin away from the
pulsar, we estimate the pulsar's proper motion to be
mas yr and mas yr, and a parallax of mas. The very long
baseline interferometry (VLBI) proper motion has significantly improved upon
the estimates from long-term pulsar timing observations. The VLBI parallax
provides the first model-independent distance constraints:
kpc, with a corresponding lower-limit of
kpc. This is the first pulsar trigonometric parallax measurement based
solely on EVN observations. Using the derived distance, we believe that PSR
J02184232 is the most energetic -ray MSP known to date. The
luminosity based on even our 3 lower-limit distance is high enough to
pose challenges to the conventional outer gap and slot gap models.Comment: 5 pages, 2 figures, 2 tables; published in the Astrophysical Journal
Letters on 2014 Feb. 1
Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field
We consider two mean-field like models which belong to the universality class
of absorbing phase transitions with a conserved field. In both cases we derive
analytically the order parameter as function of the control parameter and of an
external field conjugated to the order parameter. This allows us to calculate
the universal scaling function of the mean-field behavior. The obtained
universal function is in perfect agreement with recently obtained numerical
data of the corresponding five and six dimensional models, showing that four is
the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.
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