18,701 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
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.
Renormalized field theory and particle density profile in driven diffusive systems with open boundaries
We investigate the density profile in a driven diffusive system caused by a
plane particle source perpendicular to the driving force. Focussing on the case
of critical bulk density we use a field theoretic renormalization
group approach to calculate the density as a function of the distance
from the particle source at first order in (: spatial
dimension). For we find reasonable agreement with the exact solution
recently obtained for the asymmetric exclusion model. Logarithmic corrections
to the mean field profile are computed for with the result for .Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.
Force Dynamics in Weakly Vibrated Granular Packings
The oscillatory force F_b^ac on the bottom of a rigid, vertically vibrated,
grain filled column, reveals rich granular dynamics, even when the peak
acceleration of the vibrations is signicantly less than the gravitational
acceleration at the earth's surface. For loose packings or high frequencies,
F_b^ac 's dynamics are dominated by grain motion. For moderate driving
conditions in more compact samples, grain motion is virtually absent, but
F_b^ac nevertheless exhibits strongly nonlinear and hysteretic behavior,
evidencing a granular regime dominated by nontrivial force-network dynamics.Comment: 4 pages, 5 figure
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
Direct analysis of aromatic hydrocarbons in purified mineral oils for foods and cosmetics applications using gas chromatography with vacuum ultraviolet detection
A decision Enhancement Service for Stakeholder Analysis to Achieve Transformations in the Public Sector
Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension
We analyse numerically the critical behavior of a conserved lattice gas which
was recently introduced as an example of the new universality class of
absorbing phase transitions with a conserved field [Phys. Rev. Lett. 85, 1803
(2000)]. We determine the critical exponent of the order parameter as well as
the critical exponent of the order parameter fluctuations in D=2,3,4,5
dimensions. A comparison of our results and those obtained from a mean-field
approach and a field theory suggests that the upper critical dimension of the
absorbing phase transition is four.Comment: 5 pages, 11 figure
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