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 $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. 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 $SE(d)$. 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 $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. 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

Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the framework of the generalized Chalker--Coddington network model. We determine the critical exponent $\alpha_0$ characterizing the scaling behavior of the local order parameter for systems with potential correlation length $d$ up to $12$ magnetic lengths $l$. Our results show that $\alpha_0$ does not depend on the ratio $d/l$. With increasing $d/l$, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behavior on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse

Very Long Baseline Interferometry Measured Proper Motion and Parallax of the γ\gamma-ray Millisecond Pulsar PSR J0218+4232

PSR J0218$+$4232 is a millisecond pulsar (MSP) with a flux density $\sim$ 0.9 mJy at 1.4 GHz. It is very bright in the high-energy X-ray and $\gamma$-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 $\gamma$-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 $\mu_{\alpha}\cos\delta=5.35\pm0.05$ mas yr$^{-1}$ and $\mu_{\delta}=-3.74\pm 0.12$ mas yr$^{-1}$, and a parallax of $\pi=0.16\pm0.09$ 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: $d=6.3^{+8.0}_{-2.3}$ kpc, with a corresponding $3\sigma$ lower-limit of $d=2.3$ kpc. This is the first pulsar trigonometric parallax measurement based solely on EVN observations. Using the derived distance, we believe that PSR J0218$+$4232 is the most energetic $\gamma$-ray MSP known to date. The luminosity based on even our 3$\sigma$ 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

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.Comment: 21 pages, 6 figure

The sensitivity of harassment to orbit: Mass loss from early-type dwarfs in galaxy clusters

We conduct a comprehensive numerical study of the orbital dependence of harassment on early-type dwarfs consisting of 168 different orbits within a realistic, Virgo-like cluster, varying in eccentricity and pericentre distance. We find harassment is only effective at stripping stars or truncating their stellar discs for orbits that enter deep into the cluster core. Comparing to the orbital distribution in cosmological simulations, we find that the majority of the orbits (more than three quarters) result in no stellar mass loss. We also study the effects on the radial profiles of the globular cluster systems of early-type dwarfs. We find these are significantly altered only if harassment is very strong. This suggests that perhaps most early-type dwarfs in clusters such as Virgo have not suffered any tidal stripping of stars or globular clusters due to harassment, as these components are safely embedded deep within their dark matter halo. We demonstrate that this result is actually consistent with an earlier study of harassment of dwarf galaxies, despite the apparent contradiction. Those few dwarf models that do suffer stellar stripping are found out to the virial radius of the cluster at redshift = 0, which mixes them in with less strongly harassed galaxies. However when placed on phase-space diagrams, strongly harassed galaxies are found offset to lower velocities compared to weakly harassed galaxies. This remains true in a cosmological simulation, even when haloes have a wide range of masses and concentrations. Thus phase-space diagrams may be a useful tool for determining the relative likelihood that galaxies have been strongly or weakly harassed

Charge Transport Properties of a Metal-free Phthalocyanine Discotic Liquid Crystal

Discotic liquid crystals can self-align to form one-dimensional semiconducting wires, many tens of microns long. In this letter, we describe the preparation of semiconducting films where the stacking direction of the disc-like molecules is perpendicular to the substrate surface. We present measurements of the charge carrier mobility, applying temperature-dependent time-of-flight transient photoconductivity, space-charge limited current measurements, and field-effect mobility measurements. We provide experimental verification of the highly anisotropic nature of semiconducting films of discotic liquid crystals, with charge carrier mobilities of up to 2.8x10$^{-3}$cm$^2$/Vs. These properties make discotics an interesting choice for applications such as organic photovoltaics.Comment: 5 pages, 5 figure

Phase Ordering of 2D XY Systems Below T_{KT}

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure