Quantitative Comparison of Sinc-Approximating Kernels for Medical Image Interpolation

Abstract. Interpolation is required in many medical image processing operations. From sampling theory, it follows that the ideal interpolation kernel is the sinc function, which is of infinite extent. In the attempt to obtain practical and computationally efficient image processing al-gorithms, many sinc-approximating interpolation kernels have been de-vised. In this paper we present the results of a quantitative comparison of 84 different sinc-approximating kernels, with spatial extents ranging from 2 to 10 grid points in each dimension. The evaluation involves the application of geometrical transformations to medical images from dif-ferent modalities (CT, MR, and PET), using the different kernels. The results show very clearly that, of all kernels with a spatial extent of 2 grid points, the linear interpolation kernel performs best. Of all kernels with an extent of 4 grid points, the cubic convolution kernel is the best (28 %- 75 % reduction of the errors as compared to linear interpolation). Even better results (44 %- 95 % reduction) are obtained with kernels of larger extent, notably the Welch, Cosine, Lanczos, and Kaiser windowed sinc kernels. In general, the truncated sinc kernel is one of the worst performing kernels.

Star formation and environmental quenching of GEEC2 group galaxies at z ∼ 1

We present new analysis from the Group Environment Evolution Collaboration 2 (GEEC2) spectroscopic survey of galaxy groups at 0.8 < z < 1. Our previous work revealed an intermediate population between the star-forming and quiescent sequences and a strong environmental dependence in the fraction of quiescent galaxies. Only ∼5 per cent of star-forming galaxies in both the group and field sample show a significant enhancement in star formation, which suggests that quenching is the primary process in the transition from the star-forming to the quiescent state. To model the environmental quenching scenario, we have tested the use of different exponential quenching time-scales and delays between satellite accretion and the onset of quenching. We find that with no delay, the quenching time-scale needs to be long in order to match the observed quiescent fraction, but then this model produces too many intermediate galaxies. Fixing a delay time of 3 Gyr, as suggested from the local Universe, produces too few quiescent galaxies. The observed fractions are best matched with a model that includes a delay that is proportional to the dynamical time and a rapid quenching time-scale (∼0.25 Gyr), but this model also predicts intermediate galaxies Hδ strength higher than that observed. Using stellar synthesis models, we have tested other scenarios, such as the rejuvenation of star formation in early-type galaxies and a portion of quenched galaxies possessing residual star formation. If environment quenching plays a role in the GEEC2 sample, then our work suggests that only a fraction of intermediate galaxies may be undergoing this transition and that quenching occurs quite rapidly in satellite galaxies (≲0.25 Gyr)

Conformal Hamiltonian Dynamics of General Relativity

The General Relativity formulated with the aid of the spin connection coefficients is considered in the finite space geometry of similarity with the Dirac scalar dilaton. We show that the redshift evolution of the General Relativity describes the vacuum creation of the matter in the empty Universe at the electroweak epoch and the dilaton vacuum energy plays a role of the dark energy.Comment: 9 pages, 1 figure, submitted to PL

Do group dynamics play a role in the evolution of member galaxies?

We examine galaxy groups from the present epoch to z ∼ 1 to explore the impact of group dynamics on galaxy evolution. We use group catalogues from the Sloan Digital Sky Survey (SDSS), the Group Environment and Evolution Collaboration (GEEC) and the high-redshift GEEC2 samples to study how the observed member properties depend on the galaxy stellar mass, group dynamical mass and dynamical state of the host group. We find a strong correlation between the fraction of non-star-forming (quiescent) galaxies and galaxy stellar mass, but do not detect a significant difference in the quiescent fraction with group dynamical mass, within our sample halo mass range of ∼1013–1014.5 M⊙, or with dynamical state. However, at z ∼ 0.4 we do find some evidence that the quiescent fraction in low-mass galaxies [log10(Mstar/M⊙) ≲ 10.5] is lower in groups with substructure. Additionally, our results show that the fraction of groups with non-Gaussian velocity distributions increases with redshift to z ∼ 0.4, while the amount of detected substructure remains constant to z ∼ 1. Based on these results, we conclude that for massive galaxies [log10(Mstar/M⊙) ≳ 10.5], evolution is most strongly correlated to the stellar mass of a galaxy with little or no additional effect related to either the group dynamical mass or the dynamical state. For low-mass galaxies, we do find some evidence of a correlation between the quiescent fraction and the amount of detected substructure, highlighting the need to probe further down the stellar mass function to elucidate the role of environment in galaxy evolution

Harmonic maps from degenerating Riemann surfaces

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles of sequences of such maps.Comment: 27 page

Probing the Environment with Galaxy Dynamics

I present various projects to study the halo dynamics of elliptical galaxies. This allows one to study the outer mass and orbital distributions of ellipticals in different environments, and the inner distributions of groups and clusters themselves.Comment: 5 pages, 2 figs, to appear in Proc. ESO Workshop, Groups of Galaxies in the Nearby Universe (5-9 Dec 2005), eds. I. Saviane, V. Ivanov & J. Borissova (Springer-Verlag

Relativistic description of electron scattering on the deuteron

Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed. This is applied to both elastic and inelastic electron scattering. As dynamical model the relativistic one boson exchange model is used. Reasonable agreement is found with a previous relativistic calculation of the elastic electromagnetic form factors of the deuteron. For the unpolarized inelastic electron scattering effects of final state interactions and relativistic corrections to the structure functions are considered in the impulse approximation. Two specific kinematic situations are studied as examples.Comment: (19 pages in revtex + 15 figures not included, available upon request.) report THU-93-10

Molecular dynamics simulation of the order-disorder phase transition in solid NaNO2_2

We present molecular dynamics simulations of solid NaNO$_2$ using pair potentials with the rigid-ion model. The crystal potential surface is calculated by using an \emph{a priori} method which integrates the \emph{ab initio} calculations with the Gordon-Kim electron gas theory. This approach is carefully examined by using different population analysis methods and comparing the intermolecular interactions resulting from this approach with those from the \emph{ab initio} Hartree-Fock calculations. Our numerics shows that the ferroelectric-paraelectric phase transition in solid NaNO$_2$ is triggered by rotation of the nitrite ions around the crystallographical c axis, in agreement with recent X-ray experiments [Gohda \textit{et al.}, Phys. Rev. B \textbf{63}, 14101 (2000)]. The crystal-field effects on the nitrite ion are also addressed. Remarkable internal charge-transfer effect is found.Comment: RevTeX 4.0, 11 figure

Changes in white matter microstructure and MRI-derived cerebral blood flow after one-week of exercise training

Exercise is beneficial for brain health, inducing neuroplasticity and vascular plasticity in the hippocampus, which is possibly mediated by brain-derived neurotrophic factor (BDNF) levels. Here we investigated the short-term effects of exercise, to determine if a 1-week intervention is sufficient to induce brain changes. Fifteen healthy young males completed five supervised exercise training sessions over seven days. This was preceded and followed by a multi-modal magnetic resonance imaging (MRI) scan (diffusion-weighted MRI, perfusion-weighted MRI, dual-calibrated functional MRI) acquired 1 week apart, and blood sampling for BDNF. A diffusion tractography analysis showed, after exercise, a significant reduction relative to baseline in restricted fraction—an axon-specific metric—in the corpus callosum, uncinate fasciculus, and parahippocampal cingulum. A voxel-based approach found an increase in fractional anisotropy and reduction in radial diffusivity symmetrically, in voxels predominantly localised in the corpus callosum. A selective increase in hippocampal blood flow was found following exercise, with no change in vascular reactivity. BDNF levels were not altered. Thus, we demonstrate that 1 week of exercise is sufficient to induce microstructural and vascular brain changes on a group level, independent of BDNF, providing new insight into the temporal dynamics of plasticity, necessary to exploit the therapeutic potential of exercise

Black hole solutions in F(R) gravity with conformal anomaly

In this paper, we consider $F(R)=R+f(R)$ theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of $F(R)$ models. Calculation of Kretschmann scalar shows that there is a singularity located at $r=0$, which the geometry of uncharged (charged) solution is corresponding to the Schwarzschild (Reissner-Nordstr\"om) singularity. Further, we discuss the viability of our models in details. We show that these models can be stable depending on their parameters and in different epoches of the universe.Comment: 12 pages, one figur