We show that the location and velocity of the harmonic oscillator with Lévy-stable noise are mutually Lévy-stable distributed. We give explicitly the associated spectral measure, exhibiting both the non independence and the non ellipticity of the location-velocity couple. We then propose measures of deviation from ellipticity.

We investigate the dependence of ellipticities of clusters of galaxies on cos-mological parameters using large-scale cosmological simulations. We determine cluster ellipticities out to redshift unity for LCDM models with different mean densities Ω m and amplitudes of mass fluctuation σ 8,0. The mean ellipticity increases monotonically with redshift for all models. Larger values of σ 8,0 , i.e.,...

Measuring ellipticity is an important area of computer vision systems. Most existing ellipticity measures are area based and cannot be easily applied to point sets such as extracted edges from real world images. We are interested in ellipse fitting and ellipticity measures which rely exclusively on shape boundary points which are practical in computer vision. They should also be calculated very...

We study transverse electron momentum distribution in strong field atomic ionization driven by laser pulses with varying ellipticity. We show, both experimentally and theoretically, that the transverse electron momentum distribution in the tunneling and over the barrier ionization regimes evolves in a qualitatively different way when the ellipticity parameter describing polarization state of th...

We use a large set of state-of-the-art cosmological N-body simulations [512 particles] to study the intrinsic ellipticity correlation functions of halos. With the simulations of different resolutions, we find that the ellipticity correlations converge once the halos have more than 160 members. For halos with fewer members, the correlations are underestimated, and the underestimation amounts to ...

We formulate deformation of relativistic stars due to the magnetic stress, considering the magnetic fields to be perturbations from spherical stars. The ellipticity for the dipole magnetic field is calculated for some stellar models. We have found that the ellipticity becomes large with increase of a relativistic factor for the models with the same energy ratio of the magnetic energy to the gra...

Weak lensing by large scale structure induces correlated ellipticities in the images of distant galaxies. The two-point correlation is determined by the matter power spectrum along the line of sight. We use the fully nonlinear evolution of the power spectrum to compute the predicted ellipticity correlation. We present results for different measures of the second moment for angular scales θ ≃ 1 ...

The precession and obliquity frequencies of the Earth’s rotational motion are functions of the dynamic ellipticity of the Earth’s gravitational figure, and this connection has provided a novel bridge between studies of palaeoclimate and geodynamics. In particular, analyses of tuned climate proxy records have yielded bounds on the mean relative perturbation in dynamic ellipticity over both the l...

PURPOSE To confirm AAPM Reports 204/220 and provide data for the future expansion of these reports by: (a) presenting the first large-scale confirmation of the reports using clinical data, (b) providing the community with size surrogate data for the head region which was not provided in the original reports, and additionally providing the measurements of patient ellipticity ratio for different ...