Related papers: Deriving accurate peculiar velocities (even at hig…
We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in…
We study the problem of computing the upper bound of the discrete Fr\'{e}chet distance for imprecise input, and prove that the problem is NP-hard. This solves an open problem posed in 2010 by Ahn \emph{et al}. If shortcuts are allowed, we…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents $p\in (1,\infty)$. Combining the derived error…
The distributions of peculiar velocities of rich clusters and of groups of galaxies are investigated for different cosmological models and are compared with observations. Four cosmological models are studied: standard ($\Omega=1$) CDM,…
We derive the conditional probability distribution of the peculiar velocity around a peak of given overdensity in a Gaussian density field. This distribution characterizes the shear field around local, isolated density peaks. We use the…
The luminosity functions of galaxies and quasars provide invaluable information about galaxy and quasar formation. Estimating the luminosity function from magnitude limited samples is relatively straightforward, provided that the distances…
We study the shortcut Fr\'{e}chet distance, a natural variant of the Fr\'{e}chet distance, that allows us to take shortcuts from and to any point along one of the curves. The classic Fr\'echet distance is a bottle-neck distance measure and…
In this paper, we develop the method of analyzing the velocity field of cosmic matter with a multiresolution decomposition. This is necessary in calculating the redshift distortion of power spectrum in the discrete wavelet transform (DWT)…
The Varying Speed of Light (VSL) model describes how the speed of light in a vacuum changes with cosmological redshift. Despite numerous models, there is little observational evidence for this variation. While the speed of light can be…
We use simulations to demonstrate that photometric redshift "errors" can be greatly reduced by using the photometric redshift probability distribution p(z) rather than a one-point estimate such as the most likely redshift. In principle this…
In this paper we propose to bridge the gap between using extremely low resolution 1-bit measurements and estimating targets' parameters, such as their velocities, that exist in a continuum, i.e., by performing Off-the-Grid estimation. To…
The results from the Supernova Cosmology Project indicate a relation between cosmic distance and redshift that corresponds to an accelerating Universe, and, as a consequence, the presence of an energy component with negative pressure. This…
The recent re-evaulation of the peculiar velocity field outside the Local Supercluster (Dekel et al. 1999, ApJ 522) has permitted a re-examination of the origins of the peculiar velocity field within the Local Supercluster using the Mark…
We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically…
Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon "small"…
The existence of critical points for the peculiar velocity field is a natural feature of the correlated vector field. These points appear at the junctions of velocity domains with different orientations of their averaged velocity vectors.…
We present the peculiar in-plane velocities derived from the LAMOST red clump stars. From the variations of the in-plane velocity with the Galactocentric radius for the young and old red clump stars, we are able to identify two types of…
We present a detailed discussion of the redshift errors associated to the ESO Slice Project measurements. For a subsample of 742 galaxies with redshifts determined both from the absorption lines (V_{abs}) and from the emission lines…
We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator. The method is characterized by its robustness. In…