Related papers: Estimating the K-function of a point process with …
We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…
We review recent advancements in cosmology with galaxy clusters. Galaxy clusters are the most massive objects in the Universe. Consequently the cluster number density as a function of cluster mass, or cluster abundance, is sensitive to…
We measure the variance in the distribution of off-plane (|b|>20 deg.) galaxies with m_K<13.5 from the 2MASS K-band survey in circles of diameter between 0.344 deg. and 57.2 deg. The use of a near-infrared survey makes negligible the…
Cosmography, as an integral branch of cosmology, strives to characterize the Universe without relying on pre-determined cosmological models. This model-independent approach utilizes Taylor series expansions around the current epoch,…
We give a simple and effective two stage algorithm for approximating a point cloud $\mathcal{S}\subset\mathbb{R}^m$ by a simplicial complex $K$. The first stage is an iterative fitting procedure that generalizes k-means clustering, while…
The mechanism for the relaxation of the cosmological constant is studied and elaborated. In the model used for the analysis of the relaxation mechanism the universe contains two components: a cosmological constant of an arbitrary size and…
We present an experimental study of the compaction dynamics for two-dimensional anisotropic granular systems. Compaction dynamics is measured at three different scales : (i) the macroscopic scale through the packing fraction $\rho$, (ii)…
The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended…
We investigate cosmological constraints on K-mouflage models of modified gravity. We consider two scenarios: one where the background evolution is free to deviate from $\Lambda$CDM (K-mouflage) and another one which reproduces a…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic…
This paper is dedicated to scrutinizing the cosmology in massive gravity. A matter field of the dark sector is coupled to an effective composite metric while a standard matter field couples to the dynamical metric in the usual way. For this…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
In this paper, we discuss improvements of the Suto et al. (2000) model, in the light of recent theoretical developments (new theoretical mass functions, a more accurate mass-temperature relation and an improved bias model) to predict the…
Part segmentation and motion estimation are two fundamental problems for articulated object motion analysis. In this paper, we present a method to solve these two problems jointly from a sequence of observed point clouds of a single…
k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…
We demonstrate the use of spatially encoded magnetic resonance to quantify ensemble dynamics of microscopic particles below the spatial resolution. By evaluating time series of k-space data-points, k-dependent motion patterns can be…
The effects of sampling are investigated on measurements of counts-in-cells in three-dimensional magnitude limited galaxy surveys, with emphasis on moments of the underlying smooth galaxy density field convolved with a spherical window. A…