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Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…
An analytic approximation to the mass function for gravitationally bound objects is presented. We base on the Zel'dovich approximation to extend the Press-Schechter formalism to a nonspherical dynamical model. A simple extrapolation of that…
We explore the possibility of putting constraints on dark energy models with statistical property of large scale structure in the non-linear region. In particular, we investigate the $w$ dependence of non-Gaussianity of the smoothed density…
In nearby clusters early-type galaxies follow isotropic orbits, while the orbits of late-type galaxies are characterized by slightly radial anisotropy. Little is known about the orbits of the different populations of cluster galaxies at…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The Fundamental Plane relates the structural properties of early-type galaxies such as its surface brightness and effective radius with its dynamics. The study of its evolution has therefore important implications for models of galaxy…
We combine HST/ACS imaging from the GEMS survey with redshifts and rest-frame quantities from COMBO-17 to study the evolution of morphologically early-type galaxies with red colors since z=1. We use a new large sample of 728 galaxies with…
We measure the morphology-density relation of galaxies at z=1 across the full three orders of magnitude in projected galaxy density available in low-redshift studies. Our study adopts techniques that are comparable with those applied at…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
We determine the evolution of the co-moving density of the most massive ($M_* \geq 10^{12} M_\odot$) early-type galaxy population in the redshift range of $z = 0.15$ - 0.45 in different stellar mass ranges using data from the Sloan Digital…
We estimate the galaxy stellar mass function and stellar mass density for star-forming and quiescent galaxies with 0.2<z<4. We construct a deep K<24 sample of 220000 galaxies selected using the UltraVISTA DR1 data release. Our analysis is…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
In this work we derive the evolution equation for the density contrast considering open system cosmology, where the influence of adiabatic particle production process on the dynamic of a homogeneous and isotropic is investigated within a…
The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for…
The main statistical properties of the Sunyaev-Zeldovich (S-Z) effect - the power spectrum, cluster number counts, and angular correlation function - are calculated and compared within the framework of two density fields which differ in…
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are…
We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and…
We study the peculiar motion of non-relativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…