We examine the power spectrum of clusters in the Press-Schechter (PS) theory and in N-body simulations to see how the power spectrum of clusters is related to the power spectrum of matter density fluctuations in the Universe. An analytic model for the power spectrum of clusters for their given number density is presented, both for real space and redshift space. We test this model against result...

The ultimate goal of any visual analytic task is to make sense of the data and gain insights. Unfortunately, the continuously growing scale of the data nowadays challenges the traditional data analytics in the ”big-data” era. Particularly, the human cognitive capabilities are constant whereas the data scale is not. Furthermore, most existing work focus on how to extract interesting information ...

Through analytic techniques veri ed by numerical calculations, we establish general relations between the matter and cosmic microwave background (CMB) power spectra and their dependence on cosmological parameters on small scales. Fluctuations in the cosmic microwave background (CMB), baryons, cold dark matter, and neutrinos receive a boost at horizon crossing. Baryon drag on the photons causes ...

Three decades ago Heath found the integral form of the exact analytic growing mode solution of linear density perturbation δ in subhorizon scales including the cosmological constant or the curvature term. Interestingly, we are able to obtain the analytic solution for general dark energy models with the constant equation of state ωde. We compare the correct analytic growing mode solution δ with ...

The N =8 , 1D analytic bi-harmonic superspace is shown to provide a natural setting for N =8 supersymmetric mechanics associated with the off-shell multiplet (4, 8, 4). The latter is described by an analytic superfield q 1,1 , and we construct the general superfield and component actions for any number of such multiplets. The set of transformations preserving the flat superspace constraints on ...

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdös and Rényi (ER), evolving networks introduced by Barabási and Albert as well as random networks with asymptotic scale-free connectivity distributions characterized by an arbitrary scaling exponent α > 2. Our resul...

Reliability generalization is a meta-analytic approach to study how reliability estimates of a test scores depend on the specific characteristics under which the test is applied and, as a consequence, the risks of inducing score reliability from previous applications of the test. The Hamilton Rating Scale for Depression (HAMD) is one the most popular measurement instruments in clinical psycholo...

One of the questions frequently asked nowadays about model theory is whether it is still logic. The reason for asking the question is mainly that more and more of model theoretic research focuses on concrete mathematical fields, uses extensively their tools and attacks their inner problems. Nevertheless the logical roots in the case of model theoretic geometric stability theory are not only cle...

We investigate analytically a large-scale coherence in the orientation of galaxies embedded in two-dimensional sheet-like structures in the frame of the tidal torque theory. Assuming that the galaxy spin and the surrounding matter fields are intrinsically aligned in accordance with the tidal torque model, we first derive analytically the probability distribution of the galaxy position angles, a...

When independent variables are measured with error, ordinary least squares regression can yield parameter estimates that are biased and inconsistent. This paper documents an inflation of Type I error rate that can also occur. In addition to analytic results, a large-scale Monte Carlo study shows unacceptably high Type I error rates under circumstances that could easily be encountered in practic...