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We use the number density of peaks in the smoothed cosmological density field taken from the 2dF Galaxy Redshift Survey to constrain parameters related to the power spectrum of mass fluctuations, n (the spectral index), dn/d(lnk) (rolling…
We investigate the upscaling of diffusive transport parameters as function of pore scale material structure using a stochastic framework. We focus on sub-REV (representative elementary volume) scale where the complexity of pore space…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Despite the fact that the mean matter density of the universe has been measured to an accuracy of a few percent within the standard $\Lambda$CDM paradigm, its median density is not known even to order of magnitude. Typical points lie in…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in $\Lambda$CDM N-body simulations. This function is universal across void size and redshift, accurately…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with…
The need for accurate photometric redshifts estimation is a topic that has fundamental importance in Astronomy, due to the necessity of efficiently obtaining redshift information without the need of spectroscopic analysis. We propose a…
We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium (MS) and Millennium-II (MS-II) simulations. The DTFE technique is based directly on the particle positions,…
Using COBE-DMR 4-year data, we find a general expression yielding the likelihood distribution in the 3-dimensional parameter space spanned by the spectral index $n$, the spectral amplitude $a_{10}$ and the false-vacuum density parameter…
The Ly$\alpha$ forest transmission probability distribution function (PDF) is an established probe of the intergalactic medium (IGM) astrophysics, especially the temperature-density relationship of the IGM. We measure the transmission PDF…
We present a new statistic-the redshift dispersion-- which may prove useful for comparing next generation redshift surveys (e.g., the Sloan Digital Sky Survey) and cosmological simulations. Our statistic is specifically designed for the…
Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of…
We derive probability density functions for the projected axial ratios of the real and mock 2PIGG galaxy groups, and use this data to investigate the intrinsic three dimensional shape of the dark matter ellipsoids that they trace. As well…
We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…
Frequentist parameter inference using profile likelihoods has received increased attention in the cosmology literature recently since it can give important complementary information to Bayesian credible intervals. Here, we give a…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
We study the non-Gaussian tail of the probability distribution function of density in cosmological N-Body simulations for a variety of initial conditions. We compare the behaviour of the non-Gaussian tail in the real space with that in the…