Related papers: Allometric Exponent and Randomness
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ which (to first order) describes stars, protostellar…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…
Cosmological models in which dark matter consists of cold elementary particles predict that the dark halo population should extend to masses many orders of magnitude below those at which galaxies can form. Here we report a cosmological…
In light of the classic impossibility results of Arrow and Gibbard and Satterthwaite regarding voting with ordinal rules, there has been recent interest in characterizing how well common voting rules approximate the social optimum. In order…
We present a non-parametric, empirically based, model for associating galaxy luminosities with halo/subhalo masses, based on a self-consistent treatment of subhalo mass loss and the subhalo mass function. We find that, at high mass, the…
Dark-matter halos show a universal density profile with a scaling such that less massive systems are typically denser. This mass-density relation is well described by a proportionality between the characteristic density of halos and the…
The paper concerns the rates of power-law growth of mutual information computed for a stationary measure or for a universal code. The rates are called Hilberg exponents and four such quantities are defined for each measure and each code:…
The system of stability equations for galactic halos is under-determined in most of the models of dark matter (DM). Conventionally, the issue is resolved by taking the temperature as a constant, and the chemical potential and the mass…
This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $\nu$ associated with such a random walk. We first establish a link of the form $\dim \nu \leq…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…
In the presence of the gravitational field, the energy density of matter no longer coincides with its mass density. A discrepancy exists, of course, also between the associated power spectra. Within the $\Lambda$CDM model, we derive a…
We propose a new method of estimation of the black hole masses in AGN based on the normalized excess variance, sigma_{nxs}^2. We derive a relation between sigma_{nxs}^2, the length of the observation, T, the light curve bin size, Delta t,…
For decades, the determination of the mean density of matter(Omega_M) has been tied to the distribution of light. This has led to a ``bias,'' perhaps as large as a factor of 2, in determining a key cosmological parameter. Recent…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
We introduce the concept of a class of equivalence of molecular clouds represented by an abstract spherically symmetric, isotropic object. This object is described by use of abstract scales in respect to a given mass density distribution.…
We support, with new fitting instruments and the analysis of more recent experimental data, the proposal of a relationship between the mass of a Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the host elliptical…
We determined the basic parameters, such as the central black hole mass ($M$), the boosting factor (or Doppler factor) ($\delta$), the propagation angle ($\Phi$) and the distance along the axis to the site of $\gamma$-ray production ($d$)…
Historically used in settings where the outcome is rare or data collection is expensive, outcome-dependent sampling is relevant to many modern settings where data is readily available for a biased sample of the target population, such as…
We present a new statistical modelling approach where the response is a function of high frequency count data. Our application is about investigating the relationship between the health outcome fat mass and physical activity (PA) measured…