Related papers: Analyzing Galaxy Catalogues with Minkowski Functio…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to $F$-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we…
A new technique for calibrating Tully-Fisher like relations by using field galaxies is proposed. Based on a null-correlation approach (NCA), the technique is insensitive to the presence of selection effects on apparent magnitude $m$ and on…
Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still…
The act of projecting data sampled on the surface of the celestial sphere onto a regular grid on the plane can introduce error and a loss of information. This paper evaluates the effects of different planar projections on non-Gaussian…
Magnification bias, an observational effect of gravitational lensing in the weak regime, allows testing the cosmological model through angular correlations of sources at different redshifts. This effect has been observed in various…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
The key probes of the growth of large-scale structure are its rate $f$ and amplitude $\sigma_8$. Redshift space distortions in the galaxy power spectrum allow us to measure only the combination $f\sigma_8$, which can be used to constrain…
Galaxy surveys provide finite catalogs of objects observed within bounded volumes, yet clustering statistics are often interpreted using theoretical frameworks developed for infinite point processes. In this work, we formulate key…
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, and provide useful formulas in application of the perturbation theory to various statistics. This formalism is an extensive generalization…
Mixed volumes, which are the polarization of volume with respect to the Minkowski addition, are fundamental objects in convexity. In this note we announce the construction of mixed integrals, which are functional analogs of mixed volumes.…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional…
Secondary particles produced in spallation reactions of cosmic rays with the interstellar gas provide valuable information that allow us to investigate the injection and transport of charged particles in the Galaxy. A good understanding of…
Galaxy models are fundamental to exploiting surveys of our Galaxy. There is now a significant body of work on axisymmetric models. A model can be defined by giving the DF of each major class of stars and of dark matter. Then the…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
At the turn of the decade we arguably move from the era of precision cosmology to the era of galaxy formation. One approach to this problem will be via the construction of comprehensive galaxy samples. In this review I take the opportunity…
We present a new methodology to generate mock halo or galaxy catalogues, which have accurate clustering properties, nearly indistinguishable from full $N$-body solutions, in terms of the one-point, two-point, and three-point statistics. In…
We investigate the evolution of the galaxy two point correlation function (CF) over a wide redshift range, 0.2 < z < 3. For the first time the systematic analysis covers the redshifts above 1 - 1.5. The catalogue of ~250000 galaxies with i+…