Related papers: A geometric approach to non-linear correlations wi…
The Hirschfeld-Gebelein-R\'enyi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal…
Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…
From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of…
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entropic regularization. Its metric tensor is given by the…
N=1, D=4 non linear sigma models, parametrized by chiral superfields, usually describe Kaehlerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kaehler when local supersymmetry becomes…
We analyze the properties of foliations in presence of non-metricity, deriving the generalized Gauss-Codazzi relations in full generality. These results are employed to study the teleparallel framework of non-metric geometry, obtaining…
We present a detailed Monte Carlo model of observational errors in observed galaxy scaling relations to recover the intrinsic (cosmic) scatter driven by galaxy formation and evolution processes. We apply our method to the stellar radial…
We work in the framework of an inflationary cold dark matter universe with cosmological constant, in which the cosmological inhomogeneities are considered as gravitational lenses for the CMB photons. This lensing deforms the angular…
A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been…
Taking the Noether gauge symmetry approach into account, we find spherically symmetric static black hole solutions of the non-minimal gauge-gravity Lagrangian of the $\mathcal{R}^\beta F^2$ model. At first, we consider a system of…
We assess evolution in the black hole mass - stellar velocity dispersion relationship (M-sigma relationship) for quasars in the Sloan Digital Sky Survey Data Release 7 for the redshift range 0.1 < z < 1.2. We estimate the black hole mass…
We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. De-localization of mass and charge is due to the presence of…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…
We present results from a kinematical study of the gas in the nucleus of a sample of three LINER galaxies, obtained from archival HST/STIS long-slit spectra. We found that, while for the elliptical galaxy NGC 5077, the observed velocity…
This thesis considers one and two dimensional supersymmetric nonlinear sigma models. First there is a discussion of the geometries of one and two dimensional sigma models, with rigid supersymmetry. For the one-dimensional case, the…
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For…
Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a sampling algorithm that seeks to adapt proposals to the local geometry of the posterior distribution. The specific form of the Hamiltonian used in RMHMC necessitates {\it…
Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…
We have studied, in a series of papers, the properties of the $M_{\bullet}$ versus $M_{G}\sigma^2$ relation and we have found that it is useful to describe the evolution of galaxies in the same way as the HR diagram does for stars and to…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…