Related papers: A geometric approach to non-linear correlations wi…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
We review briefly direct and indirect methods of measuring the masses of black holes in galactic nuclei, and then focus attention on supermassive black holes in active nuclei, with special attention to results from reverberation mapping and…
The realization of fundamental relations between supermassive black holes and their host galaxies would have profound implications in astrophysics. To add further context to studies of their co-evolution, an investigation is carried out to…
Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is an ubiquitous task in all of physics. In this work we present a covariant generalization…
We study the biasing relation between dark-matter halos or galaxies and the underlying mass distribution, using cosmological $N$-body simulations in which galaxies are modelled via semi-analytic recipes. The nonlinear, stochastic biasing is…
The effect of the correlations in the diluteness pattern in the systems with non-integral dimensionality, on $\nu=\frac{4}{5}$ superdiffusion process is considered in this paper. These spatial correlations have proved to be very effective…
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size,…
Many of the tools available for robot learning were designed for Euclidean data. However, many applications in robotics involve manifold-valued data. A common example is orientation; this can be represented as a 3-by-3 rotation matrix or a…
We find large classes of non-asymptotically flat Einstein-Yang-Mills-Dilaton (EYMD) and Einstein-Yang-Mills-Born-Infeld-Dilaton (EYMBID) black holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass.…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation…
Accurate analyses of present and next-generation galaxy surveys require new ways to handle effects of non-linear gravitational structure formation in data. To address these needs we present an extension of our previously developed algorithm…
We analyse the scatter in the correlation between super-massive black hole (SMBH) mass and bulge stellar mass of the host galaxy, and infer that it cannot be accounted for by mergers alone. The merger-only scenario, where small galaxies…
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative $D$-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the…
A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression…
We present a review on Lagrangian models admitting spherically symmetric regular black holes, and cosmological bounce solutions. Non-linear electrodynamics, non-polynomial gravity, and fluid approaches are explained in details. They consist…