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The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
We consider the problem of graph estimation in a zero-inflated Gaussian model. In this model, zero-inflation is obtained by double truncation (right and left) of a Gaussian vector. The goal is to recover the latent graph structure of the…
We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive $(q,p)$-inequalities of…
We present several new quadrature formulas in the triangle for exact integration of polynomials. The points were computed numerically with a cardinal function algorithm which imposes that the number of quadrature points $N$ be equal to the…
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string…
The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space-time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the…
In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by…
We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and…
We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$…
The $k$-method is the isogeometric method based on splines (or NURBS, etc.) with maximum regularity. When implemented following the paradigms of classical finite element methods, the computational resources required by the $k-$method are…
A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the…
In this paper we consider the two-dimensional metric $f(R)$-gravity model for the metric tensor depending on two variable: time and one spacelike coordinate. We obtain exact analytical vacuum solutions for different forms of function $ f(R)…
We study numerical integration of functions $f: \mathbb{R}^{s} \to \mathbb{R}$ with respect to a probability measure. By applying the corresponding inverse cumulative distribution function, the problem is transformed into integrating an…
In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a…
Based on the work of Chen and Its [{\em J. Approx. Theory} {\bf 162} ({2010}) {270--297}], we further study orthogonal polynomials with respect to the singularly perturbed Laguerre weight $w(x;t,\alpha) = {x^\alpha}{\mathrm e^{-…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity…
This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error…