Related papers: Gravitational Dimensionality Reduction Using Newto…
Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian gradient descent algorithms address these issues but fail…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation…
Recently a new -quantum motivated- theory of gravity has been proposed that modifies the standard Newtonian potential at large distances when spherical symmetry is considered. Accordingly, Newtonian gravity is altered by adding an extra…
In this thesis special emphasis is put on the quantization of the spherically reduced Einstein-massless-Klein-Gordon model using a first order approach for geometric quantities, because phenomenologically it is probably the most relevant of…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
Endowing robots with human-like physical reasoning abilities remains challenging. We argue that existing methods often disregard spatio-temporal relations and by using Graph Neural Networks (GNNs) that incorporate a relational inductive…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
For Einstein's General Relativity (GR) or the alternatives suggested up to date the vacuum energy gravitates. We present a model where a new measure is introduced for integration of the total action in the D-dimensional space-time. This…
The calculation of the underground density field from measured gravity data has been done by a variety of methods of varied types. The use of the vector gravity components is here addressed in order to develop one accurate gravity inversion…
Due to advancements in digital cameras, it is easy to gather multiple images (or videos) from an object under different conditions. Therefore, image-set classification has attracted more attention, and different solutions were proposed to…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional…