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Einstein field equations are notoriously challenging to solve due to their complex mathematical form, with few analytical solutions available in the absence of highly symmetric systems or ideal matter distribution. However, accurate…
Gravitational field modelling is an important tool for inferring past and present dynamic processes of the Earth. Functions on the sphere such as the gravitational potential are usually expanded in terms of either spherical harmonics or…
With a large number of software tools dedicated to the visualisation and/or demonstration of properties of geometric constructions and also with the emerging of repositories of geometric constructions, there is a strong need of linking…
A multi-TeraFlop/TeraByte machine will enable the application of the Einstein theory of gravity to realistic astrophysical processes. Without the computational power, the complexity of the Einstein theory restricts most studies based on it…
The simplest flavor of the Effective Field Theory of Large Scale Structure is based on Newtonian equations and describes the nonlinear matter density and velocity using Einstein-de-Sitter kernels. Even in the presence of massive neutrinos,…
By viewing Einstein's field equations -- reduced to two dimensions -- as an integrable system, one can simultaneously obtain exact solutions to both the equations themselves and their associated Lax pair via a canonical Wiener-Hopf…
In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed.…
Although researchers have devoted considerable attention to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables. To help users construct join queries for exploring…
We present time-dependent analytic solutions to the Einstein equations coupled with a dilaton (scalar) field. The background geometry for the solutions is a product of an N-dimensional spherically symmetric space and a d-dimensional flat…
We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii)…
Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
It is now possible to directly access, via the Internet, a bibliographical database on Gravitational Lensing (GL) literature. The Interactive Gravitational Lensing Bibliography (IGLB) totalizes more than 2400 titles of published articles in…
Genetic interactions and protein co-dependencies shape cellular fitness, buffering capacity, and disease vulnerability. However, systematic integration of co-dependency relationships across heterogeneous datasets remains limited. Here, we…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
Generative Retrieval (GR) has emerged as a promising paradigm to unify indexing and search within a single probabilistic framework. However, existing approaches suffer from two intrinsic conflicts: (1) an Optimization Blockage, where the…
Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the…
Astrophysical black holes arise as exact solutions of the Einstein field equations. Therefore, any alternative, such as a gravastar, must satisfy the same level of mathematical rigor and internal consistency. A physically viable gravastar…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…