Related papers: Embedding diagrams in stationary spacetimes
Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for…
We introduce $(k,l)$-regular maps, which generalize two previously studied classes of maps: affinely $k$-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean…
We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the…
In this paper we construct some invariants of spatial graphs by disk-summing the constituent knots and show the delta edge-homotopy invariance of them. As an application, we show that there exist infinitely many slice spatial embeddings of…
We consider dynamical spherically symmetric spacetimes, which are conformal to the static spherically symmetric metrics, and find new solutions of Einstein equations by symmetry considerations. Our study help us classify various conformal…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where $\tau$ could be a time point or time interval. Temporal knowledge graphs may exhibit…
We develop a comprehensive geometric framework for defining spaces $\mathcal{G}(M,E)$ of nonlinear generalized sections of vector bundles $E \to M$ containing spaces of distributional sections $\mathcal{D}'(M, E)$. Our theory incorporates…
The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. This is done including both Poynting-Robertson effect and stellar wind. The solutions are stationary in semimajor…
Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…
Stationary compact astrophysical objects such as black holes and neutron stars behave as classical systems from the gravitational point of view. Their (observable) curvature is everywhere "small". Here we investigate whether mergers of such…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
Local estimates of the maximal curvatures of admissible spacelike hypersurfaces in de Sitter space for k-symmetric curvature functions are obtained. They depend on interior and boundary data.
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $\gamma:V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
The purpose of the present paper is to extend the Variable Rest Mass (VRM) Interpretation and the telemetric system of measurment to the case of stationary but non-static spacetimes, especially the Kerr solution.