Related papers: Embedding diagrams in stationary spacetimes
The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms…
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds…
A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to…
We study fixed points of isometries of the higher-dimensional Kerr-NUT-(A)dS spacetimes that form generalizations of symmetry axes. It turns out that, in the presence of nonzero NUT charges, some parts of the symmetry axes are necessarily…
Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that…
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we…
Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of…