Related papers: Studying null and time-like geodesics in the class…
Spatial representation learning is essential for GeoAI applications such as urban analytics, enabling the encoding of shapes, locations, and spatial relationships (topological and distance-based) of geo-entities like points, polylines, and…
It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics. We extend such a result to a…
Time is an important feature in many applications involving events that occur synchronously and/or asynchronously. To effectively consume time information, recent studies have focused on designing new architectures. In this paper, we take…
This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime within the Lambda Cold Dark Matter ({\Lambda}CDM) model. Using the radial free motion solutions,…
A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent…
In temporal ( event-based ) networks, time is a continuous axis, with real-valued time coordinates for each node and edge. Computing a layout for such graphs means embedding the node trajectories and edge surfaces over time in a 2D+t space,…
Spatial and temporal interactions are central and fundamental in many activities in our world. A common problem faced when visualizing this type of data is how to provide an overview that helps users navigate efficiently. Traditional…
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifically, we study geodesic connectedness. We give…
Recent time-contrastive learning approaches manage to learn invariant object representations without supervision. This is achieved by mapping successive views of an object onto close-by internal representations. When considering this…
We apply a recent formalism of quantum geodesics to the well-known bicrossproduct model $\lambda$-Minkowski quantum spacetime $[x^i,t]=\imath\lambda_p x^i$ with its flat quantum metric as a model of quantum gravity effects, with $\lambda_p$…
We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with Lambda<0 and compare with the results for the Levi-Civita metric, when Lambda=0. This is used to derive new stability results about the geodesics' dynamics…
Vision transformers have recently emerged as an effective alternative to convolutional networks for action recognition. However, vision transformers still struggle with geometric variations prevalent in video data. This paper proposes a…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
A class of exact solutions of the geodesic equations in (anti-)de Sitter AdS$_4$ and dS$_4$ spacetimes is presented. The geodesics for test particles in AdS$_4$ and dS$_4$ spacetimes are respectively sinusoidal and hyperbolic sine world…
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
In reality, it is often more efficient to ask for help than to search the entire space to find an object with an unknown location. We present a learning framework that enables an agent to actively ask for help in such embodied visual…
General relativity describes gravitation in terms of the geometry of spacetime. It predicts the existence of gravitational waves (GWs) that stretch and compress spacetime and were detected recently by state-of-the-art interferometer…
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…