The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.
problem Determining if a spacetime is conformally AdS based on null geodesic travel times.
method Analyzing all null geodesics from a point to its antipodal point, considering various spacetime conditions.
result The spacetime is conformally AdS if and only if all null geodesics from a point refocus at its antipodal point.
Same travelling times imply identical obstacles in Riemannian manifolds.
problem Determining if two sets of obstacles are identical based on travel times.
method Analyzing curvature conditions and geodesic intersections.
result Disjoint convex obstacles with identical travel times are identical.
Paper addresses travel time tomography stability and statistical inversion.
problem Determining conformal factors of metrics from geodesic lengths.
method Established forward and inverse stability estimates; applied to Bayesian statistical inversion.
result Consistency of statistical inversion technique for travel time tomography.
Billiard trajectories in curved spaces have predictable travel times.
problem Understanding travel times in billiard trajectories on curved surfaces.
method Analyzing geodesic flows and sectional curvature to prove time-preserving conjugacy.
result Billiard trajectories with almost identical obstacles have identical shapes.
Method recovers obstacles from travel times on curved surfaces.
problem Recovering obstacles from travel times on curved surfaces.
method Extending Noakes and Stoyanov's method to Riemannian surfaces with curvature constraints.
result Obstacles can be recovered from travel times on Riemannian surfaces under certain curvature conditions.
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two obstacles satisfy some generic regularity conditions and have (almost) the same trave…
An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and space-like geodesics and invariant 1-form on the space of null geodesics. We prove a…
Groups with specific curvature have a regular language of geodesics.
problem Understanding the language of geodesics in non-positively curved triangle groups.
method Proving finitely many cone types and regularity of geodesic languages.
result The language of lexicographically first geodesics is regular and satisfies the fellow traveller property.
Penrose limit results for specific 3-surfaces in space-time.
problem Understanding Penrose limits for specific geometric configurations.
method Analyzing Penrose limits along null geodesics in umbilic 3-surfaces.
result Penrose limit of a specific 3-surface results in a diagonalisable plane-wave.
Study null geodesics on specific spacetimes, finding contact manifolds and Engel geometry applications.
problem Computing the space of null geodesics for a family of spacetimes.
method Computed the contact manifold of null geodesics for a specific family of spacetimes using Engel geometry.
result Characterized the contact manifolds of null geodesics and retrieved the spacetime.
We clarify the relationship between the null geodesic completeness of an Einstein Lorentz manifold and its conformal Kobayashi pseudodistance. We show that an Einstein manifold has at least one incomplete null geodesic if its pseudodistancfe is nontrivial. If its pseudodistance is nondegenerate, all of its null geodesi…
Researchers compute contact structures for null geodesics on specific spacetimes.
problem Understanding the canonical contact structure of null geodesics in spacetimes.
method Explicit calculations for specific spacetimes, including lens spaces and three-dimensional spacetimes.
result Contact structures on null geodesics are derived from the Lorentz prolongation of spacetimes.
The paper explores traveling along broken geodesics in Finsler submersions.
problem Analyzing the attainable sets of analytic vector fields in Finsler submersions.
method Investigates the dual leaves and attainable sets of horizontal broken geodesics.
result Proves that in compact Finsler manifolds with positive flag curvature, the attainable sets coincide with orbits.
We survey the correct definition of a generalized Dirac operator on a Space--Time and the classical result about propagation of singularities. This says that light travels along light--like geodesics. Finally we show this is also true for generalized Dirac operators.
Study on geodesics in Kropina metrics with applications.
problem Existence of connecting and closed geodesics in Kropina metrics.
method Analytical proofs and applications to null geodesics and navigation problems.
result Proves existence of geodesics in Kropina metrics.
Null geodesics in Kerr spacetimes cannot be closed or bounded.
problem Existence of closed null geodesics in Kerr spacetimes.
method Analytical proof of non-existence of closed null geodesics in Kerr spacetimes.
result Null geodesics in Kerr spacetimes cannot be closed or contained in a compact subset.
Injectivity of geodesic ray transform on specific Finsler manifolds proven.
problem Injectivity of geodesic ray transform on spherically symmetric reversible Finsler manifolds.
method Reduction to invertibility of generalized Abel transforms using angular Fourier series and Taylor expansions of geodesics.
result Injectivity of geodesic ray transform proven on specified Finsler manifolds.
We study geodesics on the modular surface, comparing WP and hyperbolic metrics.
problem Comparing geodesics on the modular surface under different metrics.
method Lift WP geodesics to the universal cover, analyze geometric properties, and compare deviations.
result WP and hyperbolic geodesics fellow-travel in the thick part of the universal cover.
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of …
Let M1n+1 be a light-like geodesically complete Lorentzian (n+1)-manifold satisfying the null energy condition. We show that null hypersurfaces properly immersed in M1n+1 are totally geodesic.
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…
Study shows contact structure on null geodesic space for specific spacetimes.
problem Understanding contact structures on null geodesic spaces of spacetimes.
method Contactomorphism and embedding techniques in spherical cotangent bundles.
result Space of null geodesics contactomorphic to canonical structure in spherical cotangent bundle.
Study null hypersurfaces in Lorentzian manifolds, proving Riemannian flow structure.
problem Properties of Lorentzian manifolds influenced by totally geodesic null hypersurfaces.
method Coupling rigging technique with null foliation existence to prove Riemann flow structure.
result Proves curvature conditions restrict causal structure of spacetime.
Kerr spacetimes without closed null geodesics for non-zero rotation.
problem Analyzing closed geodesics in Kerr spacetimes.
method Analytic extension and geodesic analysis.
result Kerr spacetimes do not admit closed null geodesics for any non-zero rotation parameter.
Study on null submanifolds in indefinite complex contact geometry.
problem Geometry of null submanifolds in indefinite complex contact manifolds.
method Analysis of quaternion null submanifolds and distributions on screen submanifolds.
result Quaternion null submanifolds are always totally geodesic.
Bayesian framework predicts post-disruption travel times in metro networks.
problem Uncertainty in post-disruption travel times in metro networks.
method Bayesian spatiotemporal modeling framework capturing train interactions and non-Gaussian distributional characteristics.
result The proposed models consistently outperform baseline specifications in point prediction and uncertainty quantification.
New findings on how conformal rescalings affect spacetime metrics.
problem Understanding how conformal rescalings impact spacetime metrics.
method Analyzing the null curvature condition and causal structure.
result Proving constraints on conformal rescalings in vacuum and non-vacuum spacetimes.
In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group. We prove that all of the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group are helices. Moreover, we obtain explicit parametric equations for non-geodesic non-null biharmon…
Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is stated which implies uniqueness and stability for this problem. If the conformal c…
Method estimates travel times on urban roads using Uber data.
problem Estimating travel times on urban roads where data is scarce.
method Graph representation, trip sampling, least-squares optimization.
result Estimates travel times on arterial roads using aggregated Uber data.
New proofs confirm travel time data determine simple metrics on a disc.
problem Determining a simple Riemannian metric from travel time data.
method Proofs based on Myers-Steenrod theorem, Lipschitz-type stability estimate.
result Travel time data determine a simple Riemannian metric on a disc up to natural gauge.
Financial derivatives based on road travel times for hedging and pricing.
problem Market risk in crypto and banking sectors.
method Modeling travel time data with CARMA models and applying risk-neutral pricing.
result Derivatives pricing based on travel time and its volatility.
Study uses neural networks to predict travel times for public transportation.
problem Inaccurate travel time predictions due to road traffic irregularities.
method Developed two neural network models (MLP and LSTM) using OD travel time matrix.
result Both models can make near-accurate predictions, but LSTM is more susceptible to noise.
Recover simple irreversible Finsler geometry from travel time data
problem Stable recovery of a simple irreversible Finsler geometry
method Use a Gromov-Hausdorff distance adapted to irreversible metric spaces
result Unique and Lipschitz-stable recovery
In building intelligent transportation systems such as taxi or rideshare services, accurate prediction of travel time and distance is crucial for customer experience and resource management. Using the NYC taxi dataset, which contains taxi trips data collected from GPS-enabled taxis [23], this paper investigates the use…
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 geometric-topological proofs of geodesic connectedness for classes of space-times to which kno…
STAD improves travel time estimation by learning from real traffic data.
problem Travel time estimation using GPS traces is inaccurate and requires offline optimization.
method STAD uses machine learning and real-time trip data to adjust travel time estimates.
result STAD reduces median absolute errors by 14% in Doha and New York City, and 29% in Porto.
The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant Λ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the pr…
The authors study a generalized notion of null geodesic defined by the Legendrian dynamics of a regular conical subbundle of the tangent bundle on a manifold. A natural extension of the Weyl tensor is shown to exist, and to depend only on this conical subbundle. Given a suitable defining function of the conical bundle,…
The study examines conditions that prevent null geodesic lines in spacetimes, impacting cosmological geometry.
problem Preventing the existence of null geodesic lines in spacetimes.
method Identifying geometric conditions on foliations of spacetimes that prevent null geodesic lines, especially for spacetimes with compact Cauchy hypersurfaces.
result Conditions on foliations can prevent null geodesic lines, leading to restrictions on cosmological spacetime geometry.
Study shows stability of travel time data reconstruction from closed subsets.
problem Reconstruction of length spaces from travel time data on a closed subset.
method Lipschitz stability proof for certain types of length spaces.
result Reconstruction of length spaces is Lipschitz stable from travel time data on a closed subset.
Boosting algorithms improve delivery time prediction in postal services.
problem Challenges in long-term travel time prediction for postal services.
method Investigated linear regression models, tree-based ensembles (random forest, bagging, boosting), and compared their performance.
result Boosting algorithms, especially light gradient boosting and catboost, outperform other methods in accuracy and runtime efficiency.
Over the last few years, traffic data has been exploding and the transportation discipline has entered the era of big data. It brings out new opportunities for doing data-driven analysis, but it also challenges traditional analytic methods. This paper proposes a new Divide and Combine based approach to do K means clust…
Model predicts travel time under rare conditions using a vector-space model.
problem Predicting travel time under rare temporal conditions (e.g., holidays, school vacations) is challenging due to limited historical data and other temporal changes.
method Presented a vector-space model for encoding rare temporal conditions, allowing coherent representation learning across different conditions.
result Increased performance for travel time prediction over different baselines when using the vector-space encoding for representing the temporal setting.
In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
problem Proving the nonexistence of closed timelike geodesics in Kerr spacetimes.
method Analyzing the Kerr-star spacetime, excluding closed null geodesics and proving the nonexistence of closed timelike geodesics.
result No closed timelike geodesics in Kerr spacetimes.
Two novel models predict bus travel times with uncertainty, improving connection assurance.
problem Improving bus connection assurance by handling travel time uncertainty.
method Two novel approaches: Deep Quantile Regression (DQR) and Bayesian Recurrent Neural Networks (BRNN).
result DQR model performs best for 80%, 90%, and 95% prediction intervals, with small underestimation.