New maps for large-scale geometry factorize into monotone and light.
problem Large-scale analogues of topological monotone and light maps.
method Introducing coarsely monotone and coarsely light maps, showing factorization system, and proving stability.
result Coarsely monotone maps are stable under pullbacks in the coarse category.
Deep learning and prior maps improve traffic light recognition for autonomous cars.
problem Recognizing traffic lights for autonomous cars in urban environments.
method Combining deep learning-based detection with prior maps for traffic light identification and state recognition.
result The proposed system correctly identified relevant traffic lights along predefined routes.
Maps complex plane polynomials to light-like polygons in Einstein Universe.
problem Mapping between complex plane polynomials and light-like polygons.
method Constructs geometric homeomorphism between moduli spaces.
result Found minimal Lagrangian maps between ideal polygons.
Study of light function singularities on surfaces.
problem Characterizing singularities of the slant function on surfaces.
method Analyzing the differential geometry of the parabolic set and its spherical image under the Gauss map.
result The type of singularities of the slant function is determined by the geometry of the parabolic set and its spherical image.
Proves energy quantization for surfaces with bounded index.
problem Energy quantization for Willmore surfaces with bounded index.
method Translated the question to the conformal Gauss map's perspective and showed convergence in specific regions.
result Conformal Gauss map converges to a light-like geodesic in De Sitter space in neck or collar regions.
Wave equation map reveals manifold's structure.
problem Reconstructing Lorentzian manifold from wave equation map.
method Analyzing Schwartz kernel and boundary light observation set.
result Full Lorentzian structure can be recovered under geometric assumptions.
The paper studies sections of time-like twistor spaces with specific covariant derivatives.
problem Sections of time-like twistor spaces with light-like or zero covariant derivatives.
method Analyzes conformal Gauss maps of time-like minimal surfaces and properties of almost paracomplex structures.
result Sections of time-like twistor spaces have light-like or zero covariant derivatives.
Automatically infers high dynamic range illumination from a single indoor photo.
problem Predicting accurate indoor illumination from a single image.
method End-to-end deep neural network trained in three steps: lighting classifier, scene light localization, and fine-tuning for intensity prediction.
result Significantly outperforms previous methods in recovering high-quality HDR illumination.
New mappings in Minkowski spacetime classified under mild conditions.
problem Characterizing mappings in Minkowski spacetime.
method Analyzing mappings under minimal assumptions.
result Mappings fall into three categories based on specific conditions.
This paper uses deep reinforcement learning to optimize traffic light timing.
problem Inefficient traffic light control leads to long delays and energy waste.
method Deep reinforcement learning model using convolutional neural network and prioritized experience replay.
result The proposed model reduces waiting time compared to existing methods.
A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed light on the relationship between the scattering construction of Graham-Zworski…
A reconstruction theorem in terms of the topology and geometrical structures on the spaces of light rays and skies of a given space-time is discussed. This result can be seen as part of Penrose and Low's programme intending to describe the causal structure of a space-time M in terms of the topological and geometrical…
We show that every inner metric space X is the metric quotient of a complete R-tree via a free isometric action, which we call the covering R-tree of X. The quotient mapping is a weak submetry (hence, open) and light. In the case of compact 1-dimensional geodesic space X, the free isometric action is via a subgroup of …
Ray-Singer torsion measures light degrees of freedom in black hole entropy.
problem Entropy of small black holes with many light particles.
method Computes partition function at genus one using mirror symmetry and Ray-Singer torsion.
result Ray-Singer torsion provides an effective quantum gravity cutoff known as the species scale.
The class of metrizable spaces M with the following approximation property is introduced and investigated: M∈AP(n,0) if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is $\e$-homotopic to g. It is shown that this class has very nice properties. For exam…
Recovering matrix valued potentials from wave equation data on stationary spacetimes.
problem Recovering a time-dependent matrix valued potential from wave equation data.
method Reduction to non-Abelian light ray transform and study of the transform.
result Sufficient conditions for solving the inverse problem on stationary spacetimes.
The abstract applies waist inequality to dynamical systems and entropy.
problem Understanding the relationship between waist inequality and dynamical systems.
method Applying waist inequality to entropy and mean dimension of dynamical systems.
result Maps between dynamical systems have positive conditional metric mean dimension under certain conditions.
We study two inverse problems on a globally hyperbolic Lorentzian manifold (M,g). The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood V⊂M of a time-like geodesic μ. Under natural causality conditions, we reconstruct the conformal type of the unknown open, relativ…
Link framings can only change when a 3-manifold has a non-separating sphere.
problem Understanding how framings of links can change in 3-manifolds.
method Using McCullough's work on mapping class groups and the Dirac trick.
result Link framings can only change in specific 3-manifolds with a non-separating sphere.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
Using open source data, we observe the fascinating dynamics of nighttime light. Following a global economic regime shift, the planetary center of light can be seen moving eastwards at a pace of about 60 km per year. Introducing spatial light Gini coefficients, we find a universal pattern of human settlements across dif…
Study subjective perception of low light restored images and develop an unsupervised QA model.
problem Lack of subjective QA for low light restored images and challenges in collecting human opinion scores.
method Create a dataset, conduct subjective QA study, develop self-supervised contrastive learning technique to extract features.
result Unsupervised NR QA model achieves state-of-the-art performance for low light restored images.
Enhances quantum machine learning models using Fock states.
problem Data-embedding bottleneck in quantum machine learning.
method Photonic-based bosonic data-encoding scheme in Fock space.
result Controlled expressive power via photon number.
The study examines light-like points on constant mean curvature hypersurfaces in Lorentzian manifolds.
problem Characterizing light-like points on constant mean curvature hypersurfaces in Lorentzian manifolds.
method Analyzing the first and second fundamental forms, and the exterior derivative of the determinant function.
result If a light-like point is degenerate, the hypersurface contains a light-like geodesic segment.
Classifies surfaces with zero mean curvature in a light cone.
problem Classifying surfaces with zero mean curvature in a light cone.
method Examined geodesics and screw motions, used Weierstrass representations.
result Complete classification of ruled zero mean curvature surfaces.
Solves surface problem in 3D light cone.
problem Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
method Solves the Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
result Constructs and classifies all rotational zero mean curvature surfaces.
Study light ray transform on Lorentzian manifolds without conjugate points.
problem Recovering spacelike singularities from weighted light ray transforms.
method Fourier Integral Operator analysis and filtered back-projection.
result Recovery of spacelike singularities from weighted light ray transforms without conjugate points.
Reconstructing manifold structure from boundary light observations.
problem Reconstructing Lorentzian manifold structure from boundary light observations.
method Constructive proof using Snell's law for reflections at the boundary.
result Topological, differentiable, and conformal structure of subsets of sources uniquely determined.
Paper extends previous result on hypersurfaces with degenerate light-like points.
problem Characterizing hypersurfaces with degenerate light-like points in Lorentzian manifolds.
method Analyzes C3-differentiable hypersurfaces, extending previous C4-differentiability result. result Same conclusion holds for C3-differentiable hypersurfaces as for C4-differentiable ones. Quantum machine learning models can approximate any continuous function.
problem Theoretical understanding of quantum feature maps in machine learning.
method Proving universal approximation property of quantum machine learning models in quantum-enhanced feature spaces.
result Quantum machine learning models are universal approximators of continuous functions.
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the space of light rays are stressed. Finally, a symplectic geometrical approach to the …
STM maps improve terrain perception for autonomous robots.
problem Perception of terrain for autonomous robots in general environments.
method Stochastic triangular mesh (STM) technique for 2.5-D surface mapping.
result STM maps are more accurate than standard elevation maps.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
problem Analyzing light ray transform in pseudo-Euclidean space.
method Investigate normal operator, derive inversion formula, analyze as Fourier Integral Operator.
result Derive an inversion formula and prove stability estimates.
The paper explores the injectivity of the light ray transform on Lorentzian manifolds.
problem Injectivity of the light ray transform on functions and tensors.
method Analyzes injectivity conditions for scalar and tensor fields on stationary and static Lorentzian manifolds.
result Injectivity of the light ray transform on functions and tensors is proven under specific conditions.
In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of nonlinear geodesic equations. Particularly, we investigate the light-like extremal su…
In this paper we prove several multiplicity results of t-periodic light rays in conformally stationary spacetimes using the Fermat metric and the extensions of the classical theorems of Gromoll-Meyer and Bangert-Hingston to Finsler manifolds. Moreover, we exhibit some stationary spacetimes with a finite number of t…
TensorMap uses tensor decompositions to create accurate topological maps from Lidar data.
problem Creating accurate topological maps from Lidar data in real-time.
method Orthogonal Tucker3 tensor decomposition.
result TensorMap accurately detects the vehicle's position in a graph-based map.
Constructs all real analytic germs of zero mean curvature surfaces in Lorentz-Minkowski 3-space.
problem Analyzing surfaces with light-like points in Lorentz-Minkowski 3-space.
method Applying the Cauchy-Kovalevski theorem for partial differential equations.
result Surfaces with light-like points in Lorentz-Minkowski 3-space contain a light-like line when they do not change causal types.
Automated classification of astronomical light curves for LSST.
problem Handling massive astronomical data from LSST.
method Gradient boosting of decision trees, feature extraction and selection, augmentation.
result Achieved one of the top results in the PLAsTiCC challenge.
Transformer model removes noise from light curves efficiently.
problem Challenges in processing astrophysical light curves due to noise.
method Denoising Time Series Transformer (DTST) model trained with masked objective.
result DTST model excels at removing noise and outliers in time series datasets.
Predict missing and future data points in light curves using scalable Gaussian Processes.
problem Gappy time-series data from commercial cameras confound light curve prediction.
method MuyGPs, a scalable framework for hyperparameter estimation of Gaussian Processes using nearest neighbors sparsification and local cross-validation.
result MuyGPs enable accurate prediction of missing and future data points in light curves.
Accelerates pulsar light curve inference with learned representations and optimization.
problem Computational expense of Markov chain Monte Carlo methods for posterior inference.
method Combining U-Net latent representations with local simulator-guided optimization.
result 120x reduction in inference time (24 hours to 12 minutes) with accuracy preserved.
One pixel can significantly alter deep neural network outputs, revealing propagation patterns and vulnerability hotspots.
problem Understanding how a single pixel modification affects deep neural networks.
method Propagation Maps and locality analysis to visualize and understand the impact of pixel modifications.
result One pixel modifications can propagate through deep networks, affecting the final output and revealing vulnerability patterns.
David Gabai proves a 4D light bulb theorem using smooth techniques.
problem Constructive smooth 4-manifold theory advancements.
method Innovative use of classical moves in a smooth construction.
result First new hands-on advance in constructive smooth 4-manifold theory in a long time.
New method for classifying disk embeddings in 4-manifolds.
problem Classifying smooth isotopy classes of neat embeddings of 2-disks in 4-manifolds.
method Using an invariant going back to Dax, constructing a group structure, and relating to mapping class groups.
result The group structure on isotopy classes of neat embeddings is usually not abelian or finitely generated.
The paper studies hypersurface evolution in a light-cone and curvature flow.
problem Investigating the evolution of hypersurfaces in a light-cone.
method Exploring variational problems associated with hypersurfaces and curvature flow.
result Established perpetual existence and smooth convergence of curvature flow to a circle.
SVM predicts regional rainfall with varying accuracy, best in central US.
problem Regional rainfall prediction for social and economic impact planning.
method Support Vector Machine (SVM) applied to sequences of daily rainfall maps.
result SVM predictions for central region outperform untrained classifier.
Novel geodesic results on affine and Lorentzian manifolds.
problem Existence and multiplicity of geodesics on manifolds.
method Path-lifting and path-continuation properties of exponential maps.
result Generalization of Hadamard-Cartan theorem to affine manifolds.