Open problems in billiards and optics from a workshop.
problem Open problems in billiards and geometric optics.
method Collection of open problems from a workshop.
result No specific key result mentioned; collection of problems.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
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48 results for “Geometrical Optics”
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
Hamilton proved a theorem about focusing light rays, leading to new mathematical concepts.
problem Focusing light rays to a single point using optical instruments.
method Original proof and symplectic geometry proof of the Malus-Dupin theorem.
result A family of light rays can be focused to a single point if they are rectangular before entering the instrument.
Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in to describe reflection of rays off a surface. Thi…
Model explains optical illusions using geometric sub-Riemannian geodesics.
problem Understanding and explaining geometrical optical illusions.
method Neuro-mathematical model based on sub-Riemannian geodesics in the Roto-Translation Group.
result Illusory contours are described as geodesics in a new metric.
Derives Levi-Civita connection formulas for specific geometries.
problem Determining geometric invariants of Lorentzian manifolds.
method Explicitly derives Christoffel symbols in terms of adapted frame fields.
result Formulas for geometric invariants of Lorentzian manifolds.
Paper optimizes fiber optic communication constellations using machine learning.
problem Improving fiber optic communication performance through better constellation shaping.
method An unsupervised learning approach embedding a fiber channel model into neural networks.
result Improved performance up to 0.13 bit/4D in simulation and experimentally up to 0.12 bit/4D.
Geometric optics describes wave behavior near convex obstacles.
problem Wave behavior near convex obstacles.
method Geometric optics in and spaces.
result Oscillations transport along grazing rays to any order.
Optimization approach for efficient sampling in optical mapping for structural variant detection.
problem Efficient sampling strategy for structural variant detection using optical mapping.
method Developed an optimization approach using a hyper-geometric distribution and probabilistic concentration inequalities.
result Optimal sampling strategy requires sampling most chromosomal fragments to detect variants at high confidence with little biological material.
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the Gauss Bonnet theorem and its applications to surfaces in optical geometry, as deve…
Quantum dynamics reveals hidden geometric structure in data.
problem Understanding complex, high-dimensional datasets through geometric structure.
method Introducing semiclassical and microlocal analysis to data analysis.
result First tractable algorithm for approximating wave dynamics and geodesics on data manifolds.
New AI algorithm improves multi-layer optical film design efficiency.
problem Traditional algorithms converge to local optima, limiting global optimal solutions.
method Deep Q-learning for global optimal multi-layer optical film design.
result Deep Q-learning model converges global optimum of optical thin film structure.
By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this kinetic term's metric. This new geometrical standpoint sheds light on some founda…
Study determines minimal surfaces from boundary data, proving topological and conformal recoverability.
problem Determining minimal surfaces from boundary data.
method Developed a semiclassical nonlinear calculus for complex geometric optics solutions.
result Minimal surfaces can be recovered from the Dirichlet-to-Neumann map under certain conditions.
The paper explores affine geometry of line congruences using singularity theory.
problem Understanding the affine geometry of line congruences and their focal sets.
method Use of singularity theory to describe generic phenomena and singularities.
result Identification of a key projective quadric in the tangent space.
Two machine learning applications for IP/Optical networks: traffic prediction and optical path performance.
problem Agile resource management and optical path performance prediction in IP/Optical networks.
method Machine learning for traffic prediction and optical performance prediction using SDN controllers.
result Efficient implementation of SDN controllers for agile resource management and optical path performance prediction.
Bayesian optical flow estimates motion with uncertainty quantification.
problem Ill-posed inverse problem of optical flow.
method Statistical approach treating optical flow as a statistical inverse problem.
result Bayesian optical flow provides statistical estimates of motion and uncertainty.
This work improves optic disc and cup segmentation for glaucoma detection.
problem Automatic segmentation of optic disc and cup on eye fundus images for glaucoma diagnosis.
method Modification of U-Net convolutional neural network.
result Our method achieves comparable quality to state-of-the-art methods, with faster prediction times.
Complex optical vortex knotsmath.GT
New method generates optical vortices in any knot shape.
problem Generating optical vortices in complex shapes beyond simple knots.
method Mathematical construction and experimental verification.
result Complex optical fields can form any knot shape.
Finsler Spinopticsmath-ph
The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. The…
Fully Convolutional Networks for Monocular Retinal Depth Estimation and Optic Disc-Cup Segmentationeess.IV
Paper tackles depth estimation and optic disc-cup segmentation from color fundus images.
problem Depth estimation and optic disc-cup segmentation from color fundus images.
method Uses fully convolutional networks for monocular retinal depth estimation and optic disc-cup segmentation.
result Demonstrates improved accuracy in depth estimation and optic disc-cup segmentation.
Method detects and locates eavesdropping in optical links.
problem Detect and locate eavesdropping in optical links with small power losses.
method Cluster-based approach using OPM data at receiver and in-line OPM data for localization.
result Subtle eavesdropping losses can be detected and localized using OPM data.
Deep learning enhances optical microscopy and image reconstruction.
problem Improving image data transformations in optical microscopy.
method Application of deep learning methods on optical microscopy and image reconstruction.
result Deep learning enables new transformations among different modes and modalities of microscopic imaging.
Optical Echo State Network Reservoir Computingphysics.optics
Optical ESNs enable flexible, efficient machine learning with reduced energy.
problem Implementing universal computational capabilities in machine learning.
method Optical implementation of ESNs leveraging stimulated Brillouin scattering.
result Efficient, scalable, and memory-capable optical reservoir computing.
GANPOP uses deep learning to estimate optical properties from single images, improving accuracy over existing methods.
problem Estimating optical properties from single wide-field images.
method Conditional generative adversarial networks trained on paired images and optical property maps.
result GANPOP estimates optical properties with 58% higher accuracy than single-snapshot optical property technique in human gastrointestinal specimens.
Paper develops a deforestation detection system using optical and SAR data.
problem Detecting tree-loss in dense forests using satellite data.
method Combines optical and SAR data, uses KL expansion for anomaly detection, and Hidden Markov Model for classification.
result Hybrid method achieves high accuracy and robustness in sparse optical data.
Optical geometriesmath.DG
Study of optical geometries with intrinsic torsion in general relativity.
problem Understanding null line distributions and their properties in Lorentzian manifolds.
method Investigation of intrinsic torsion and congruences of null curves, extending to generalized optical geometries.
result Characterization of conformal properties of null line distributions and congruences.
Optical DNNet boosts accuracy with multiple frequency-channels.
problem Improving the accuracy of optical neural networks.
method Developed a novel optical diffractive deep neural network with multiple frequency-channels.
result Multiple frequency-channels significantly increase network accuracy.
Paper develops machine learning to translate SAR to optical images for easier interpretation.
problem Difficulty in human interpretation of SAR images due to non-adapted human vision to microwave scattering.
method Develops a novel reciprocal GAN scheme to train machine intelligence on co-registered SAR and optical images.
result The proposed translation network works well under various SAR and optical image resolutions and polarizations.
Express Wavenet reduces neural network parameters to 1% of standard networks.
problem Optical neural networks with high parameter count.
method Wavelet modulation, random shift wavelets, expressway structure.
result Express Wavenet achieves high accuracy with significantly fewer parameters.
Novel video prediction method for complex urban scenes using optical flow.
problem Making accurate future frame predictions in complex urban scenes.
method Optical flow conditioned method using video sequences and optical flow sequences.
result Empirical evaluations show the effectiveness of the method on KITTI and Cityscapes datasets.
The paper solves the isoperimetric problem in Riemannian optical geometry, proving circles minimize lengths with area constraints.
problem Optical geometry of static spherically symmetric spacetimes.
method Applying isoperimetric problem results to curves in Riemannian optical geometry.
result Length-minimizing curves with area constraints are circles, with implications for photon spheres.
Neural networks reduce DBP complexity in fiber optics.
problem Complexity in digital backpropagation implementations.
method Neural-network-based approach to implement DBP.
result Learned DBP reduces complexity by 32x100 km fiber-optic link.
Machine Learning-Based Optimization of Chiral Photonic Nanostructures: Evolution- and Neural Network-Based Designphysics.optics
Designs chiral photonic structures using machine learning for efficient optical properties.
problem Optimizing chiral photonic nanostructures for light-matter interactions.
method Evolutionary algorithm and neural network approach for rapid optimization.
result Frequency-dependent modification in reflected light's degree of circular polarization.
Novel approach localizes optic disc and fovea centers efficiently.
problem Localizing optic disc and fovea centers in retinal images.
method Simultaneously process optic disc and fovea, modeling their relative geometry and appearance.
result Improves localization and recognition by incorporating object-object relations.
Authors argue Lin's system is not a deep neural network.
problem Mischaracterization of Lin's system as a deep neural network.
method Lin's system uses a passive, strictly linear optical setup for pattern classification.
result Authors argue Lin's system is not a deep neural network.
Locally maximizing orbits studied in twist maps and billiards.
problem Characterize orbits in locally maximizing class for twist maps.
method Geometric and variational analysis of orbits in the cotangent bundle of a torus or ball bundle over a sphere.
result Two generating functions for the Birkhoff billiard map have the same class of locally maximizing orbits.
New methods for constructing null fluid metrics and solving optical lift conjectures.
problem Constructing null fluid metrics and solving optical lift conjectures.
method Explicit parameterization of null fluid metrics under Kerr type optical structures.
result New explicit metrics, including Kerr black holes and Ricci flat examples.
Recent advances in twistor theory are applied to geometric optics in . The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming w…
Optical flow enhances semantic segmentation for automated driving.
problem Improving semantic segmentation for automated driving systems.
method Constructed four architectures using RGB, flow, RGBF, and two-stream RGB + flow.
result Two-stream architecture achieves best results with 4% IoU improvement.
Active learning improves EDFA model accuracy with binary features.
problem Lack of labeled training data for EDFA devices.
method Active learning strategy for binary features using sparse linear models.
result Improved prediction and accelerated query generation.
Paper proposes a graph model for optimal AP deployment in indoor optical wireless networks.
problem Challenges in deploying optical wireless networks due to LoS requirement and limited range.
method Graph modeling approach to identify minimum number of APs and their optimal locations.
result Optimal deployment of APs ensures connectivity and minimizes interference in indoor environments.
Machine learning improves network analysis and self-management in optical communications.
problem Complexity and data heterogeneity in optical networks require advanced mathematical tools.
method Application of Machine Learning techniques to analyze and manage network data.
result Machine learning enables automated network self-configuration and fault management.
Improved signal processing for long-distance optical signals.
problem Compensating walk-off effect in long-distance optical signals.
method Sub-banded DSP architecture with deep learning for walk-off compensation.
result 2.8 dB SNR improvement over linear equalization.
A neural network and evolutionary algorithm framework designs nonlinear optical molecules.
problem Designing efficient nonlinear optical materials.
method Multi-stage Bayesian neural network (msBNN) and corrected Lewis-mode group contribution method (cLGC) combined with evolutionary algorithm (EA).
result Accurately and efficiently designs molecules with different optical properties using a small data set.
Optical co-processor speeds up neural network training.
problem Expensive training costs for large neural networks.
method Direct feedback alignment, optical error projection.
result Optical co-processor trains neural networks for handwritten digit recognition.
Paper develops deep learning for signal recognition in long perimeter fiber optic sensors.
problem Difficult signal-jamming environments and stringent error requirements.
method Two-level event detection architecture with ensemble of deep convolutional networks.
result Efficient and robust multiclass detection algorithms with high adaptability.
We consider the problem of developing a method to reconstruct a potential from the partial data Dirichlet-to-Neumann map for the Schrödinger equation on a fixed admissible manifold . If the part of the boundary that is inaccessible for measurements satisfies a flatness condition in one directio…