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.
169,341 papers · 148 categories
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48 results for “complex geometrical optics”
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…
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.
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.
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.
Method reconstructs potential from partial boundary measurements on admissible manifolds.
problem Reconstructing potential from partial data on admissible manifolds.
method Develops a method using the geodesic ray transform and complex geometrical optics solutions.
result Reconstructs potential locally and globally under certain conditions.
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.
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.
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.
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.
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.
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…
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.
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.
Deep learning reduces complexity of solving nonlinear Schrödinger equation in fiber optics.
problem Inverting the nonlinear Schrödinger equation in real-time for fiber-optic communications.
method Jointly optimizing filters using deep learning to reduce complexity.
result Reduced complexity to around 2-6 times that of linear equalization.
Almost Robinson geometriesmath.DG
Study on almost Robinson geometries, focusing on their intrinsic torsion and leaf space properties.
problem Investigating the geometry of almost Robinson manifolds, a Lorentzian analog of almost Hermitian manifolds.
method Classification based on intrinsic torsion, analysis of leaf space properties, and conformal invariants.
result Comprehensive classification of almost Robinson manifolds based on their intrinsic torsion.
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.
In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a c…
A fast method for learning MZI parameters in optical neural networks.
problem Time-consuming learning of MZI parameters in optical neural networks.
method Customized complex-valued derivatives and a chain rule for Wirtinger derivatives, incorporated into a function module.
result 20 times faster learning compared to conventional AD in MNIST task.
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…
Derives exact gradients for linear optics with single photons.
problem Gradient estimation for linear optics with single photons.
method Generalized parameter shift rule for linear optics.
result Derives analytical formula for gradients in linear optics.
Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstructionphysics.comp-ph
Bayesian optimization outperforms other methods in nano-optical shape optimization and parameter reconstruction.
problem Optimizing nano-optical structures with non-convex objective functions.
method Benchmarked five global optimization methods including Bayesian optimization.
result Bayesian optimization yields significantly better results in a fraction of the time.
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.
EASTER improves OCR efficiency and scalability.
problem Efficient and scalable Optical Character Recognition (OCR) for machine printed and handwritten text.
method 1-D convolutional layers without recurrence, parallel training, synthetic dataset generation.
result EASTER achieves comparable performance to complex RNN models with less data and outperforms them on benchmark datasets.
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.
The Stone-Weierstrass theorem aids in solving inverse problems on specific manifolds.
problem Inverse problems on holomorphically separable Kähler manifolds and conformally transversally anisotropic manifolds.
method Application of the Stone-Weierstrass theorem to show uniqueness in inverse problems.
result Generalization and simplification of earlier results in inverse problems.
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. T…
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.
We recover phase from intensity measurements using optics-based random projections.
problem Recovering phase from intensity measurements with unknown transmission matrix.
method Our method leverages conjugation of rows in the unknown matrix and interference with reference signals to cast the problem as a Euclidean distance geometry.
result We accurately recover the missing phase and mitigate quantization and sensitivity effects.
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.
We prove that a potential can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator in a fixed admissible 3-dimensional Riemannian manifold . We also show that an admissible metric in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Δ_…
We study the geometric properties of holomorphic distributions of totally null -planes on a -dimensional complex Riemannian manifold , where and . In particular, given such a distribution , say, we obtain algebraic conditions on the Weyl tensor and t…
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.
Physics-based deep learning improves fiber-optic communication efficiency.
problem Improving signal propagation in fiber-optic communication systems.
method Parameterizing the split-step method of solving the nonlinear Schrödinger equation as a deep neural network.
result Filters can be pruned to as few as 3 taps/step without sacrificing performance.