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.
In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method: in particular, the case of a soap film only partially wetting a space curve, a …
Solves the film scheduling and staggered showtimes problem for movie theaters.
problem Maximize attendance and revenue by scheduling films with staggered showtimes.
method Binary integer linear optimization to find optimal schedules for each cluster of neighboring locations.
result Optimal scheduling cannot be done for all locations at once, but must be done for each cluster.
A new multi-hop FiLM approach improves visual reasoning tasks.
problem Challenging multi-modal tasks like visual question-answering and dialogue.
method Generate FiLM layer parameters in a multi-hop fashion, alternating between attending to language and generating parameters.
result Multi-hop FiLM generation achieves state-of-the-art performance on visual dialogue tasks.
In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces mee…
Soap films collapse only if their bulk has negative pressure, forming convex shapes.
problem Understanding soap film behavior and collapse conditions.
method Variational analysis of capillarity theory.
result Soap films collapse only if their bulk has negative pressure, forming convex shapes.
Derives equilibrium law for Plateau borders in wet soap films and foams.
problem Equilibrium law for Plateau borders in wet foams and films.
method Rigorous derivation using Gauss' capillarity theory, homotopic spanning condition, and effective compactness theorems.
result Sharp regularity properties of energy minimizers for Plateau borders in wet foams and films.
We introduce a general-purpose conditioning method for neural networks called FiLM: Feature-wise Linear Modulation. FiLM layers influence neural network computation via a simple, feature-wise affine transformation based on conditioning information. We show that FiLM layers are highly effective for visual reasoning - an…
Extends symmetry and rigidity to surfaces with soap film-like singularities.
problem Symmetry and rigidity of minimal surfaces with singularities.
method Method of moving planes applied to surfaces with Plateau-like singularities.
result Extends classical results to surfaces with singularities.
Study soap films hanging from frames, proving surface limits and curvature conditions.
problem Understanding soap films with gravity and minimal surfaces.
method Compactness theorem for surfaces with vanishing mean curvature and fixed/converging boundaries.
result Minimal surfaces represent all possible limits of almost-minimal surfaces.
We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, …
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place without canceling each other out and to model triple junctions without introducing …
Develops a geometric framework for soap film instabilities.
problem Soap film instabilities on minimal surfaces.
method Björling representation of minimal surfaces.
result Jacobi fields are maximally localized with lowest eigenfunction amplitude.
GNN-FiLM uses feature-wise linear modulation to improve graph neural networks.
problem Improving graph neural networks for better performance.
method Feature-wise linear modulation applied to target node representations in GNNs.
result GNN-FiLM outperforms baseline methods on a regression task for molecular graphs.
What are the possible shapes of various things and why? For instance, when a closed wire or a frame is dipped into a soap solution and is raised up from the solution, the surface spanning the wire is a soap film. What are the possible shapes of soap films and why? Or, for instance, why is DNA like a double spiral stair…
Smoothness of collapsed regions in soap films is proven, indicating wetted singularities.
problem Smoothness of collapsed regions in soap films.
method Study of generalized minimizers in capillarity model.
result Collapsed regions are smooth outside of dimensionally small singular sets.
Classifies soap film surfaces with vertical potentials.
problem Classifying soap film surfaces with vertical potentials.
method Variational characterization of n-elastic curves. result Obtains a full description of n-elastic curves. For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.
A deep learning algorithm designs low-cost SPP films.
problem Designing SPP films with high accuracy and low cost.
method Guided deep learning algorithm with low-cost sample replacement.
result Deep CNN learns to replace precious metals with ordinary metals, reducing cost.
FiLM improves deep learning for long-term time series forecasting.
problem Preserving historical information without overfitting noise.
method Applies Legendre Polynomials and Fourier projections, adds low-rank approximation.
result Significantly improves multivariate and univariate forecasting accuracy.
We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoi…
Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable (n−2)-dimensional submanifold M of Rn. If M is connected, we say a compact set X "spans" M if X intersects every Jordan curve whose linking number with M is 1. Picture a soap fi…
Automated malaria diagnosis from field slides achieves accurate results.
problem Challenges in analyzing field-prepared thin blood film microscopy images.
method Fully automated framework using machine learning, including CNNs trained on diverse field samples.
result Results are close to sufficient for drug resistance monitoring and clinical use-cases.
Improved continual learning method using variational inference and FiLM layers.
problem Training models on new tasks and datasets in an online fashion.
method Generalized Variational Continual Learning (GVCL) with likelihood-tempering and FiLM layers.
result GVCL outperforms existing baselines in both small and large datasets, providing better calibration.
Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant −κ2. Using the cone total curvature TC(Γ) of a graph Γ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…
New method finds all thin film structures from reflectometry data.
problem Computational prohibitive for standard algorithms, leading to unreliable analysis.
method Prior-Amortized Neural Posterior Estimation (PANPE) combining simulation-based inference and adaptive priors.
result Identifies all realistic structures in seconds, setting new standards in reflectometry.
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.
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.
Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow…
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.
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.
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.
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …
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.
Glaucoma is the second leading cause of blindness all over the world, with approximately 60 million cases reported worldwide in 2010. If undiagnosed in time, glaucoma causes irreversible damage to the optic nerve leading to blindness. The optic nerve head examination, which involves measurement of cup-to-disc ratio, is…
We describe two applications of machine learning in the context of IP/Optical networks. The first one allows agile management of resources at a core IP/Optical network by using machine learning for short-term and long-term prediction of traffic flows and joint global optimization of IP and optical layers using colorles…
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.
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.
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.
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.
This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4πmust be smoothly embedded. Related results are proved for varifolds and for soap film surfaces.
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.