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.
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…
Optical coherence tomography (OCT) based measurements of retinal layer thickness, such as the retinal nerve fibre layer (RNFL) and the ganglion cell with inner plexiform layer (GCIPL) are commonly used for the diagnosis and monitoring of glaucoma. Previously, machine learning techniques have utilized segmentation-based…
Imaging fluorescent disease biomarkers in tissues and skin is a non-invasive method to screen for health conditions. We report an automated process that combines intraoral fluorescent porphyrin biomarker imaging, clinical examinations and machine learning for correlation of systemic health conditions with periodontal d…
The paper introduces vortex nerve complexes and new Betti numbers in CW spaces.
problem Understanding the structure and properties of CW complexes and their nerves.
method Introducing vortex nerve complexes and defining new Betti numbers for CW complexes.
result New Betti numbers (vortex Bvtex, vortex nerve BvNrv, shape Bsh) are introduced and studied. This paper uses Ghrist barcodes to track persistent shapes in video frames.
problem Detecting and tracking persistent shapes in video frames.
method Introduces Ghrist barcodes for persistent Betti numbers derived from vortex nerve complexes in triangulated video frames.
result Persistent Betti numbers of vortex nerves are k+2 for k edges. Graev's nerve implies invariant Einstein metrics on homogeneous spaces.
problem Existence of invariant Einstein metrics on homogeneous spaces.
method Lie-theoretic definition of Graev's nerve and curvature estimates.
result Detailed description of Graev's work and curvature estimates.
We show that a regular cover of a general topological space provides structure similar to a triangulation. In this general setting we define analogues of simplicial maps and prove their existence and uniqueness up to homotopy. As an application we give simple proofs of sharpened versions of nerve theorems of K. Borsuk …
The Rips complex at scale r is homotopy equivalent to the nerve of a cover of diameter r.
problem Reconstructing spaces using Rips complexes and covers.
method Functorial Dowker-Nerve Diagram, homotopy equivalence, cover of diameter r.
result General framework for reconstructing spaces by Rips complexes.
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive proximity. A 1-cycle is a closed, connected path with a zero boundary in a simplicial c…
This paper defines ribbons and ribbon complexes in CW spaces and analyzes their topological properties.
problem Characterizing and analyzing topological structures in CW spaces.
method Introducing planar ribbons, ribbon complexes, and ribbon nerves in Alexandroff-Hopf-Whitehead CW spaces, and studying their topological properties.
result Characterization of ribbons and ribbon nerves by Betti numbers and homotopy types.
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.
problem Generalizing bundle gerbes over groupoids and their properties.
method Developed a functorial correspondence between PB groupoids and bundle gerbes over groupoids.
result Built a correspondence between PB groupoids and bundle gerbes over groupoids, including partial quotients.
Ultrasound (US) is the most widely used fetal imaging technique. However, US images have limited capture range, and suffer from view dependent artefacts such as acoustic shadows. Compounding of overlapping 3D US acquisitions into a high-resolution volume can extend the field of view and remove image artefacts, which is…
Unified framework for Morita invariant cohomology of Lie groupoids.
problem Proving Morita invariance of cohomology theories for Lie groupoids.
method Viewing cohomology as sheaves of modules on the nerve of the groupoid and establishing criteria for Morita invariance.
result Established criteria for Morita invariant cohomology theories.
Multi-layer optical film has been found to afford important applications in optical communication, optical absorbers, optical filters, etc. Different algorithms of multi-layer optical film design has been developed, as simplex method, colony algorithm, genetic algorithm. These algorithms rapidly promote the design and …
We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending …
The boundary of certain hyperbolic groups is like a Menger curve.
problem Characterizing boundaries of hyperbolic Coxeter groups.
method Analyzing the nerve of hyperbolic right-angled Coxeter groups.
result Many triangulations and disks have boundaries homeomorphic to the Menger curve.
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.
The main results of this paper are: (1) If a space X can be embedded as a cellular subspace of Rn then X admits arbitrary fine open coverings whose nerves are homeomorphic to the n-dimensional cube Dn; (2) Every n-dimensional cell-like compactum can be embedded into (2n+1)-dimensional …
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…
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.
GWHD dataset offers 4,700 high-res images of wheat heads.
problem Challenges in wheat head detection from high-resolution imagery.
method Large, diverse dataset with detailed metadata.
result Benchmark for wheat head detection methods.
Multi-head attention outperforms single-head in in-context linear regression tasks.
problem Comparing performance of transformer with single-/multi-head attention in in-context learning.
method Theoretical analysis of performance of transformers with different attention mechanisms in linear regression tasks.
result Multi-head attention with a substantial embedding dimension outperforms single-head attention in in-context linear regression tasks.
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…
We give a necessary and sufficient condition for a hyperbolic Coxeter group with planar nerve to have Sierpiński curve as its Gromov boundary.
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.
New theory shows how multi-head attention reduces variance and decorrelates outputs.
problem Understanding and optimizing multi-head attention in neural networks.
method Developed a statistical theory linking multi-head attention to ensemble Nadaraya-Watson estimators.
result MHA variance reduction depends on head decorrelation, not just head count.
Geometric theory of projection heads in self-supervised learning.
problem Dimensional collapse and information invariance trade-off in projection heads.
method Geometric modeling of projection heads as Riemannian metrics, analyzing Hessian eigenvalues, and tracking optimization geometry.
result Smooth nonlinear heads induce negative curvature, preventing collapse; linear and ReLU heads cannot.
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.
Improved language models with talking-heads attention.
problem Language model perplexity and quality issues.
method Added linear projections in multi-head attention.
result Better perplexities and quality in language tasks.
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.
New approach improves multi-head attention by making heads less similar.
problem Multi-head attention can lead to similar features, reducing model expressiveness.
method Proposes a non-parametric approach using Bayesian techniques to make heads repel each other.
result Improves feature diversity, leading to better representations and performance.
Paper introduces regularization for multi-head attention to spot keywords.
problem Redundancy in multi-head attention leads to lack of rich information.
method Regularization technique to enforce orthogonality between attention heads.
result Significant improvement in keyword spotting performance.
Deep forecasting models show output heads significantly improve performance on fat-tailed financial returns.
problem Improving deep learning models for forecasting fat-tailed financial returns.
method Comparison of backbone architectures and output heads (point, Gaussian, Gaussian mixture) on S&P 500 monthly log-returns.
result Switching from point to Gaussian heads improves CRPS by about 1.3 percent, and from Gaussian to mixture adds another 2.4 percent.
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.
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.
One-layer transformers can't solve induction heads task efficiently.
problem Solving the induction heads task efficiently with one-layer transformers.
method Communication complexity argument showing exponential size requirement.
result No one-layer transformer can solve the induction heads task efficiently.
We discuss recently emerging applications of the state-of-art deep learning methods on optical microscopy and microscopic image reconstruction, which enable new transformations among different modes and modalities of microscopic imaging, driven entirely by image data. We believe that deep learning will fundamentally ch…
Despite the advantages of all-weather and all-day high-resolution imaging, SAR remote sensing images are much less viewed and used by general people because human vision is not adapted to microwave scattering phenomenon. However, expert interpreters can be trained by compare side-by-side SAR and optical images to learn…
The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on two parameters can be focused to a single point by an optical instrument made of reflecting or refracting surfaces if and only if, before ente…