Proves elliptic operator images are closed on Hilbert bundles.
problem Closedness of images of elliptic operators on Hilbert bundles.
method Analyzes tensor product of elliptic operators and compares images.
result Establishes closedness of images with respect to natural topology.
The paper studies hyperbolic phenomena on closed surfaces using bicorn curves.
problem Understanding hyperbolic phenomena on curve graphs of closed surfaces.
method Using the theory of bicorn curves to analyze the curve graphs of closed surfaces.
result Proves that the curve graph of any closed surface is 15-hyperbolic with one exception.
This paper benchmarks OoDD methods for medical imaging.
problem Medical models trained for one domain may fail on images from a different domain.
method Defined 3 categories of OoD examples and benchmarked methods in 3 medical imaging domains.
result Simple binary classifier on feature representation yields best accuracy and AUPRC.
New surfaces in 3D manifolds are found that cannot be smoothly deformed into each other.
problem Finding surfaces in 3D manifolds that cannot be smoothly deformed into each other.
method Constructing infinite families of homotopic surfaces in closed genus-g surfaces, showing they are not smoothly image-concordant. result Closed surfaces with common framed dual sphere can be π1-injective but not smoothly image-concordant. Paper proves certain closed affine manifolds without invariant lines don't exist.
problem Proving non-existence of closed affine manifolds with invariant lines.
method Developing map, holonomy, invariant line, large open subsets, modified proof.
result Developing image cannot meet invariant line if affine holonomy acts purely by translations.
A new method, REC, compresses images by encoding their latent representations efficiently.
problem Efficiently compressing single images with latent representations.
method Relative Entropy Coding (REC) that directly encodes latent representations with codelength close to relative entropy.
result REC is more efficient for single image compression compared to previous methods and is competitive for lossy compression.
New method denoises images without clean reference using Tweedie distributions.
problem Image denoising without clean reference images.
method Combining Tweedie distributions, Noise2Score, and saddle point approximation.
result General closed-form denoising formula for various noise distributions.
Uniform bound on geodesic images for surfaces using bicorn curves.
problem Bounding geodesic images on closed surfaces.
method Utilizing bicorn curves and properties of 1-slim triangles.
result Uniform bound of 44 for non-annular subsurfaces, 3 for specific cases.
Tensor networks reveal limitations for efficient text description but suggest potential for images.
problem Efficiently describing large text and image data sets using tensor networks.
method Investigation of mutual information scaling, introduction of mutual information estimators, and use of autoregressive and convolutional neural networks.
result Text data cannot be efficiently described by 1D tensor networks, while images may be better described by 2D tensor networks.
Study on the parity of fold map singular points, showing non-invariance for odd-dimensional manifolds.
problem Parity of connected components of fold map singular points for odd-dimensional manifolds.
method Constructive proofs using open book decompositions, round fold maps, and allowable moves.
result Parity of connected components is not a homotopy invariant for odd-dimensional manifolds.
A famous result of Bennequin states that for any braid representative of the unknot the Bennequin number is negative. We will extend this result to all n-trivial closed n-braids. This is a class of infinitely many knots closed under taking mirror images. Our proof relies on a non-standard parametrization of the Homfly …
Let e denote the Euler class on the space Hom(Γg,PSL(2,R)) of representations of the fundamental group Γg of the closed surface Σg of genus g. Goldman showed that the connected components of Hom(Γg,PSL(2,R)) are precisely the inverse images e−1(k), for 2−2g≤k≤2g−2, and t…
Square can fit inside curves close to smooth ones.
problem Finding inscribed squares in nearly smooth curves.
method Using curvature and a map to relate curves, proving existence of inscribed squares.
result Curves close to smooth ones contain inscribed squares.
Improved image generation quality using closed-form discriminator guidance in diffusion models.
problem Enhancing the quality of images generated by diffusion models.
method Theoretical framework to analyze GAN discriminator's effect on Langevin sampling, proposing IPM-GAN optimization as smoothed score-matching.
result Closed-form kernel-based discriminator guidance improves metrics like CLIP-FID and KID.
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points. Dynamical properties for the space of geodesics are also proved.
Generates high-resolution images from low-resolution inputs.
problem Generating realistic images from low-resolution inputs.
method Latent Adversarial Generator (LAG) using perceptual loss.
result Samples of high-resolution images from low-resolution inputs.
We show that the volume of any Riemannian metric on a three sphere is bounded below by the length of the shortest closed curve that links its antipodal image. In particular, the volume is bounded below by the minimum of the length of the shortest closed geodesic and the minimal distance between antipodal points.
The paper studies hypersurfaces with constant weighted mean curvature in Gaussian space.
problem Characterizing hypersurfaces with specific properties of their Gauss map.
method Analyzing the Gauss map and its image in the Gaussian space.
result Hypersurfaces with certain properties of their Gauss map are either hyperplanes or generalized cylinders.
HW2MP-GAN tackles ancient handwritten text recognition.
problem Automatic text recognition from ancient handwritten records.
method Conditional Generative Adversarial Network (HW2MP-GAN) with Sliced Wasserstein distance and U-Net architectures.
result HW2MP-GAN outperforms state-of-the-art models in image-to-image translation and handwritten recognition.
Cohomology fractals are visual representations of cohomology classes on hyperbolic 3-manifolds.
problem Visualizing cohomology classes on hyperbolic 3-manifolds.
method Cohomology fractals are images associated to cohomology classes. They are related to limit sets of Kleinian groups but differ in key aspects. An implementation using ideal triangulations and ray-casting is presented.
result Cohomology fractals allow for real-time zooming in any direction at arbitrary depth.
We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the pow…
Dual energy computed tomography (DECT) imaging plays an important role in advanced imaging applications due to its material decomposition capability. Image-domain decomposition operates directly on CT images using linear matrix inversion, but the decomposed material images can be severely degraded by noise and artifact…
Paper uses CNN to predict stock price movement as an image classification problem.
problem Predicting stock price movement using machine learning.
method CNN-based model for classifying stock price movement based on the first hour of trading.
result The algorithm effectively separated between stock price movement classes and outperformed other strategies.
A method uses image processing and deep learning for financial market state prediction.
problem Low signal-to-noise ratio in financial time series data.
method Wavelet transform for denoising, convolutional neural network for pattern extraction.
result Competitive prediction accuracy of market states 'Up' and 'Down' on S&P 500 data.
We show that central extensions of the mapping class group Mg of the closed orientable surface of genus g by Z are residually finite. Further we give rough estimates of the largest N=Ng such that homomorphisms from Mg to SU(N) have finite image. In particular, homomorphisms of Mg into $SL([\sqrt{g+1}],…
TinyBayes detects crop diseases from images on edge devices with high accuracy and minimal resources.
problem Automated disease detection for cocoa crops in resource-constrained settings.
method Combines YOLOv8-Nano for lesion localisation, MobileNetV3-Small for feature extraction, and Jacobi prior for Bayesian classification.
result Achieves 78.7% accuracy on Amini Cocoa Contamination Challenge dataset with 9.5 MB model size and 150 ms inference time.
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
Paper proposes faster incremental subclass discriminant analysis.
problem Efficiently classify subclasses in incremental data.
method Exact and approximate linear and kernelized solutions.
result Superior training time and accuracy compared to existing methods.
A new measure scales MMD to assess distribution closeness.
problem Testing statistical significance of distribution closeness.
method Norm-adaptive MMD (NAMMD) for distributional discrepancy.
result NAMMD-based DCT has higher test power than MMD-based DCT.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
problem Improving state-space radio interferometric imaging in the presence of heavy-tailed noise
method Stochastic Approximation Expectation Maximization
result Significant improvement in reconstruction fidelity and robustness to radio-frequency interference
New model separates images into independent factors quickly and easily.
problem Separating high-dimensional data like images into independent latent factors.
method Combines bijective feature maps with linear ICA model on the Stiefel manifold.
result Models converge quickly and achieve better unsupervised latent factor discovery.
The paper characterizes simple closed curves on surfaces using profinite rigidity.
problem Characterizing simple closed curves on surfaces using profinite rigidity.
method Proving that elements with the same images under all finite groups are simple closed curves.
result The set of simple closed curves is closed in the profinite topology of the surface group.
A GMM-based method generates new 3D structures from medical images.
problem Generating new medical images from limited data and different modalities.
method Gaussian Mixture Model (GMM) for point-cloud generation.
result Generated point-clouds closely match training samples from the same class.
Let M be an orientable closed connected 3-manifold. We introduce the notion of amalgamated Heegaard genus of M with respect to a closed separating 2-manifold F, and use it to show that the following two statements are equivalent: (i) a compact connected 3-manifold Y can be embedded in M so that the exterior of the imag…
A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle structures with strongly irreducible monodromy.
Paper proposes a tensor data model for incomplete imaging data.
problem Prognostics models for incomplete imaging data.
method Supervised tensor dimension reduction with TTF supervision and optimization.
result Model effectively extracts low-dimensional features from incomplete data.
We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many solutions to the hyperbolic gluing equation whose associated representations are conj…
Convolutional neural networks (CNNs) have shown promising results on several segmentation tasks in magnetic resonance (MR) images. However, the accuracy of CNNs may degrade severely when segmenting images acquired with different scanners and/or protocols as compared to the training data, thus limiting their practical u…
Generic metrics make geodesic nets dense.
problem Density of geodesic nets under generic metrics.
method Proving density for Baire-generic metrics.
result Union of geodesic nets images is dense.
Data-efficient reinforcement learning (RL) in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. We consider a particularly important instance of this challenge, the pixels-to-torques problem, where an RL agent learns a closed-loop con…
Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers such as the BM3D. They are typically trained to minimize the mean squared error (MSE) between the output image of a deep neural network (DNN) and a ground truth image. Thus, it is important for deep-learning-based …
We propose a simple kernel based nearest neighbor approach for handwritten digit classification. The "distance" here is actually a kernel defining the similarity between two images. We carefully study the effects of different number of neighbors and weight schemes and report the results. With only a few nearest neighbo…
Paper detects biases in medical imaging ML models using counterfactual analysis.
problem Bias in medical imaging ML models negatively impacts generalization performance.
method Counterfactual invariance framework combining conditional latent diffusion models and statistical hypothesis testing.
result The method identifies and quantifies biases without direct access to counterfactual data.
In coronary CT angiography, a series of CT images are taken at different levels of radiation dose during the examination. Although this reduces the total radiation dose, the image quality during the low-dose phases is significantly degraded. To address this problem, here we propose a novel semi-supervised learning tech…
Deep-learning method estimates bone 3D structure from X-ray images.
problem Estimating bone 3D structure from X-ray images.
method Triplet loss-trained neural network selecting closest 3D bone shape from predefined set.
result Average RMS distance of 1.08 mm between predicted and true shapes.
Improves diversity of text-to-image models without sacrificing FID.
problem Lack of diversity and tendency to recreate training set images.
method Adds sparse repellency terms to diffusion SDE to guide trajectories away from a reference set.
result Improves diversity of diffusion models with minimal impact on FID.
Introduction 1. The two-eigenvalue problem 2. Hecke algebra representations of braid groups 3. Duality of Jones-Wenzl representations 4. Closed images of Jones-Wenzl sectors 5. Distribution of evaluations of Jones polynomials 6. Fibonacci representations
Authors prove a formula relating the Gaussian curvature of polyhedral vertex stars to their Gauss images.
problem Proving a formula connecting discrete Gaussian curvature to the algebraic area of Gauss images.
method Comparing winding numbers and critical point index of a normal vector to deduce the formula.
result Formula significantly limits possible shapes of Gauss images of polyhedral vertex stars.