Quaternion CNN outperforms traditional CNN in color image reconstruction.
problem Efficient image processing with small or heterogeneous datasets.
method Introducing quaternion-valued convolutional neural networks (QCNN) to learn internal and external relations.
result QCAE outperforms CAE in reconstructing unseen color images.
A new input-free attack reduces query complexity for black-box adversarial examples.
problem Efficiently generating adversarial examples in black-box scenarios with minimal queries.
method Input-free attack approach, using gray images and perceptible perturbations.
result Successfully perturbs a gray image to any target class with high success rate using only 1,701 queries.
Paper presents a method for satellite imagery classification using texture features.
problem Object identification in urban areas using satellite imagery.
method Pixel-level study with various features (correlation, homogeneity, energy, contrast). Supervised classification using SVM and Naive Bayes.
result Naive Bayes outperforms SVM with an overall accuracy of 76%.
Extends RCNNs to handle hypercomplex-valued data.
problem Processing high-dimensional data.
method Develops mathematical background and conditions for hypercomplex-valued RCNNs.
result Hypercomplex-valued RCNNs can always settle at an equilibrium.
Explains compactification for heterotic superstrings on Calabi-Gray manifolds.
problem Compactification of heterotic superstrings with torsion.
method Generalized Calabi-Gray geometry.
result Expository overview of compactification methods.
The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.
problem Non-Kähler complex manifolds with explicit geometry.
method Demonstrates the use of generalized Calabi-Gray manifolds to address non-Kähler geometry questions.
result Generalized Calabi-Gray manifolds provide a framework to answer specific non-Kähler geometry problems.
The paper proves stability for contact groupoids and deformations.
problem Stability of contact groupoids and deformations.
method Proof of Gray stability for compact contact groupoids.
result Stability results for deformations of induced Jacobi bundles.
Proves a tree of shapes for n-D images in optimal time.
problem Proving the mathematical structure of tree of shapes in n-D images.
method Optimal quasi-linear time algorithm for computing the tree of shapes.
result The tree of shapes is the self-dual morphological hierarchical structure of n-D gray-level images.
We define the thin fundamental Gray 3-groupoid S3(M) of a smooth manifold M and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps S3(M)→C(H), where H is a 2-crossed module of Lie groups and C(H) is the Gray 3-groupoid naturally constructed f…
The aim of this paper is to describe a large class of Hermitian Gray manifolds.
The aim of this research is the study of Gray curvature identities, introduced by Alfred Gray in \cite{kn:Gra76} for the class of almost hermitian manifolds. As known till now, there is no equivalent for the class of almost contact manifolds. For this purpose we use the Boohby-Wang fibration and the warped manifolds co…
We give a parameterization of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid using Jacobi's elliptic functions. This parameterization avoids some problems present in the original depiction of these surfaces.
In this paper we determine the Gray-Hervella classes of the compatible almost complex structures on the twistor spaces of oriented Riemannian four-manifolds considered by G. Deschamps
Generative models improve image classifier explanations by realistically removing features.
problem Perturbation-based explanations often produce unrealistic counterfactual samples.
method Integrate generative inpainters into attribution methods to remove input features.
result Improved explanation methods in object localization, deletion, and saliency metrics.
In the 3-gauge theory, a 3-connection is given by a 1-form A valued in the Lie algebra g, a 2-form B valued in the Lie algebra h and a 3-form C valued in the Lie algebra l, where (g,h,l) constitutes a differential 2-crossed modu…
Deep learning ensemble improves Alzheimer vs. Mild Cognitive Impairment diagnosis.
problem Differentiating Alzheimer Disease from Mild Cognitive Impairment.
method Hybrid deep learning ensemble framework using MRI slices, pretrained models, and stacked ensemble learning.
result State-of-the-art accuracy (99.21%) for Alzheimer vs. Mild Cognitive Impairment classification.
Harmonic almost complex structures on specific Lie groups and solvmanifolds identified.
problem Characterizing harmonic almost complex structures on almost abelian Lie groups and solvmanifolds.
method Adapted Gray-Hervella classification to almost abelian Lie groups, characterized harmonic structures.
result Examples of harmonic almost complex structures in different Gray-Hervella classes on compact almost abelian solvmanifolds.
Study of complex structures on product twistor spaces for 4D manifolds.
problem Understanding complex structures on product twistor spaces.
method Analyzing the product bundle of twistor spaces with Riemannian metrics and almost complex structures.
result Determined Gray-Hervella classes for 4D manifolds.
We characterize quasi Kähler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related with the third Gray identity and in the almost Kähler case implies the integrability. Our main tool is the existence of generalized holomorphic f…
Improved upper bound for mass partitioning problem using Gray codes.
problem Partitioning masses on a high-dimensional space with hyperplanes.
method Classifying Gray code patterns and utilizing group actions.
result An improved bound for the Grünbaum-Hadwiger-Ramos problem.
New conditions for GRW space-times to be perfect-fluid space-times.
problem Conditions for GRW space-times to be perfect-fluid.
method Gray's decomposition of the gradient of the Ricci tensor, determining Ricci tensor forms in invariant subspaces.
result For most GRW space-times, the Ricci tensor is Einstein or perfect fluid.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Specifically, we experiment with low-pass filtering, PCA, JPEG compression, low resolution wavelet approximation, and soft-thresholding. We evalu…
The paper extends Gray's result to quaternion-Kähler manifolds.
problem Understanding quaternion-Kähler manifolds with non-negative quaternionic sectional curvature.
method Introducing quaternionic sectional curvature, proving Wolf spaces have non-negative curvature, and using nearly Kähler twistor spaces.
result Every quaternion-Kähler manifold with non-negative quaternionic sectional curvature is a Wolf space.
This paper evaluates power consumption and inference time for face emotion recognition on embedded systems.
problem Lack of information on power consumption and inference time for face emotion recognition on embedded systems.
method Identified state-of-the-art methods, collected new dataset, evaluated on three embedded devices.
result Gray images are more suitable for embedded systems, and power consumption and inference time are limiting factors.
The paper examines conditions for Einstein-like classes in doubly warped product manifolds.
problem Conditions for a factor manifold to be in the same Einstein-like class as the entire doubly warped product manifold.
method Analysis of the Ricci tensor and warping functions.
result Sufficient and necessary conditions for a factor manifold to inherit the Einstein-like class of the entire manifold.
We classify, up to a local isometry, all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost Kahler 4-manifolds satisfy the third curvature condition of A. Gr…
The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray mo…
Novel framework for medical image segmentation using deep learning.
problem Class imbalance and domain adaptation in medical image segmentation.
method Biophysics-based domain adaptation and automatic segmentation of white, gray, and cerebrospinal fluid.
result Improved segmentation performance, especially with the biophysics-based domain adaptation.
Characterizes a class of almost Hermitian 4-manifolds using integral identities.
problem Global characterization of almost Hermitian 4-manifolds.
method Using an integral identity from Sekigawa's work, proving a uniqueness result on Lie algebras.
result Global characterization of the class AH1 of almost Hermitian 4-manifolds. Learning the distribution of natural images is one of the hardest and most important problems in machine learning. The problem remains open, because the enormous complexity of the structures in natural images spans all length scales. We break down the complexity of the problem and show that the hierarchy of structures …
This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of d-dimensional histograms having n bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a (d+1)-partite graph with (d+1)n nodes and dndd+1 arcs,…
New findings on GRW space-times with constant scalar curvature.
problem Understanding GRW space-times in different subspaces.
method Analyzing orthogonal subspaces of Gray's decomposition.
result Generalized quasi-Einstein GRW space-times reduce to known types of space-times.
The aim of this paper is to describe Kahler surfaces which admit an opposite almost Hermitian structure satisfying the first Gray condition
MRI image quality affects statistical and predictive analysis of brain morphology.
problem Impact of MRI image quality on statistical and predictive analysis of brain morphology.
method Systematic testing of image quality on univariate statistics and machine learning classification using three large datasets.
result Low-quality MRI data significantly affects detecting significant sex/gender differences in smaller samples, but not in larger ones.
We give a description of Gray AC^{\perp} manifolds (M,g) whose Ricci tensor has two eigenvalues of multiplicity 1 and dim M-1.
Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian foliations of any open subset of Pn of codimension one. As a consequence …
Gray-box attack improves on white-box methods for trading agents.
problem Robustness of Deep RL trading agents against adversarial attacks.
method Hybrid Deep Neural Network policy for gray-box adversarial attack.
result Adversary can reduce trading agent's reward by 214.17%.
Data-driven approach learns effective equations for phase field interfaces.
problem Learning accurate equations for phase field interface dynamics.
method Data-driven identification of partial differential equations from phase field data.
result Data-driven equations outperform analytical approximations in certain regimes.
New method improves model robustness against adversarial attacks.
problem Models trained with adversarial samples can be vulnerable to simple attacks.
method Graybox Adversarial Training using intermediate models to seed adversaries.
result Models trained with Graybox Adversarial Training are more robust to simple attacks.
The aim of this paper is to classify bi-Hermitian compact surfaces (M,g) whose Ricci tensor ρ satisfies the relation ∇Xρ(X,X)=31Xτg(X,X).
Study of contact-complex Riemannian submersions in various manifold classes.
problem Characterizing submersions in specific manifold classes.
method Analyzing properties of O'Neill invariants and discussing integrability and minimality.
result Main properties of O'Neill invariants and integrability/minimality of fibres discussed.
MimickNet approximates clinical ultrasound post-processing without proprietary data.
problem Matching proprietary clinical-grade ultrasound post-processing techniques.
method Deep learning framework MimickNet that transforms raw DAS beams into post-processed images.
result MimickNet achieves high SSIM scores (0.930-0.967) on test sets.
This paper defines systematic value investing as an empirical optimization problem. Predictive modeling is introduced as a systematic value investing methodology with dynamic and optimization features. A predictive modeling process is demonstrated using financial metrics from Gray & Carlisle and Buffett & Clark. A 31-y…
The structure of nearly Kähler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces ov…
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.
Evaluates SHIELD's effectiveness against adaptive adversaries in various threat models.
problem Evaluating SHIELD's efficacy against adaptive adversaries in different threat models.
method Empirical analysis of SHIELD's robustness against adaptive attacks using Projected Gradient Descent (PGD) attacks in various threat models (white-box, gray-box).
result The targeted PGD attack success rate drops from 64.3% to 48.9% when models are trained from scratch instead of retrained.
Two embedding methods in spectral graph clustering yield different but valid groupings.
problem Clustering vertices of a graph without true groupings.
method Spectral graph clustering using Laplacian or Adjacency spectral embedding.
result Laplacian embedding captures left hemisphere/right hemisphere structure, while adjacency embedding captures gray matter/white matter structure.