Study classifies rotational hypersurfaces with prescribed mean curvature.
problem Classifying rotational hypersurfaces with prescribed mean curvature.
method Phase space analysis to classify hypersurfaces.
result Delacunay-type classification for even prescribed functions.
In this paper, we construct Delaunay type constant mean curvature surfaces along a nondegenerate closed geodesic in a 3-dimensional Riemannian manifold.
Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction speciali…
The paper constructs solutions to a critical Dirac equation on spheres.
problem Solving the critical Dirac equation on spheres with singularities.
method Constructing Delaunay-type solutions and another kind of singular solutions.
result The constructed solutions are building blocks for singular solutions on Spin manifolds.
In this paper we produce families of complete non compact Riemannian metrics with positive constant σk-curvature by performing the connected sum of a finite number of given n-dimensional Delaunay type solutions, provided 2≤2k<n. The problem is equivalent to solve a second order fully nonlinear elliptic eq…
We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity $(-Δ)^γw = c_{n, γ} w^{\frac{n+2γ}{n-2γ}}, w>0 \ \mbox{in} \ \mathbb{R}^n \backslash \{0\}$ We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates.
It has been showed by Byde that it is possible to attach a Delaunay-type end to a compact nondegenerate manifold of positive constant scalar curvature, provided it is locally conformally flat in a neighborhood of the attaching point. The resulting manifold is noncompact with the same constant scalar curvature. The main…
The purpose of this paper is to study immersed surfaces in the product spaces M2(κ)×R, whose mean curvature is given as a C1 function depending on their angle function. This class of surfaces extends widely, among others, the well-known theory of surfaces with constant mean curvature. In th…
We prove the existence of a countable family of Delaunay type domains Ω_j in M^n x R, where M^n is the Riemannian manifold S^n or H^n and n is at least 2, bifurcating from the cylinder B^n x R (where B^n is a geodesic ball of radius 1 in M^n) for which the first eigenfunction of the Laplace-Beltrami operator with zero …
In this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the eigenvalues of its Schouten tensor. Also, we study conformal metrics on the spher…
We study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter functional under a volume constraint. We establish the existence of a smooth branch of periodic cylinders in RN, N≥2, all of th…
We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl(2, R). In particular, all constant mean curvature spheres in those spaces are described explicitly, proving that they are not always embedded. Besides new examples of Dela…
Minimal surfaces in hyperbolic and anti-de Sitter spaces constructed using loop group methods.
problem Constructing minimal surfaces in hyperbolic and anti-de Sitter spaces.
method Loop group factorization methods.
result Minimal surfaces in hyperbolic and anti-de Sitter 3-space with n-punctured sphere topology. We are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold. First we prove the nonlocal analogue of the Alexandrov result characterizing sph…
New method constructs translationally equivariant hyperbolic affine spheres.
problem Constructing translationally equivariant hyperbolic affine spheres.
method Noncompact Iwasawa factorization via DPW method and Weierstrass elliptic functions.
result Every translationally equivariant hyperbolic affine sphere is equiaffinely equivalent to one with a circle, hyperbola, or parabola slice curve.
In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces φ:Mn→Hn+1 and a class of conformal metrics on domains of the round sphere Sn. Some of the key aspects of the correspondence and its consequences have dimensional restrictions $…
The study constructs and classifies hypersurfaces with constant curvature in product spaces.
problem Finding hypersurfaces with constant curvature in product spaces.
method Developed a general method for constructing hypersurfaces with constant r-th mean curvature. result Constructed and classified complete Hr-hypersurfaces in various ambient spaces. Paper presents a new framework for sequence classification.
problem Sequence classification in real-world applications.
method Reference-based sequence classification framework.
result New sequence classification algorithms achieve comparable accuracy.
Dual-stage sEMG classification improves gesture recognition accuracy.
problem Improving accuracy in hand gesture recognition from sEMG signals.
method Dual-stage classification approach: first stage groups similar activities, second stage classifies within groups.
result Dual-stage classification yields significantly higher accuracy than single-stage approach.
A novel method for classification with rejection using ensemble of cost-sensitive classifiers.
problem Avoid risky misclassification in error-critical applications.
method Learning an ensemble of cost-sensitive classifiers.
result Improved classification accuracy and flexibility in loss selection.
The number of possible methods of generalizing binary classification to multi-class classification increases exponentially with the number of class labels. Often, the best method of doing so will be highly problem dependent. Here we present classification software in which the partitioning of multi-class classification…
Few-shot image classification is improved by correcting CNNs' texture bias.
problem Few-shot image classification performance is hindered by CNNs' texture bias.
method Corrected CNNs' texture bias using a simpler method than state-of-the-art approaches.
result State-of-the-art performance on miniImageNet task achieved.
New NHCAs improve multi-category classification efficiency.
problem Efficient multi-category classification for real-world problems.
method Twin SVM (TWSVM), Generalized eigenvalue proximal SVM (GEPSVM), Regularized GEPSVM (RegGEPSVM), and Improved GEPSVM (IGEPSVM) with OAA, BT, and TDS approaches.
result TDS-TWSVM outperforms other methods in classification accuracy.
Paper compares XGB and BPNN for music style classification.
problem Efficient music style classification using different methods.
method Feature extraction for timbral texture, rhythmic content, and pitch content; comparative evaluation of XGB and BPNN.
result XGB outperforms BPNN for small datasets in music classification.
Classification outperforms regression in portfolio construction, yielding higher Sharpe ratios.
problem Determining which machine learning approach (classification vs. regression) is more effective for portfolio construction.
method Used stacking ensemble of gradient boosted tree, random forest, and neural network models.
result Classification yields higher Sharpe ratios and economically significant alphas compared to regression.
C-HMCNN(h) improves HMC classification by leveraging class hierarchy.
problem Hierarchical multi-label classification with class hierarchy constraints.
method Exploits class hierarchy to produce coherent predictions for multi-label classification.
result C-HMCNN(h) outperforms state-of-the-art models in HMC classification.
Advances few-shot classification by treating it as supervised learning and proposing new training techniques.
problem Formulating the ability of humans to learn from limited data in machine learning.
method Formulated few-shot classification as a supervised learning problem and introduced multi-episode and cross-way training techniques.
result Proposed training strategies accelerate the training process without accuracy loss.
Improves NILM with multi-label SRC, outperforming state-of-the-art.
problem Non-intrusive load monitoring (NILM) for energy disaggregation.
method Modified multi-label sparse representation based classification (SRC).
result Significant improvement over state-of-the-art techniques with minimal training data.
New approach improves classification guarantees by focusing on direction rather than regression risk.
problem Improving classification guarantees in binary classification problems.
method Establishing a geometric distinction between classification and regression, leveraging scale invariance.
result Improved guarantees for classification risk compared to regression risk.
Study selective classification with halfspaces, achieving error bounds under Gaussian distributions.
problem Modeling relationships in subsets of data defined by selection rules.
method Sparse linear classifiers for subsets defined by halfspaces, focusing on Gaussian feature distributions.
result First PAC-learning algorithm for homogeneous halfspace selectors with error guarantee $\bigO*{\sqrt{\mathrm{opt}}}$.
New method for robust trajectory classification without parameters.
problem Trajectory classification accuracy and robustness.
method Parameter-free approach to find best trajectory partition and dimension combination.
result Promising preliminary results show improved robustness.
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable classification problem for general realizations is rigorously formulated and an algori…
A new network-based high-level data classification method using betweenness centrality.
problem Traditional data classification techniques focus on physical features, while high-level classification considers semantic meaning.
method Proposes a network-based high-level classification technique using betweenness centrality.
result Competent classification performance in nine real datasets compared to traditional models.
This thesis evaluates text-based vs audio-based classification of mental health interviews.
problem Classifying psychiatric illness using text-based methods.
method Design and evaluate a text classification network on mental health interviews, using belabBERT.
result Text-based classification is a strong alternative to audio-based methods.
Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
This review explores resampling techniques for imbalanced binary classification.
problem Imbalanced classes lead to poor prediction results in classification.
method Classical, cost-sensitive, and Neyman-Pearson paradigms with resampling techniques and classification methods.
result Complex dynamics among resampling techniques, base methods, metrics, and imbalance ratios.
Directly compute classification by learning features with class scores.
problem Classification efficiency and accuracy on various datasets.
method PCA for feature encoding, supervised learning model with encoder-decoder structure.
result Effective classification performance on multiple datasets.
Conventional techniques for supervised classification constrain the classification rules considered and use surrogate losses for classification 0-1 loss. Favored families of classification rules are those that enjoy parametric representations suitable for surrogate loss minimization, and low complexity properties suita…
This paper tackles tweet classification by identifying purpose and position.
problem Difficulties in determining user intention and attitude in short, informal tweets.
method Transformed tweet classification into a multi-label problem and applied a multi-label classification method with post-processing.
result The method effectively classifies tweet purpose and position, outperforming individual classification methods.
Text classification on drug SMILES strings yields competitive drug type classification results.
problem Classifying drug types using conventional text classification methods.
method Treated drug SMILES as sentences and applied basic NLP methods for classification.
result Competitive drug type classification results achieved.
BERT improves fine-grained sentiment classification.
problem Fine-grained sentiment classification of text.
method Used BERT for fine-grained sentiment classification.
result BERT outperforms other models for fine-grained sentiment classification.
Paper proposes fully Bayesian approach for RVM classification, improving accuracy especially in imbalanced data.
problem Difficulty in conducting RVM classification due to lack of closed-form solution for weight parameter posterior.
method Proposes Generic Bayesian and Fully Bayesian approaches with hierarchical hyperprior structure.
result Improves classification performance, especially in imbalanced data.
CRCEN neural network tackles imbalanced classification.
problem Challenges in training conventional classifiers on imbalanced datasets.
method CRCEN neural network with a novel weighted cross entropy loss function.
result CRCEN outperforms baseline models on benchmark datasets.
A new method combines topological features with graph convolutional networks for improved paper classification.
problem Classifying papers based on their content and structure.
method Combining topological features of nodes with information propagation through Graph Convolutional Networks (GCN).
result The method improves classification accuracy on CiteSeer and Cora datasets, matching or exceeding text-based classification results.
This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
Proposes an angle-based framework for multicategory cost-sensitive classification.
problem Cost-sensitive multicategory classification challenges.
method Angle-based cost-sensitive classification framework without sum-to-zero constraint.
result Proposed boosting algorithms yield competitive classification performances.
Optimal fuzzy classification aggregation functions are weighted means.
problem Characterizing optimal fuzzy classification aggregation functions.
method Proving optimality of weighted arithmetic means for fuzzy classification.
result Optimal fuzzy classification aggregation functions are weighted means.
Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with N sets of observations, where each set is labeled with class information, and the prediction of a class label is performed a…