Smooth rigid spherical hypersurfaces in C^2 are real analytic.
problem Classifying smooth rigid spherical hypersurfaces in C^2.
method Proving real-analyticity through smoothness.
result Every smooth rigid spherical hypersurface in C^2 is real analytic.
Study projective structures and rational curves to understand Painlevé equations.
problem Analyzing projective structures and rational curves on surfaces.
method Analytic classification, normal forms, pencil/fibration decomposition, infinitesimal symmetries.
result Deduced transcendental results about Painlevé equations.
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
The paper classifies actions of a specific group on certain manifolds.
problem Classifying analytic actions of a specific semi-orthogonal group on manifolds.
method Adapting Uchida's construction, the paper explicitly constructs actions on specific manifolds and demonstrates that any action is covered by these.
result Any analytic action of the semi-orthogonal group on a closed, connected manifold is covered by the constructed actions.
We extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for arbitrary projective mor…
Symplectic classification for a specific type of singularity in integrable systems.
problem Symplectic classification of integrable systems near singular points of type An. method Real-analytic symplectic normal forms and classification of Lagrangian foliations.
result All integrable systems are symplectically equivalent near singular points of this type.
Predictive analytics classify self-care problems in children with disability using ICF-CY.
problem Complex classification of functioning and disability in children with ICF-CY.
method Implemented Random Forest, SVM, Naive Bayes, Hoeffding tree, and Lazy locally weighted learning; used Boruta for dimensionality reduction.
result Random Forest achieved 84.75% classification accuracy.
Deep neural networks classify unbounded Gaussian mixture data without dimensionality issues.
problem Binary classification of unbounded Gaussian mixture data.
method Deep ReLU neural networks with non-asymptotic upper bounds and convergence rates.
result Deep ReLU networks can classify unbounded Gaussian mixture data without dimensionality constraints.
Analytic curves are classified w.r.t. their symmetry under a regular and separately analytic Lie group action on an analytic manifold. We show that an analytic curve is either exponential or splits into countably many analytic immersive curves, each of them discretely generated by the symmetry group (i.e., each such cu…
Analyzes smoothness and classification of maps between manifolds.
problem Analyzing interpolating sesqui-harmonic maps between Riemannian manifolds.
method Derives a conservation law and uses it to show smoothness of weak solutions; obtains classification results.
result Smoothness of weak solutions and classification results for interpolating sesqui-harmonic maps.
New activation functions improve neural network performance for exoplanet classification.
problem Optimizing neural network performance for exoplanet classification with hard attribute removal.
method Investigation of novel activation functions using ODE and fixed point theory, followed by empirical validation.
result Optimal neural network performance achieved without tuning, comparable to traditional functions.
New method improves classification performance in Bayesian networks.
problem Estimating conditional probability tables in Bayesian networks.
method Hierarchical Multinomial-Dirichlet model for joint estimation of conditional distributions.
result Significantly improved classification performance compared to traditional methods.
The paper classifies symplectic invariants of specific singularities in integrable Hamiltonian systems.
problem Classifying symplectic invariants of singularities in integrable Hamiltonian systems.
method Smooth C∞ symplectic classification of Lagrangian fibrations near singularities. result Action variables form complete C∞ symplectic invariants for parabolic orbits and cuspidal tori. Study classifies non-removable singularities in Minkowski 3-space equations.
problem Classifying non-removable singularities in Minkowski 3-space equations.
method Classification through real analytic solutions of the prescribed mean curvature equation.
result Classification of non-removable isolated singularities.
We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove that such connections exist. This classification relies in a local result that cla…
Unified scalable GPCs for various likelihoods using additive noise.
problem Scalability issues and intractable inference in GPC for big data and non-Gaussian likelihoods.
method Additive noise to unify scalable GPCs for multiple likelihoods, using variational inference.
result Empirically superior results for binary/multi-class classification tasks with up to two million data points.
New bounds enable training of probabilistic models for deep networks.
problem Training scalable latent variable models for deep networks.
method Introducing new variational bounds for specific output layers of neural networks.
result Analytical bounds for certain output layers allow training without re-parameterization or Monte Carlo approximations.
We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on usi…
Interactive learning improves real-time tweet classification for situational awareness.
problem Difficulty in identifying relevant tweets from noisy social media data.
method Interactive learning framework that incorporates user feedback in real-time.
result Our approach outperforms state-of-the-art models in real-time tweet classification.
Classifies gradient Ricci solitons with harmonic Weyl curvature in dimensions 5 and above.
problem Classifying gradient Ricci solitons with harmonic Weyl curvature in higher dimensions.
method Developed a novel method of refined adapted frame fields and used geometric arguments.
result Local and complete classifications of gradient Ricci solitons with harmonic Weyl curvature.
SBAF activation function improves ANN for exoplanet habitability classification.
problem Classifying exoplanets into habitable and non-habitable categories.
method Developed Saha-Bora Activation Function (SBAF) for ANN, demonstrating its analytical properties and improved performance.
result SBAF activation function outperforms traditional functions in ANN for exoplanet habitability classification.
Proves existence of Hermitian-Einstein metrics on stable bundles.
problem Analytic stability of vector bundles and instantons/monopoles.
method Analyzes curvature decay and proves existence of Hermitian-Einstein metrics.
result Existence of Hermitian-Einstein metrics on analytically stable bundles.
Tree-based models biased when trained on imbalanced data, requiring new calibration methods.
problem Bias in tree-based models trained on imbalanced datasets.
method Analytical calibration of random forest models, demonstrating bias in decision trees.
result Calibrating tree-based models on imbalanced data negatively impacts predictions, especially for the minority class.
We obtain a classification up to isomorphism of complex-analytic supermanifolds with underlying space CP1 of dimension 1∣3 with retract (k,k,k), where k∈Z. More precisely, we prove that classes of isomorphic complex-analytic supermanifolds of dimension 1∣3 with retract (k,k,k) are in o…
Zero entropy found in entire Grauert tubes of certain manifolds.
problem Analyzing the geodesic flow on Grauert tubes with zero entropy.
method Examined entire Grauert tubes on real analytic Riemannian manifolds.
result Geodesic flow on entire Grauert tubes has zero topological entropy.
Surveying pluriclosed flow on complex surfaces, suggesting a geometrization conjecture.
problem Understanding the long-term behavior of pluriclosed flow on complex surfaces.
method Analytic techniques to establish existence and convergence results.
result A geometrization conjecture for complex surfaces.
Developing a visual platform for faster astronomical source cataloging.
problem Speeding up cataloging of large area surveys in radio astronomy.
method Integration of advanced source finding and classification tools into a visual analytic platform.
result Improvement and acceleration of cataloging process in astronomical surveys.
This document describes the R package UBL that allows the use of several methods for handling utility-based learning problems. Classification and regression problems that assume non-uniform costs and/or benefits pose serious challenges to predictive analytic tasks. In the context of meteorology, finance, medicine, ecol…
2DSCNs improve image data analytics by extending SCN to handle spatial information.
problem Limitation of 1D SCNs in preserving spatial information of images.
method Extend SCN to 2DSCNs by stochastically configuring hidden nodes in a matrix-inputs framework.
result 2DSCNs outperform 1D SCNs in image data analytics tasks.
Analyzes tt*-structures from ADE-type Stokes data.
problem Classifying tt*-structures over C∗. method Isomonodromic deformations with upper unitriangular real Stokes matrices.
result Establishes a direct analytic realization of the ADE classification. An important part of the classical theory of real or complex manifolds is the theory of (smooth, real analytic or complex analytic) vector bundles. With any vector bundle over a manifold (M,F) the sheaf of its (smooth, real analytic or complex analytic) sections is associated which is a locally free sheaf of F-modules,…
Visual analytics tool detects and corrects concept drift in data streams.
problem Concept drift causes inaccurate predictions in evolving data.
method DriftVis combines drift detection and visualization.
result Visual analytics supports detection, examination, and correction of concept drift.
Analyzes double descent in binary classification models with different losses.
problem Understanding the double descent phenomenon in binary classification models.
method Analytic study of gradient descent with logistic and square losses on binary linear classification models.
result The double descent phenomenon persists but with differences compared to logistic loss.
We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the first and second derivatives, and with holomorphic coefficients.
Paper studies equations for a type of soliton with applications.
problem Analyzing a specific type of soliton structure.
method Analytic techniques to establish elliptic and integral equations.
result Established basic structural equations for almost Ricci-harmonic solitons.
ODTLearn learns optimal decision trees for predictive and prescriptive tasks.
problem Learning optimal decision trees for high-stakes predictive and prescriptive tasks.
method Mixed-integer optimization framework and object-oriented design.
result Implementation of optimal decision trees for various tasks.
The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either $\mathds{S}^3$, $\erre\times\mathds{S}^2$ or $\erre^3$, under some very weak conditions on the vector fi…
Generators for the module of vector fields liftable over corank 1 stable complex analytic maps from an n-manifold to an (n+1)-manifold are found. This is applied to the classification of the singularities occuring in generic one-parameter families of maps between these spaces.
Anomaly detection aids in labeling fast-running processes for machine learning.
problem Manual labeling of fast-running processes for machine learning models.
method Anomaly detection to assist in labeling data, specific metrics for model validation.
result Possibility to manually classify data for training machine learning models.
Most of the banks' operational risk internal models are based on loss pooling in risk and business line categories. The parameters and outputs of operational risk models are sensitive to the pooling of the data and the choice of the risk classification. In a simple model, we establish the link between the number of ris…
A new method for compressive classification using bridge regression.
problem Efficient pattern classification with compact representation.
method Proposed a deterministic bridge regression solution for compressive classification.
result Validation of the proposed solution through numerical studies on simulated and real-world data.
Let M1 denote the space of solutions z(x,y) to an elliptic, real analytic Monge-Ampère equation det(D2z)=φ(x,y,z,Dz)>0 whose graphs have a non-removable isolated singularity at the origin. We prove that M1 is in one-to-one correspondence with M2×Z2, where…
Hyperbolic SVM improves classification in complex networks.
problem Accurately classifying points in hyperbolic space with hierarchical relationships.
method Introducing hyperbolic SVM, a hyperbolic formulation of SVM classifiers.
result Hyperbolic SVM outperforms Euclidean SVM in multi-class prediction tasks.
We study graphs of positive extrinsic curvature with a non-removable isolated singularity in 3-dimensional warped product spaces, and describe their behavior at the singularity in several natural situations. We use Monge-Ampère equations to give a classification of the surfaces in 3-dimensional space forms which are em…
In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu…
Proposes TAGI for efficient Gaussian inference in Bayesian neural networks.
problem Efficient inference in Bayesian neural networks with complex architectures.
method Analytical method for tractable approximate Gaussian inference (TAGI).
result Matches performance of gradient-based methods with O(n) computational complexity. GMVAE improves open-set classification by clustering latent representations.
problem Improving open-set classification accuracy and robustness.
method Cooperative learning of reconstruction and clustering in the latent space of a GMVAE.
result Achieved an average F1 improvement of 29.5% in open-set classification.
The study evaluates AI model performance measures for medical use.
problem Selecting appropriate performance measures for AI models in medical practice.
method Assessed 32 performance measures across five domains for binary outcomes.
result 17 measures are both proper and reflect decision-analytic performance.