Classifies hexagonal circular 3-webs with cubic polar curves.
problem Classifying hexagonal circular 3-webs with algebraic polar curves of degree three.
method Analyzes hexagonal circular 3-webs on unit sphere with polar points on a twisted cubic.
result Completes the classification of hexagonal circular 3-webs with algebraic polar curves of degree three.
Novel fusion network combines polarization and radiomics features for liver cancer classification.
problem Challenges in histopathological diagnosis of HCC and ICC.
method Two-tier fusion approach: feature-level and classification-level.
result Significantly enhances classification accuracy, even at reduced resolutions.
Study polar actions on Damek-Ricci spaces, proving existence and finding examples.
problem Characterize polar actions on Damek-Ricci spaces.
method Prove criteria for isometric actions to be polar, find examples, and classify actions.
result Non-trivial polar actions exist on all Damek-Ricci spaces.
Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine wh…
We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifol…
Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.
problem Classifying totally geodesic submanifolds and polar actions on Stiefel manifolds.
method Classification through polar actions and cohomogeneity-one actions.
result Classification of orbits of polar actions on Stiefel manifolds.
We obtain the full classification of coisotropic and polar actions of compact Lie group on irreducible Hermitian symmetric spaces.
The study classifies Riemannian homogeneous spaces with polar isotropy actions.
problem Characterizing Riemannian homogeneous spaces with polar isotropy actions.
method Analyzing simply connected Riemannian homogeneous spaces of compact semisimple Lie groups and various non-compact spaces.
result Classification and non-polar isotropy actions for specific spaces.
New hexagonal circular 3-webs with reducible curves classified.
problem Classifying hexagonal circular 3-webs with reducible polar curves of degree 3.
method New examples and classifications presented.
result Classification of hexagonal circular 3-webs with reducible polar curves of degree 3.
The paper analyzes how multiple classifiers' disagreement and polarization affect overall accuracy.
problem Improving accuracy through ensembling multiple classifiers.
method The paper derives an upper bound for polarization, proposes a neural polarization law, and presents a tight upper bound for the error of majority vote classifiers.
result Disagreement and polarization among classifiers are linearly correlated with the target, and polarization is nearly constant for a dataset.
The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.
We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…
The paper finds symplectic mapping class relations using pencil pairs.
problem Understanding symplectic mapping class relations in 4-manifolds.
method Applying classification results for Fano 3-folds and polarized K3 surfaces to a general methodology of finding pencil pairs.
result Symplectic mapping class relations between products of positive Dehn twists.
Simple multilingual sentiment analysis framework outperforms existing methods.
problem Multilingual sentiment analysis in social media.
method A simple and easy-to-implement multilingual framework for sentiment classification.
result Outperforms existing methods in multiple languages, including SemEval, TASS, and SENTIPOLC.
Survey on submanifolds in noncompact symmetric spaces.
problem Classification of submanifolds in symmetric spaces.
method Construction of examples and classification problems.
result Introduction to submanifolds in noncompact symmetric spaces.
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.
We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.
Improved crude oil price forecasting using multi-dimensional LLM sentiment signals.
problem Challenges in predicting crude oil prices due to unstructured news.
method Extracted five sentiment dimensions from GPT-4o, Llama 3.2-3b, and FinBERT models on energy-sector news articles.
result Combining GPT-4o and FinBERT yields the best predictive performance for weekly WTI crude oil futures returns.
Uniform K-stability holds for close polarizations if original is canonical or anti-canonical.
problem Conditions for uniform K-stability of projective varieties.
method Analysis of stability conditions for close polarizations.
result Uniform K-stability is preserved for close polarizations if original is canonical or anti-canonical.
The paper studies how Kähler polarizations degenerate to mixed polarizations on toric varieties.
problem Degeneration of Kähler polarizations to mixed polarizations on toric varieties.
method Constructing polarizations by Hamiltonian actions, finding one-parameter families of Kähler polarizations, and analyzing convergence of spaces of holomorphic sections.
result Kähler polarizations degenerate to mixed polarizations as k increases, with specific convergence results for one-parameter families. Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation $\Cal F$ (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution (E,J). Polarized means that (E,J) is roughly speaking invariant by $\Cal F$. Both structures ar…
A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic polarity with respect to a triangle, the polarities with respect to high-degree algebr…
The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…
Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.
problem Reconstructing anisotropic cosmic polarization rotation from CMB data.
method Extended ResUNet-CMB to handle gravitational lensing and patchy reionization.
result ResUNet-CMB outperforms standard quadratic estimator in reconstructing all three effects.
New method polarizes anisotropic Heisenberg groups.
problem Polarizing anisotropic Heisenberg groups.
method Implementing a technique to polarize anisotropic Heisenberg groups.
result New class of polarizable Carnot groups expanded.
The study introduces polarization of generalized Nijenhuis torsions and their relevance in operator fields.
problem Characterization of Haantjes C∞(M)-modules of operator fields. method Introducing polarization of generalized Nijenhuis torsions and proving algebraic identities.
result Polarizations of generalized Nijenhuis torsions are relevant in the characterization of Haantjes C∞(M)-modules of operator fields. Classifies polar foliations on symmetric spaces.
problem Classifying polar foliations on symmetric spaces.
method Orbit equivalence and classification up to codimension two.
result Foliations are either hyperpolar or extensions of rank one foliations.
Paper examines trading polarity to predict market crashes.
problem Insufficient investigation of trading imbalance at high frequency.
method Investigates trading polarity from Shenzhen Stock Exchange data.
result Trading polarity correlates with market crashes and returns.
The paper studies polar normalizations of skew ruled surfaces in 3D space.
problem Understanding the properties and invariants of polar normalized skew ruled surfaces.
method Determination of invariants and analysis of Tchebychev and support vector fields.
result Special polar normalizations lead to degenerate curves.
New classification for 4-manifolds with specific fundamental groups.
problem Classifying 4-manifolds with fundamental group Z/ptimesZ. method Using quadratic 2-type and intersection form, along with generalizations to infinite groups.
result Homotopy type determined by quadratic 2-type and Z/p-valued intersection form. The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.
POLAR framework interprets word embeddings using polar opposites.
problem Lack of interpretability in pre-trained word embeddings.
method Adopt semantic differentials and polar opposites to transform embeddings.
result Interpretable word embeddings maintain performance comparable to original embeddings.
Study empty polar varieties' impact on singular function-germs.
problem Topology of singular function-germs with nonisolated singularities.
method Analysis of empty polar varieties.
result Topology implications of nonempty polar varieties.
For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue …
Totally geodesic sections found in polar actions.
problem Understanding sections of polar actions on Riemannian manifolds.
method Elementary proof of a folklore result.
result Sections of polar actions are totally geodesic.
Carnot groups can be polarized if they have specific coordinate systems.
problem Understanding when Carnot groups can be polarized.
method Proving Carnot groups with certain coordinate systems are polarizable.
result Carnot groups with suitable horizontal polar coordinates are polarizable.
The paper bounds abnormal and Goh-abnormal sets for metabelian Lie groups with polarizations.
problem Bounding abnormal and Goh-abnormal sets for metabelian Lie groups.
method Analyzing rank 2 polarizations and sub-Riemannian structures on metabelian Lie groups.
result Metabelian Lie groups with polarizations satisfy the minimizing Sard property.
In this paper, we generalize the polar transforms of spacelike isothermic surfaces in Q14 to n-dimensional pseudo-Riemannian space forms Qrn. We show that there exist c−polar spacelike isothermic surfaces derived from a spacelike isothermic surface in Qrn, which are into Srn+1(c), Hr−1n+1(c)…
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
Study shows horizontal diameter of unit spheres is π for specific foliations.
problem Understanding horizontal diameter in unit spheres with specific foliations.
method Analyzing singular Riemannian foliations on unit spheres.
result Horizontal diameter of unit spheres is π for polar and infinitesimally polar actions.
The paper introduces polarizations in symplectic and orthogonal settings.
problem Understanding polarizations in symplectic and orthogonal contexts.
method Exposition of symplectic and orthogonal polarizations, emphasizing symmetry.
result Grassmannians of polarizations in symplectic and orthogonal settings.
We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.
We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.
Investigates polar tangential angles of curves and their monotonicity.
problem Behavior of polar tangential angles of plane curves.
method Proof of monotonicity for certain curves of monotone curvature.
result Nonexistence results for an obstacle problem involving free elasticae.
Proved inequality for anti-self-polar polytopes.
problem Proving an inequality for anti-self-polar polytopes.
method Using Kalai's combinatorial inequality based on Whiteley's result.
result Proved a conjecture by Katz about anti-self-polar polytopes.
New method shows unitarity in quantization for toric manifolds.
problem Unitarity in quantization commutes with reduction for toric manifolds.
method Generalized coherent state transform (gCST) and geodesic rays of toric Kähler polarizations.
result Quantization commutes unitarily with reduction for the new mixed polarization.
Classifies foliations on specific symmetric spaces.
problem Classifying foliations on symmetric spaces of rank one.
method Orbit equivalence classification.
result Polar homogeneous foliations classified.
In this paper, assuming that a polarized algebraic manifold (X,L) is strongly K-stable, we shall show that the polarization class c1(L) admits a constant scalar curvature Kaehler metric.