A new index ASI quantifies angular separation of network communities in hyperbolic space.
problem Quantifying angular separation of network communities in high-dimensional data.
method Introducing Angular Separability Index (ASI) and a statistical test.
result ASI reveals significant phenomena in network geometry, including dimensionality jumps and intrinsic dimensionality detection.
Derives equations of motion for systems with angular momentum on Finsler geometries.
problem Equations of motion for dynamical systems with angular momentum on Finsler geometries.
method Apply Souriau's Principle of General Covariance to derive diffeomorphism invariant equations of motion.
result Generalizes Mathisson-Papapetrou-Dixon equations to Finsler geometries and finds conserved quantities.
Study reformulates Finsler metrizability problems using geodesic invariance.
problem Finsler metrizability problems for sprays.
method Reformulate problems in terms of geodesic invariance of tensors (metric and angular).
result Gyroscopic sprays have geodesically invariant angular metric.
Proves no-hair theorem for certain vacuum black holes.
problem No-hair theorem for stationary vacuum black holes.
method Proof of no-hair theorem, definition of surface gravity and angular velocity, analysis of near-horizon geometries.
result Completion of no-hair theorem proof for specified black holes.
New algorithms for topic modeling using conic geometry.
problem Unknown number of topics in nonparametric topic modeling.
method Analysis of topic simplex's concentration and angular geometry.
result Accuracy comparable to Gibbs sampler, fast compared to state-of-the-art techniques.
Study finds area inequalities for black hole horizons in 5D minimal supergravity.
problem Bounding the area of black hole horizons in 5D minimal supergravity.
method Established area-angular momentum-charge inequalities for stable marginally outer trapped surfaces with U(1)2 symmetry. result Unique geometries saturating the inequalities correspond to extreme black hole solutions.
Develops a universal Hermitian projective calculus for complex hyperbolic two-space
problem Complex hyperbolic geometry
method Algebraic invariant calculus
result Denominator-cleared identities for various geometric quantities
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LVY, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized field momentum obs…
Paper classifies curvature measures and confirms a conjecture.
problem Classifying curvature measures and proving the angularity conjecture.
method Investigation of translation-invariant angular curvature measures and use of isometric immersions and Lipschitz-Killing algebra.
result Confirmation of the angularity conjecture.
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which p…
Study the Hessian geometry of an ideal gas in a centrifuge.
problem Understanding the Hessian geometry of an ideal gas in a centrifuge.
method Investigate the Hessian geometry associated with an ideal gas in a spherical centrifuge, using the action of the Euclidean rotation group.
result The Hessian geometry of a spherical rigid body is isometric to a hyperbolic space in the high angular velocity limit.
In a recent paper (arXiv:math-ph/0609076) the authors investigated the basic global geometry of congruence moduli curves and shape curves of 3-body motions with vanishing angular momentum. Here the study is extended to the case of planary 3-body motions in general. In particular, the results on the separation of the si…
Polyhedra can mimic constant curvature surfaces, even with self-intersections.
problem Understanding curvature constraints in discrete vs. smooth settings.
method Constructive proof showing any surface can be realized as a polyhedral surface with uniform angular defect.
result Closed surfaces can be realized as polyhedral surfaces with constant angular defect.
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
problem Deriving transformation formulae for mass and angular momentum under BMS transformations.
method Two approaches: from curvature tensor and metric coefficients.
result Exact expressions for Drey-Streubel angular momentum of a general section.
Study improves speaker verification accuracy using angular based embedding learning.
problem Improving discriminative power of embeddings for open-set speaker verification.
method Optimizes angular distance and adds margin penalty, applying various angular margin embedding strategies and proposing inter-class regularization.
result Achieved impressive results with 16.5% improvement in EER and 18.2% improvement in minimum detection cost function.
The study proves the existence and uniqueness of near-horizon geometries for 5D black holes.
problem Existence and uniqueness of near-horizon geometries for 5-dimensional black holes.
method Proved existence and uniqueness of bi-axisymmetric near-horizon geometries with specific topologies and charges.
result Existence and uniqueness of near-horizon geometries for 5D black holes established up to isometry.
New method resolves ambiguity in measuring black hole merger angular momentum.
problem Ambiguity in measuring angular momentum during black hole mergers.
method Quasilocal mass and optimal isometric embedding theory.
result New definition of angular momentum free of supertranslation ambiguity.
New method constructs axial vector fields and defines quasi-local spin-angular momentum.
problem Constructing axial vector fields on Riemannian two-spheres.
method Using centre-of-mass unit sphere reference systems and Lie-propagated unit sphere reference systems.
result Constructive definition of quasi-local spin-angular momentum and balance relations.
Study proves inequality linking black hole properties and angular momentum.
problem Establishing a Penrose-type inequality for black holes with 3-sphere horizons.
method Analyzing biaxially symmetric, maximal, asymptotically flat initial data sets for the Einstein equations.
result Equality holds only for stationary Myers-Perry black holes.
Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.
problem Supertranslation invariance of CWY angular momentum in double null gauge.
method Identified and proved supertranslation ambiguity; showed CWY angular momentum is free of this ambiguity.
result CWY angular momentum is supertranslation invariant in double null gauge.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
problem Defining angular momentum at null infinity and ensuring its continuity across different cross-sections.
method Introducing cross-section continuity as a criterion and proving it for specific angular momentum definitions.
result The Chen-Wang-Yau definition of angular momentum satisfies cross-section continuity, while the Compere-Nichols modification does not.
New algebra structure for curvature measures in complex space forms.
problem Understanding curvature measures in complex space forms.
method Explicitly describing the algebra structure of dual unitarily invariant curvature measures.
result Characterization of invariant valuations on complex space forms.
Formulae track evolution of angular momentum and center of mass at null infinity.
problem Tracking the evolution of conserved quantities at null infinity.
method Evolution formulae in Bondi-Sachs coordinates, expressed in terms of shear and news tensors.
result Supertranslation invariance of fluxes, conservation law of angular momentum, duality paradigm.
New definition of angular momentum avoids supertranslation ambiguity.
problem Supertranslation ambiguity in angular momentum calculations.
method Derived from quasilocal angular momentum and defined at null infinity.
result First supertranslation-invariant definition of angular momentum.
Proposes AE for robust PCA, improving robustness to outliers.
problem PCA's sensitivity to outliers.
method Angular Embedding (AE) and Truncated Angular Embedding (TAE).
result AE/TAE outperforms state-of-the-art RPCA methods.
Establishes a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
problem Establishing a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
method Maximal, axisymmetric initial data for the Einstein-Maxwell equations satisfying the weak energy condition. Rigidity statement proven.
result Reduces to the conjectured Penrose inequality with angular momentum and charge under certain conditions.
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
problem Estimating the angular measure in high-dimensional data with different distributions.
method Established bounds for the maximal deviations of the empirical angular measure from the true measure, using rank transformation and analyzing the most extreme observations.
result The bounds provide performance guarantees for statistical learning procedures in extreme regions, such as binary classification and anomaly detection.
Study limits of quasi-local angular momentum at infinity of gravitating systems.
problem Understanding limits of quasi-local angular momentum at infinity of gravitating systems.
method Based on optimal isometric embedding and quasilocal mass theory, the study defines and analyzes the limits of quasi-local angular momentum at spatial and null infinity.
result Limits of quasi-local angular momentum are discussed at spatial and null infinity of an isolated gravitating system.
New memory effect discovered in gravitational wave behavior.
problem Understanding gravitational wave behavior in spacetimes with angular momentum.
method Mathematical analysis of Minkowski spacetime and Kerr black holes.
result Angular momentum memory effect observed at future null infinity.
Study finds mass bound for 3-manifolds with boundary, angular momentum, and charge.
problem Establishing precise mass lower bound for asymptotically flat 3-manifolds.
method Analyzes nonnegative scalar curvature and minimal surface boundary conditions, without simple connectivity and completeness.
result Proves mass lower bound in terms of angular momentum and charge, without restrictive assumptions.
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suffer a triple collision. Motivation for the result comes from the dream of building a symbolic dynamics for the three-body problem, one whose …
Paper proposes angular loss for better face recognition and object classification.
problem Improving intra-class compactness and preventing overfitting in face recognition and object classification.
method Angular loss function to maximize angular gradient, reducing overfitting and requiring only one adjustable constant.
result Our method outperforms other methods in accuracy, discriminative information, and time-efficiency.
Study of harmonic maps with extreme Kerr-like singularities.
problem Analyzing harmonic maps with specific singularities.
method Asymptotic analysis of harmonic maps from 3D Euclidean space to hyperbolic plane.
result Existence and classification of tangent harmonic maps at extreme black hole horizons.
Establishes inequalities linking body size, mass, angular momentum, and charge.
problem Understanding the relationship between a body's size, mass, angular momentum, and charge.
method Analyzes axisymmetric initial data sets for the Einstein equations, using a computable notion of size.
result Provides black hole existence criteria even in the time-symmetric case.
We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-Ó Murchadha-Regge-T…
Generative models improve angular variable simulation in high dimensions.
problem Lack of flexibility and scalability in simulating multivariate angular variables.
method Introducing generative adversarial networks, normalizing flows, and flow matching.
result Deep learning methods outperform classical parametric models in complex data structures.
We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …
New method uses neural networks for accurate angle estimation in noisy conditions.
problem Accurately estimate angles from noisy measurements in various applications.
method Directed Graph Neural Networks (GNNSync) for end-to-end trainable framework.
result GNNSync achieves competitive performance, even at high noise levels.
We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which …
AngularGrad optimizes CNNs by considering gradient direction, improving convergence.
problem Dying gradient problem and inefficiency in exploiting gradient curvature.
method AngularGrad considers gradient direction/angle, generating a score for step size control.
result AngularGrad outperforms state-of-the-art optimizers in benchmark tests.
In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…
We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…
AGCA approximates angular variation on the unit sphere, reducing extremal dependence problems to eigenanalysis.
problem Approximating angular variation in multivariate extremes.
method Anchored geodesic component analysis (AGCA) approximates angular variation by great subspheres constrained to pass through a chosen reference direction.
result AGCA finds concentrated tail directions in daily equity-portfolio losses, explaining about 91% of anchored variation.
Researchers prove a black hole inequality involving area, angular momentum, and charge.
problem Establishing a new inequality for black holes with a positive cosmological constant.
method Reduced to minimizing an area functional related to a harmonic map energy, maps from 2-sphere to complex hyperbolic plane.
result The inequality is saturated for extreme Kerr-Newman-de Sitter horizons.
Investigates physical properties on surfaces of rotation using Clairaut's theorem.
problem Understanding specific energy and angular momentum on surfaces of rotation.
method Used Clairaut's theorem with geodesic conditions to derive specific energy and angular momentum.
result Physical expressions for specific energy and angular momentum on surfaces of rotation were derived.
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…
Researchers calculate limits of angular momentum and center-of-mass at null infinity.
problem Evaluating angular momentum and center-of-mass limits for spacelike two-spheres approaching null infinity.
method Defined quasi-local angular momentum and center-of-mass by Chen-Wang-Yau, calculated limits for asymptotically flat spacetimes.
result Explicit expressions for angular momentum and center-of-mass at future null infinity derived in terms of spacetime observables.
New method reduces dMRI scan times by achieving sparser representations.
problem Accelerate dMRI reconstruction while maintaining high resolution.
method Joint spatial-angular sparse coding with separable dictionaries.
result Significantly sparser representations of HARDI achieved.