New loss function improves adversarial robustness without sacrificing standard accuracy.
problem Adversarial robustness requires more samples than standard accuracy, and new data collection is costly.
method Proposed Max-Mahalanobis center (MMC) loss to concentrate feature points in the feature space.
result Empirical results show MMC loss significantly improves robustness under strong adaptive attacks.
A new method centers outliers in robust PCA without manual intervention.
problem Outliers in robust PCA require manual centering, complicating the analysis.
method Introduces a 'bias trick' to automatically center non-outliers.
result First optimal RPCA algorithm with automatic centering.
Center identified in stated skein algebra for quantum traces.
problem Understanding the center of the stated skein algebra.
method Analyzing the algebra as a generalization of Kauffman bracket skein algebra, focusing on the case when the quantum parameter is a root of unity.
result Simple description and dimension calculation of the center over the center module.
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the kernel, such centers are called a radial center or an illuminating center, respec…
Refines geometric center of mass analysis for Einstein field equations.
problem Analyzing the geometric center of mass of Willmore surfaces in initial data for Einstein field equations.
method Refined Lyapunov-Schmidt analysis to study geometric center of mass of area-constrained Willmore surfaces.
result The geometric center of mass agrees with the Hamiltonian center of mass under specific conditions.
Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center…
We investigate centers of a body (the closure of a bounded open set) defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson's integral. These centers, in general, depend on parameters and move with respect to the parameters. We give a necessary and suffici…
We prove the existence of a center, or continuous selection of a point, in the relative interior of C1 embedded k-disks in Riemannian n-manifolds. If k≤3 the center can be made equivariant with respect to the isometries of the manifold, and under mild assumptions the same holds for k=4=n. By contrast, for…
This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i) centering results in a different but equivalent parameterization for artificial neural …
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
problem Clustering concatenated noisy vectors from multiple sources.
method Asymptotic analysis of weighted sum of distances to a common cluster center.
result The clustering approach outperforms naive methods in terms of average distortion.
In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the …
This article briefly introduced Arthur and Vassilvitshii's work on \textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…
Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.
problem Understanding the dynamics of absolutely partially hyperbolic surface endomorphisms.
method Showed the existence of a center foliation and leaf conjugacy to the linearization.
result Absolutely partially hyperbolic surface endomorphisms have a dynamically coherent center foliation.
Suppose one is faced with the challenge of tissue segmentation in MR images, without annotators at their center to provide labeled training data. One option is to go to another medical center for a trained classifier. Sadly, tissue classifiers do not generalize well across centers due to voxel intensity shifts caused b…
Introduces Quantum Data Center for quantum era benefits.
problem No specific problem stated; focuses on future potential.
method Combines QRAM and quantum networks.
result QDC offers efficiency, security, and precision.
Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
Characterizes G2-structures on Lie algebras with non-trivial center.
problem Classifying Lie algebras with G2-structures.
method Analyzing Lie algebras with non-trivial center, using contactization and symplectic properties.
result Six unimodular Lie algebras with non-trivial center admit closed G2-structures.
Paper introduces new center of mass for flat manifolds.
problem Defining center of mass for asymptotically flat manifolds.
method Using double forms of Kulkarni and Labbi to prove existence and well-definedness.
result Existence and well-definedness of the Gauss-Bonnet-Chern center of mass.
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
problem Proving the uniqueness of the mass center system in non-Euclidean geometries and deriving a generalized Pappus' theorem.
method Revisiting and simplifying G.A. Galperin's proof, extending the mass center system to manifolds, and deriving a generalized Pappus' theorem.
result Unified and simpler proofs for Pappus' theorem in Euclidean, spherical, and hyperbolic geometries.
New features for quantum calculations learn N-center Hamiltonian matrix elements.
problem Quantum calculations need features for N-center Hamiltonians, not just atom-centered ones.
method Developed fully equivariant N-center features for machine learning.
result Learned matrix elements of N-center Hamiltonians efficiently.
Smoothly conjugate perturbations of certain toral automorphisms.
problem Smoothly conjugating perturbations of partially hyperbolic toral diffeomorphisms.
method Study of perturbations of partially hyperbolic toral automorphisms with smooth center foliations.
result Existence of smooth leaf conjugacy for small perturbations of L with smooth center foliation.
For nearly spherical bodies, the unique center is proven under certain conditions.
problem Finding the unique center of nearly spherical bodies.
method Using regularized Riesz potential and asphericity measure.
result The $r^{\an}$-center is unique for sufficiently close bodies to a ball.
We show that the center of the Goldman algebra associated to a closed oriented hyperbolic surface is trivial. For a hyperbolic surface of finite type with nonempty boundary, the center consists of closed curves which are homotopic to boundary components or punctures.
Diameters of ball intersections decrease as centers move apart.
problem Behavior of intersections of moving balls in Riemannian manifolds.
method Continuous decrease of intersection diameter as centers move apart.
result Diameter of intersections decreases continuously.
The paper studies properties of stated SL(n)-skein algebras and their centers.
problem Properties of stated SL(n)-skein algebras and their centers.
method Quantum trace maps and embeddings into quantum tori.
result Finitely generation and PI-degrees of centers of stated SL(n)-skein algebras.
The center of a quotient group of piecewise linear homeomorphisms is trivial.
problem Understanding the structure of a specific group of homeomorphisms.
method Analyzing a quotient of piecewise linear homeomorphisms of the real line.
result The center of the quotient group is trivial.
The classical notion of center of mass for an isolated system in general relativity is derived from the Hamiltonian formulation and represented by a flux integral at infinity. In contrast to mass and linear momentum which are well-defined for asymptotically flat manifolds, center of mass and angular momentum seem less …
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…
Let f:M→M be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of f is one-dimensional, then the volume of center leaves must be bounded in M.
Proposes a new ridge estimator for smooth covariates with adaptive centering.
problem Estimating coefficients and center function for smooth covariates in linear models.
method SACR framework with convex formulation, roughness penalty, and adaptive centering.
result Improves prediction and variable selection for smooth covariates.
Classifies a specific type of Lie groups related to Einstein geometry.
problem Classifying Einstein Lorentzian 3-nilpotent Lie groups with 1-dimensional nondegenerate center.
method Complete classification through mathematical analysis.
result A full classification of the specified Lie groups.
Anosov flow found in specific partially hyperbolic systems.
problem Characterizing partially hyperbolic diffeomorphisms with center foliation.
method Analyzing transitive dynamically coherent systems with one-dimensional center foliation.
result Discretized Anosov flow found in systems satisfying f(W)=W for center leaves. Method computes centers of Poisson and skein algebras for loops on surfaces.
problem Computing centers of Poisson and skein algebras associated to loops on surfaces.
method Systematic method using Goldman and Wolpert's Poisson algebras and Turaev's skein algebras.
result Computed centers of various Poisson and skein algebras for finite type hyperbolic surfaces.
This paper examines the impact of centering in PCA and SVD.
problem The influence of centering in PCA and SVD.
method Detailed exploration of centering in PCA and SVD.
result Two PCA embeddings derived from SVD with and without centering can be aligned under certain conditions.
Study on Poncelet polygons' centers and circumcenters in various geometries.
problem Understanding Poncelet polygons' geometric centers in different geometries.
method Analyzing the Circumcenter of Mass and Center of Mass of Poncelet polygons, proving Dan Reznik's invariants, and exploring spherical geometry.
result Proof of Dan Reznik's invariants for billiard trajectories and insights into Poncelet polygons' centers in spherical geometry.
Study centers of quantum tori and skein algebras for even roots of unity.
problem Understanding the center of quantum tori and skein algebras for even roots of unity.
method Analyzing quantum tori and skein algebras, computing PI-degree, and decomposing matrices.
result PI-degrees of quantum tori and skein algebras are the same.
New Lie groups generalize H-type groups with nondegenerate centers.
problem Generalizing H-type groups with nondegenerate centers.
method Defined and investigated 2-step nilpotent Lie groups.
result Geometric properties of new Lie groups investigated.
Study the monodromy and center-focus problems for rational maps defined by products of generic lines.
problem Monodromy and center-focus problems for rational maps defined by products of generic lines.
method Analyze the 1-homology group and meromorphic 1-forms to characterize vanishing Abelian integrals.
result Characterize meromorphic 1-forms whose Abelian integrals vanish on cycles around a center singularity.
Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at ze…
Study partially hyperbolic dynamics on 3-manifolds with quasi-isometric center.
problem Characterize dynamics on 3-manifolds with specific center properties.
method Analyzes partially hyperbolic diffeomorphisms with quasi-isometric center under non-wandering conditions.
result Volume-preserving diffeomorphisms are ergodic without su-tori, confirming a conjecture. A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin, and that these representatives are unique up to Möbius transformations of the sphere. Motivated by this result, various papers investigate the prob…
We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the sa…
The paper explores uniform perfectness and centers in Morse boundaries.
problem Detecting κ-center exhaustivity in uniformly perfect Morse boundaries. method Analyzes CAT(0) and geodesic spaces, using visual boundary data and metric transforms.
result Fixed-basepoint uniform perfectness is insufficient for κ-center exhaustivity. MDCN improves treatment effect estimation in multicenter observational studies.
problem Incongruities in multicenter observational studies due to center-specific protocols and treatment reactions.
method MDCN learns a new feature embedding to address selection bias and strengthen information sharing between similar centers.
result MDCN provides more accurate treatment insights for new, unobserved centers compared to existing methods.
Study Einstein metrics on nilpotent Lie groups, focusing on degenerate centers and degenerate Euclidean subalgebras.
problem Characterize Lorentzian left invariant Einstein metrics on nilpotent Lie groups.
method Analyzing Lie algebras and using double extension process to classify metrics.
result All nilpotent Lie groups up to dimension 5 with Lorentzian Einstein metrics have degenerate center.
Study centers of generalized skein algebras, showing almost Azumaya properties.
problem Understanding the center of generalized skein algebras.
method Generalized skein algebra generated by loops and arcs, computed center, discussed implications.
result Center of Muller-Roger-Yang skein algebra is almost Azumaya.
Extends orbital integral evaluation to center of enveloping algebra.
problem Evaluate semisimple orbital integrals for arbitrary elements in the center of the enveloping algebra.
method Explicit geometric evaluation of Casimir operator to arbitrary elements in the center of the enveloping algebra.
result Extension of orbital integral evaluation to center of enveloping algebra.