Combines local and global smoothing for multivariate density estimation.
problem Non-parametric multivariate density estimation.
method Combines local and global smoothing techniques.
result Simulation shows effectiveness of the method.
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169,341 papers · 148 categories
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48 results for “global smoothing”
Smooth distributions on subcartesian spaces can be globally finitely generated.
problem Understanding smooth distributions on subcartesian spaces.
method Embedding in Euclidean space, Whitney Embedding Theorem, and distribution theory.
result Smooth generalized distributions and subbundles on connected subcartesian spaces are globally finitely generated.
It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard . Similarly, a smooth 4-manifold homeomorphic to the produc…
The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.
problem Conditions for global smoothings of special Lagrangian submanifolds with isolated conical singularities.
method Proof of weaker conditions for global smoothings.
result Global smoothings are possible under weaker hypotheses than previously known.
Global and local blowups of manifolds are proven equivalent.
problem Equivalence of global and local blowups in differential topology.
method Proof of equivalence between global and local constructions of blowups.
result Global and local constructions of blowups are shown to be equivalent.
Smooth convergence shown for curve diffusion flows.
problem Embeddedness and global existence of curves.
method Exponentially fast convergence established.
result Smooth convergence for curve diffusion flows.
Smooth actions on manifolds can be globally defined under certain conditions.
problem Globalizing partial smooth actions of Lie groupoids on smooth manifolds.
method Providing necessary and sufficient conditions for globalizability and analyzing orbit and stabilizer spaces.
result There exists a unique differentiable structure on the quotient space for free and proper actions.
This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks , where is a smooth manifold equipped with a smooth proper action by a Lie group . The characterization is described in terms of the action of the connected componen…
We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is based on smooth approximations of non-smooth space-times by families (or sequences…
Global moduli theory for symplectic varieties proven.
problem Proving global moduli theory for symplectic varieties.
method Developed global moduli theory following Beauville's approach.
result Proved a global Torelli theorem for symplectic varieties.
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime admits a smooth time function whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth…
Given a globally hyperbolic spacetime , we show the existence of a {\em smooth spacelike} Cauchy hypersurface and, thus, a global diffeomorphism between and .
We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation g…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volu…
New potentials found for sheaves on Calabi-Yau 4-folds.
problem Understanding sheaves on Calabi-Yau 4-folds.
method Derived Quot-stacks and Lagrangian distributions.
result Globally defined -shifted potentials on sheaves.
Paper studies smoothness of bi-conformal heat flow on 4-manifolds.
problem Smoothness of bi-conformal heat flow on 4-manifolds.
method Introduces bi-conformal heat flow (bi-CHF) and proves global smoothness without finite time singularities.
result Global smoothness and no finite time singularity for bi-conformal heat flow.
Geroch's theorem about the splitting of globally hyperbolic spacetimes is a central result in global Lorentzian Geometry. Nevertheless, this result was obtained at a topological level, and the possibility to obtain a metric (or, at least, smooth) version has been controversial since its publication in 1970. In fact, th…
The paper investigates how Global Self-attention improves GCNs.
problem Improving expressive power and addressing overfitting in GCNs.
method Applying Global Self-attention mechanism over graph features.
result GSA mechanism enhances expressive power and mitigates overfitting and over-smoothing in GCNs.
New algorithm finds global minima in smooth nonconvex problems.
problem Smooth nonconvex optimization problems with specific properties.
method Second-order trust-region algorithm converging efficiently to global minimizer.
result Proves convergence to a global minimizer without special initializations.
The study examines differential smoothness in specific Artin-Schelter regular algebras of dimension 5.
problem Investigating the differential smoothness of Artin-Schelter regular algebras of dimension 5.
method Analyzing the relationship between the number of generators and Gelfand-Kirillov dimension to identify structural obstructions.
result Certain two- and four-generator AS-regular algebras of global dimension five fail to admit a differential calculus, while a five-generator graded Clifford algebra provides a positive example.
We describe the global structure of holomorphic webs in codimension one, and in particular their singularity (caustic). Various concepts are introduced, which have no interest locally near a regular point, such as the type, the reducibility, the quasi-smoothness, the CI property (complete intersection), the dicriticity…
Establishes unique weak solution to complex flow on smooth manifolds.
problem Existence of weak solutions to complex flow equations.
method Applying viscosity theory to prove existence of unique solution.
result Unique global weak solution exists for smooth manifolds.
StochasticRank optimizes ranking metrics efficiently and guarantees global convergence.
problem Optimizing discrete ranking metrics due to their ill-posed nature.
method Stochastic smoothing, gradient estimate, debiasing, and Stochastic Gradient Langevin Boosting.
result Global convergence and superior performance on ranking datasets.
We prove a global smooth isometric immersion for negatively curved surfaces with finite total curvature.
problem Finding a sufficient condition for a complete negatively curved surface to be isometrically embedded in R^3.
method Developed new techniques to overcome slow decay and oscillations of Gauss curvature, reformulating the Gauss-Codazzi equations as a symmetric hyperbolic system.
result Proved the global existence of a smooth solution to the Gauss-Codazzi system, achieving a global smooth isometric immersion of the surface into R^3.
Global solutions and smoothing effects for reaction-diffusion equations on manifolds.
problem Global existence and smoothing effects for reaction-diffusion equations on Riemannian manifolds.
method Functional analytic methods, Sobolev and Poincaré inequalities.
result Existence of global solutions under certain conditions on the manifold.
StoSOO optimistically maximizes noisy, locally smooth functions.
problem Global maximization of noisy, locally smooth functions with unknown semi-metric.
method StoSOO uses optimistic upper confidence bounds to iteratively decide on the next evaluation point.
result StoSOO performs almost as well as the best tuned algorithms, even without knowing the semi-metric.
The paper studies boundedness of pseudo-differential operators on smooth manifolds.
problem Boundedness of pseudo-differential operators in - spaces on smooth manifolds.
method Using global symbols and extending Hörmander's condition, the paper investigates -boundedness, - estimates, and - boundedness for Fourier multipliers and pseudo-differential operators.
result The paper proves - boundedness for the range .
The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.
problem Understanding the smooth mapping class groups of certain 4-manifolds.
method Geometric and Teichmüller-theoretic methods.
result Proves a global Torelli theorem for generalized Enriques manifolds.
We address some global solvability issues for classes of smooth nonsingular vector fields in the plane related to cohomological equations in geometry and dynamical systems. The first main result is that is not surjective in iff the geometrical condition -- the existence of separatrix str…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant -discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to…
The paper proves global existence of solutions for rough differential equations on smooth manifolds.
problem Global existence of solutions for rough differential equations on smooth manifolds.
method Sufficient conditions involving a complete Riemannian metric and bounded covariant derivatives of driving fields and their commutators.
result Global solutions exist for rough differential equations under certain conditions.
An application of Cartan's equivalence method to Hirschowitz's conjecture on the formal principlemath.AG
The formal principle holds for certain globally generated vector bundles on Fano manifolds and smooth rational curves.
problem Proving the formal principle for globally generated vector bundles on compact complex manifolds.
method Applying Cartan's equivalence method to a differential system on the universal family of the Douady space.
result The formal principle is true for Fano manifolds and smooth rational curves under specific conditions.
New methods solve non-Lipschitz smooth problems with guaranteed convergence.
problem Non-Lipschitz smooth problems in machine learning and signal processing.
method Bregman-divergence based algorithms for relatively smooth problems.
result Guaranteed convergence to second-order stationary points for any relatively smooth problem.
The paper extends local calibration pairs to global ones and finds mass-minimizing submanifolds.
problem Extending local calibration pairs to global ones in various Riemannian manifolds.
method Analyzing mass-minimizing properties and using conformal classes.
result Homologically mass-minimizing submanifolds exist in some Riemannian manifolds that cannot be calibrated by smooth calibrations.
Study curve flows with a global forcing term, proving distance comparison and convexity.
problem Analyzing the behavior of curves under curve shortening flow with a global forcing term.
method Distance comparison principle, finite time exclusion of singularities, convexity and convergence analysis.
result Convexity and smooth exponential convergence to a circle for closed curves.
Study curve flows with global forcing terms using a distance comparison principle.
problem Analyse the behavior of curves under curve flows with global forcing terms.
method Prove a distance comparison principle for curve shortening flow with arbitrary global forcing terms.
result Established a distance comparison principle for curve flows with global forcing terms.
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
Smooth, globally PŁ functions are essentially nonlinear least-squares.
problem Understanding the structure of functions satisfying the Polyak-Łojasiewicz condition.
method Analyzing smooth functions on Riemannian manifolds with the PŁ condition.
result Smooth, globally PŁ functions are of the form .
SGD converges to global minimum for certain non-convex functions.
problem Theoretical challenges in optimizing non-convex functions in machine learning.
method Perturbed SGD on a broad class of non-convex functions.
result SGD converges to global minimum for certain non-convex functions.
The abstract generalizes logarithmic derivatives for maps into homogeneous spaces and reconstructs them from infinitesimal data.
problem Reconstructing smooth maps into homogeneous spaces from infinitesimal data.
method Generalizing Cartan's logarithmic derivative to homogeneous spaces and analyzing the global monodromy obstruction.
result Determines the global monodromy obstruction and reconstructs maps from infinitesimal data.
New methods optimize functions on hyperbolic and spherical spaces, matching Euclidean rates up to logarithmic factors.
problem Optimizing functions on non-Euclidean spaces like hyperbolic and spherical geometries.
method Introduced accelerated global first-order methods for -smooth and geodesically convex functions on hyperbolic and spherical spaces.
result Achieved the same rates as accelerated gradient descent in Euclidean space, up to logarithmic factors.
Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundarymath.AP
Global calculus for manifolds with boundary, solving evolution problems.
problem Global solvability of evolution problems on manifolds with boundary.
method Established global functional calculus and Gårding inequality for pseudo-differential operators without local coordinates.
result Global solvability for a class of evolution problems.
The paper characterizes global hyperbolicity in Lorentzian manifolds without relying on manifold topology.
problem Characterizing global hyperbolicity in smooth Lorentzian manifolds without assuming manifold topology.
method Two formulations of global hyperbolicity: one using chronological diamonds and the other using properties of the Lorentzian distance function.
result The second formulation is equivalent to the definition of `Lorentzian metric space' and introduces the concept of -reflectivity.
Global weak solution found for harmonic map flow into Lorentzian manifolds.
problem Existence of global weak solutions for harmonic map flow into Lorentzian manifolds.
method Proved existence of a unique global weak solution with regularity except for finitely many singular points.
result Global weak solution found for harmonic map flow into Lorentzian manifolds.
New method finds global minima using function evaluations and kernel approximations.
problem Finding global minima of smooth functions with limited evaluations.
method Approximates the function using infinite sums of square smooth functions and solves the optimization problem with polynomial time complexity.
result Achieves optimal number of function evaluations with theoretical guarantees and nearly optimal convergence rate.
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
New method finds global Lagrangians for variational systems.
problem Constructing global variational principles for variational systems.
method Analyzing Lepage 2-forms and finding global Lagrangians for systems defined by homogeneous functions of degree \(c
eq 0, 1\).
result Locally variational systems defined by homogeneous functions of degree \(c
eq 0, 1\) are globally variational.
This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. S…