In this article, we obtain a strict inequality between the conjugate Hardy kernels and the Bergman kernels on planar regular regions with boundary components, which is a conjecture of Saitoh.
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17 results for “L^2-kernel”
Improved outlier detection in hierarchical Gaussian Processes using Wasserstein-2 kernels.
problem Outlier detection limitations in stacked Gaussian Processes.
method Proposed a hybrid kernel combining Euclidean and Wasserstein-2 distances, emphasizing variance in Wasserstein-2 computations.
result Improved performance and enhanced out-of-distribution detection on various datasets.
We propose a new analytical approximation to the kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments show the new approximation leads to improved performance in image classification and …
We give results about the L^2 kernel and the spectrum of the Dirac operator on a complete Riemannian manifold which is conformally equivalent to the interior of a Riemannian manifold with nonempty boundary.
The paper proves conditions for the triviality of -harmonic forms on Riemannian manifolds.
problem Conditions for the triviality of -harmonic forms on Riemannian manifolds.
method Study of a covariant Schrödinger operator and its -kernel.
result Sufficient conditions for the triviality of the -kernel of .
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (). Interestingly, for a …
Taming Nonconvexity in Kernel Feature Selection -- Favorable Properties of the Laplace Kernelmath.ST
Laplace kernel feature selection offers statistical guarantees for nonparametric models with few samples.
problem Statistical guarantees for kernel-based feature selection in nonconvex optimization problems.
method Sharp characterization of the gradient of the objective function for Laplace kernel feature selection.
result Model-selection consistency for Laplace kernel-based feature selection in nonparametric settings with samples.
The paper characterizes Eguchi-Hanson space and its higher-dimensional analogs using Lichnerowicz Laplacian.
problem Characterizing complete Ricci-flat ALE orbifolds.
method Analytical proof using Lichnerowicz Laplacian and dimension constraints.
result Uniqueness of Eguchi-Hanson space and its higher-dimensional analogs among Ricci-flat Kähler ALE orbifolds.
We prove that many complete, noncompact, constant mean curvature (CMC) surfaces are nondegenerate; that is, the Jacobi operator has no kernel. In fact, if has genus zero and is contained in a half-space, then we find an explicit upper bound for the dimension of the j…
New method finds 198,846 toric-colorable seeds of Picard number 5.
problem Enumerating toric-colorable seeds of Picard number 5.
method Binary matroid approach and dynamic programming algorithm.
result 198,846 mod 2 toric-colorable seeds of dimension four and Picard number five.
Study proves existence, uniqueness, and stability for specific stochastic Volterra equations.
problem Analyzing existence, uniqueness, and stability of affine stochastic Volterra equations with -kernels.
method Approximations with -kernels, stability result, duality argument, deterministic Riccati--Volterra integral equation.
result Established weak uniqueness for the equations using Fourier--Laplace transform and a deterministic Riccati--Volterra integral equation.
We study the geometry of families of hypersurfaces in Eguchi-Hanson space that arise as complex line bundles over curves in and are three-dimensional, non-compact Riemannian manifolds, which are foliated in Hopf tori for closed curves. They are negatively curved, asymptotically flat spaces, and we compute the com…
Novel heat flow estimates on ALE manifolds for Schrödinger operators.
problem Estimating heat flows on ALE manifolds with non-trivial -kernel.
method Combining Fredholm theory for Dirac type operators and heat kernel advances.
result Established decay estimates for heat flows.
Monotone 2D Integration Scheme for Mean-CVaR Optimization via Fourier-Trained Transition Kernelsmath.OC
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
We study the use of "sign -stable random projections" (where ) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and near-neighbor search). After the processing by sign stable random projections, the inner pr…
Paper proposes a new GPR-HS framework for accurate VCV estimation in global equity indices.
problem Accurate forecasting of Volatility-Covariance Matrix (VCV) for regulatory processes.
method Hybrid Gaussian Process Regression-Historical Simulation (GPR-HS) framework.
result GPR-HS framework achieves regulatory compliance and outperforms static VaR benchmarks.
This study evaluates Bayesian optimization algorithms on a wide range of problems.
problem Assessing the performance of Bayesian optimization algorithms across diverse problems.
method A comprehensive investigation using the COCO benchmark, comparing various design choices.
result Optimizing acquisition criteria and initial budget can significantly improve BO performance.