arXiv research

Proposes LRR and LRLR for improving stock prediction accuracy.

Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.

Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally dif…

Local classification of surfaces and hypersurfaces with radial mean curvature.

In this paper we find strictly locally convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed curvature and boundary. The main result is that if the given data admits a strictly locally convex radial graph as a subsolution, we can find a radial graph realizing the prescribed curvature and boundary. As an applicatio…

Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.

We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing problems arising from market models with multiple stochastic factors. We demons…

A physics-based method improves data interpolators and regression tasks.

K-StoNet improves neural networks by avoiding local minima and assessing uncertainty.

A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors tha…

While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationar…

Paper studies rigidity phenomena for elliptic systems on Riemannian manifolds.

The asymptotic Plateau problem asks for the existence of smooth complete hypersurfaces of constant mean curvature with prescribed asymptotic boundary at infinity in the hyperbolic space $\mathbb{H}^{n+1}$. The modified mean curvature flow (MMCF) was firstly introduced by Xiao and the second author a few years back, and…

For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpol…

We show theoretical similarities between the Least Squares Support Vector Regression (LS-SVR) model with a Radial Basis Functions (RBF) kernel and maximum a posteriori (MAP) inference on Bayesian RBF networks with a specific Gaussian prior on the regression weights. Although previous works have pointed out similar expr…

GPRNs accurately model stellar activity affecting RV measurements of exoplanets.

We obtain $C^2$ a priori estimates for solutions of the nonlinear second-order elliptic equation related to the geometric problem of finding a strictly locally convex hypersurface with prescribed curvature and boundary in a space form. Under the assumption of a strictly locally convex subsolution, we establish existenc…

This paper is devoted to $C^2$ a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature …

The study explores various localized bases and their duals for scattered data approximation.

Echo state network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the variance of the tea…

New exponential decay estimate for Hermitian Yang-Mills metrics near branch points.

Paper proves minimal resistance for a body in a fluid with decreasing density.

The paper generalizes radial curvature bounds on manifolds.

New research shows logistic regression can achieve optimal error rate for agnostic learning of halfspaces.

This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by …

s-RBFN integrates multiple hypotheses for efficient and diverse prediction.

In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a war…

The paper proves new Minkowski inequalities for flows in warped spaces.

We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order, namely the radial coordinate and the generalized support function. Under various assumptions we prove longtime existence and smooth convergence to a coordinate slice. We apply this result to ded…

We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in $N \times \mathbb{R}$, where $N$ is an $n$-dimensional complete Riemannian manifold with radial sectional curvature $K_{N} \leq κ$. When the immersion is minimal our estimates are sharp. We also show that …

Study examines maximal domains of radial harmonic functions across different curvature types.

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all r…

New method converts LVAs into linear projections for better understanding of complex models.

The study characterizes harmonic spaces and their radial eigen-functions and vector fields.

We give a generalization of a theorem of Bôcher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a classification of continuous radially symmetric viscosity solutions.

Tensor Neural Networks improve regression accuracy and efficiency.

No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.

A new multi-kernel RBFNN design improves performance and speed.

Study complete gradient Ricci solitons with zero radial Weyl curvature.

On a flat plane, convexity of a set is preserved by both radial expansion and contraction of the set about any point inside it. Using the Poincaré disk model of hyperbolic geometry, we prove that radial expansion of a hyperbolic convex set about a point inside it always preserves hyperbolic convexity. Using stereograph…

Study on flat singularities of area-minimizing currents in codimension one.

Paper introduces $\ell$-DER for regression tasks using morphological operators and convex-concave procedure.

Method learns radial basis function distributions from samples.

We consider smooth radial solutions to the Hamiltonian stationary equation which are defined away from the origin. We show that in dimension two all radial solutions on unbounded domains must be special Lagrangian. In contrast, for all higher dimensions there exist non-special Lagrangian radial solutions over unbounded…

New topologies for star-shaped sets without boundedness.

New algorithm radVI improves variational inference by optimizing radial profiles.

The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to …

Proves conditions for radial Kaehler metrics to be Kaehler-Einstein.