arXiv research

New non-trivial Kaehler-Ricci solitons found in infinite dimensional complex space forms.

Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area enclosed by the evolving curve, and this fact is used to prove a gene…

Unified framework for imbalanced data resampling improves classification performance.

Extends potential theory to Carnot groups, estimating Hausdorff dimension.

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 …

Paper proposes new methods for improving interatomic potentials.

The paper characterizes potential functions whose level sets are orbits in mechanical systems.

This paper derives radial fields on manifolds of symmetric positive definite matrices.

The study examines exceptional sets for radial limits of superharmonic functions on curved manifolds.

We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally arises in the study of Ricci solitons structures. We prove existence and nonexistence results, focusing on the radial case, under some gene…

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…

We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of the potential into a smaller closed region contained in the interior of the body, …

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…

Data imbalance remains one of the most widespread problems affecting contemporary machine learning. The negative effect data imbalance can have on the traditional learning algorithms is most severe in combination with other dataset difficulty factors, such as small disjuncts, presence of outliers and insufficient numbe…

We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by radial measures, and find the complete asymptotic expansion of the corresponding reproducing kernels for Kähler potentials, both in the flat and bounded setting.

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…

The paper proves geometric comparisons on metric measure spaces with integral Bakry-Émery Ricci tensor bounds.

Study regularity of Schrödinger eigenfunctions with Coulomb-type potentials.

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the…

The paper generalizes radial curvature bounds on manifolds.

This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "Landau-Ginzburg potentials" that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and Zhang's trigonometric…

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

Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.

Study automates feature selection and clustering for HFT stock price forecasting.

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

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

Study complete gradient Ricci solitons with zero radial Weyl curvature.

In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product with $(n-1)$-dimensional…

Study on rigidity and characterization of generalized quasi-Einstein manifolds.

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.

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…

Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support-they assign zero…

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

Radial graphs with constant mean curvature found in Euclidean space.

Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. The main goal of this paper is to estimate the lower bound for the interval (0,T], where these two eigenfunctions must assume different values…

Study proves radial symmetry in convex cones using subharmonic functions.

We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian $n$-manifold $M$ having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …

We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher acc…

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

Study on manifolds with density using modified Hessians for curvature comparison.

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.