arXiv research

The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or O(n*log(n)) for constructing a classifier, where n is the number of sampling instances.…

Bayesian inference engines improve density estimation accuracy and scalability.

Interactive privacy mechanisms improve spectral density estimation under local differential privacy.

This article proposes a novel density estimation based algorithm for carrying out supervised machine learning. The proposed algorithm features O(n) time complexity for generating a classifier, where n is the number of sampling instances in the training dataset. This feature is highly desirable in contemporary applicati…

Study on regularity of optimal transport maps on convex domains with quadratic cost.

Robustly infers manifold density and geometry under high-dimensional noise.

We propose a natural definition of the weighted $σ_k$-curvature for a manifold with density; i.e.\ a triple $(M^n,g,e^{-φ}\mathrm{dvol})$. This definition is intended to capture the key properties of the $σ_k$-curvatures in conformal geometry with the role of pointwise conformal changes of the metric replaced by pointw…

Proves well-posedness for Einstein equations with specific boundary conditions.

Study minimax robustness in statistical estimation under Wasserstein contamination.

MFRDE uses medians of forest estimators to robustly estimate densities in noisy data.

EagleEye detects localized density anomalies in multivariate data.

Proposes DISCO, the first CVI for density-based clustering with noise.

This paper provides a neural approach to represent option implied information.

The paper analyzes Laplace learning for Gaussian measure data in infinite dimensions, proving convergence.

FourNet approximates financial transition densities using Fourier transforms.

Given a compact manifold $N^n \subset \mathbb{R}^ν$, $s \ge 1$ and $1 \le p < \infty$, we prove that the class of smooth maps on the cube with values into $N^n$ is strongly dense in the fractional Sobolev space $W^{s, p}(Q^m; N^n)$ when $N^n$ is $\lfloor sp \rfloor$ simply connected. For $sp$ integer, we prove weak den…

Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no pr…

The purpose of this paper is to study pointwise pseudo-slant warped product submanifolds of a Kähler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a pointwise pseudo-slant submanifold of $\widetilde{M}$. The nec…

We introduce the notions of pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, pointwise slant submanifolds, semi-slant submanifolds, and pointwise semi-slant submanifolds. We have characterizations and investigate the integrability of distrib…

As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of pointwise slant submanifolds and pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of pointwise slant submanifolds,…

Study properties of pointwise k-slant submanifolds in Kähler manifolds.

The paper studies a new type of submanifolds in product spaces.

Introduces $k$-slant distributions and submanifolds in various geometric settings.

Study on slant submanifolds with new conditions and transitivity.

In this paper, we study rotational surfaces of elliptic, hyperbolic and parabolic type with pointwise 1-type Gauss map which have spacelike profile curve in four dimensional pseudo Euclidean space E4-2 and obtain some characterizations for these rotational surfaces to have pointwise 1-type Gauss map.

We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hyper…

In this paper we contribute a novel algorithm family, which generalizes many unsupervised techniques including unnormalized and energy models, and allows us to infer different statistical modalities (e.g. data likelihood and ratio between densities) from data samples. The proposed unsupervised technique, named Probabil…

In this paper, we proved a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

Language models can predict numeric values as strings.

The paper studies geometric properties of a specific type of submanifolds in Kaehler manifolds.

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space E41. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface…

In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Cl…

Study bounds derivatives of solutions to a specific equation on domains.

Paper introduces second-order Esscher densities for continuous-time models.

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if…

Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation dimension. There are two major difficulties in estimation based on this method. …

An affine hypersurface $M$ is said to admit a pointwise symmetry, if there exists a subgroup $G$ of ${\rm Aut}(T_p M)$ for all $p\in M$, which preserves (pointwise) the affine metric $h$, the difference tensor $K$ and the affine shape operator $S$. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. $S…

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

In this paper, we study some properties of warped product pointwise bi-slant submanifolds in locally metallic Riemannian manifolds and we construct some examples in Euclidean spaces.

It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant s…

It is proved that if an almost Kähler manifold of dimension greater or equal to 8 is of pointwise constant antiholomorphic sectional curvature, then it is a complex space form.

Researchers develop neural networks for approximating functions in Banach spaces.

This paper, focusing on the growth rate of the measure, gives pointwise bounds of solutions of eigenvalue equations of the Laplace-Beltrami operator on noncompact Riemannian manifolds.

Paper provides estimates for varifolds with critical mean curvature.

Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models. Based on finite sample variances, confidence inte…

Study constructs scattering theory for massless Dirac field on Kerr spacetime.