Related papers: Weakly-normal basis vector fields in RKHS with an …

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

For the case of algebraic curves - compact Riemann surfaces - it is shown that de Rham cohomology group $H^{1}_{\mathrm{dR}}(X,\mathbb{C})$ of a genus $g$ Riemann surface $X$ has a natural structure of a symplectic vector space. Every…

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Groebner bases.…

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of…

For a planar domain $\Omega$, we consider the Dirichlet spaces with respect to a base point $\zeta\in\Omega$ and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note,…

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access to their local data streams. We focus on the case where agents seek…

Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space $X$, our paper studies elements of vector analysis, $L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to…

We study reproducing kernel Hilbert spaces introduced as ranges of generalized Ces\`aro-Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…

Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…

The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…

Mutually unbiased bases and discrete Wigner functions are closely, but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime $N=d^n$, which describes a composite…

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…