Related papers: Deconvolution of 3-D Gaussian kernels

It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In…

The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly…

We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if…

A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…

Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schr\"odinger operators for Calogero-Sutherland-type quantum systems. For the generalized…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

We compute explicitly the Bergman kernels of all two dimensional monomial polyhedra, a class of domains including the Hartogs triangle and some of its generalizations. The kernel is computed from the representation of such domains as…

In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite…

We extensively develop a method of implementing mean-field calculations for deformed nuclei, using the Gaussian expansion method (GEM). This GEM algorithm has the following advantages: (i) it can efficiently describe the energy-dependent…

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…

We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of…

We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels…

The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality…

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…

We study generalized Hermite polynomials with rectangular matrix arguments arising in multivariate statistical analysis and the theory of zonal polynomials. We show that these are well-suited for expressing the Wiener-Ito chaos expansion of…

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kahler manifold X, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the N=2…

Existing ultrasound deconvolution approaches unrealistically assume, primarily for computational reasons, that the convolution model relies on a spatially invariant kernel and circulant boundary conditions. We discard both restrictions and…

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables…