English
Related papers

Related papers: Deconvolution of 3-D Gaussian kernels

200 papers

We introduce a generalized Rayleigh-quotient on the tensor product of Grassmannians enabling a unified approach to well-known optimization tasks from different areas of numerical linear algebra, such as best low-rank approximations of…

Optimization and Control · Mathematics 2011-12-01 O. Curtef , G. Dirr , U. Helmke

This paper makes two main contributions. First, we present a pedagogical review of the derivation of the three-term recurrence relation for Legendre polynomials, without relying on the classical Legendre differential equation, Rodrigues'…

Computational Engineering, Finance, and Science · Computer Science 2025-07-15 Michal Béreš

We derive expressions required in generalizing the Gutzwiller approximation to models comprising arbitrarily degenerate localized orbitals.

Condensed Matter · Physics 2009-10-30 Takuya Okabe

In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($\Gamma$) matrices as the degrees of freedom on each site. We show that these models result in…

Statistical Mechanics · Physics 2022-08-31 Yash Chugh , Kusum Dhochak , Uma Divakaran , Prithvi Narayan , Amit Kumar Pal

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…

Artificial Intelligence · Computer Science 2011-09-22 Andrew Cotter , Joseph Keshet , Nathan Srebro

We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of…

Numerical Analysis · Mathematics 2020-01-10 Toni Karvonen , Simo Särkkä

The method of covariant perturbation theory allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the covariant effective action introduces the universal…

General Relativity and Quantum Cosmology · Physics 2021-03-31 Yuri Vladimirovich Gusev

A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…

Quantum Physics · Physics 2007-05-23 Jiannis Pachos

In this paper, we derive some explicit expansion formulas associated to Brenke polynomials using operational rules based on their corresponding generating functions. The obtained coefficients are expressed either in terms of finite double…

Classical Analysis and ODEs · Mathematics 2023-02-01 H. Chaggara , A. Gahami and , N. Ben Romdhane

In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…

Classical Analysis and ODEs · Mathematics 2023-05-23 Leon A. Luxemburg , Steven B. Damelin

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Machine Learning · Computer Science 2014-03-18 John Moeller , Parasaran Raman , Avishek Saha , Suresh Venkatasubramanian

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical…

Machine Learning · Statistics 2012-12-17 Nicolas Durrande , David Ginsbourger , Olivier Roustant , Laurent Carraro

Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…

Mathematical Physics · Physics 2015-01-28 Mark W. Coffey

New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional…

Quantum Physics · Physics 2009-11-10 N. Debergh , J. Ndimubandi , B. Van den Bossche

We discuss a (i) quantized version of the Jordan decomposition theorem for a complex Borel measure on a compact Hausdorff space, namely, the more general problem of decomposing a general noncommutative kernel (a quantization of the standard…

Operator Algebras · Mathematics 2022-02-04 Joseph A. Ball , Gregory Marx , Victor Vinnikov

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals…

General Mathematics · Mathematics 2020-09-29 Jack C. Straton

We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…

Analysis of PDEs · Mathematics 2012-12-17 Habib Ammari , Daewon Chung , Hyeonbae Kang , Han Wang

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

Numerical Analysis · Mathematics 2023-05-19 Alex Barnett , Philip Greengard , Manas Rachh

Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite-Laguerre Gauss modes in terms of a Jones vector, traditionally used to…

Optics · Physics 2019-08-06 R. Gutiérrez-Cuevas , M. R. Dennis , M. A. Alonso

In this paper, a polynomial-time algorithm is given to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Groebner basis of the Z[x]-module generated by the column vectors of F. The algorithm…

Symbolic Computation · Computer Science 2016-07-22 Rui-Juan Jing , Chun-Ming Yuan , Xiao-Shan Gao