Related papers: Multiplication kernels
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
In this article, we study higher Nil $K$-groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$-groups in terms of binary complexes.
We introduce a method to construct general multivariate positive definite kernels on a nonempty set $X$ that employs a prescribed bounded completely monotone function and special multivariate functions on $X$.\ The method is consistent with…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula and explicit formula. We find a connection between multidimensional permutations…
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…
Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated uniformly in the framework of localizable spaces of…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a…
We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group $G$ lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian $LG$-manifolds arising from…
This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…
This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the…
The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and…
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…
We introduce the notion of "binary" positive and complex geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. We also define open and closed "cluster…