Related papers: Kernel Formula Approach to the Universal Whitham H…

Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…

We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial…

We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where…

While there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping…

We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order in perturbation theory. In particular we…

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two…

We present a new kernel-based algorithm for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method reorganizes the typical single-layer kernel-based model into a deep…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative examples. It is shown…

A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…

It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy…

An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…

We quantize Hamiltonian structures with hydrodynamic leading terms using the Heisenberg vertex algebra. As an application, we construct the quantum dispersionless KdV hierarchy via a non-associative Weyl quantization procedure and compute…

To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable…

Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…

This article presents a formula for some dispersionless equations and a brief review of the operators which have been used for the dispersionless KP hierarchy.

We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial value problem for the zero dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem,…

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on…

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced…