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We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…
We apply a systematic inverse design approach to discover foundry-compliant, multilayer grating couplers that can efficiently couple a number of independent waves from free space to on-chip propagating modes. For visible- and near-infrared…
Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and…
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using…
A relatively simple and accurate analytical model for studying the reflectivity of neutron multilayer monochromators and supermirrors is proposed. Design conditions that must be fulfilled in order to reach the maximum reflectivity are…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
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…
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
Perfect single-crystal neutron interferometers are adversely sensitive to environmental disturbances, particularly mechanical vibrations. The sensitivity to vibrations results from the slow velocity of thermal neutrons and the long…
Blind image deblurring is a challenging low-level vision task that involves estimating the unblurred image when the blur kernel is unknown. In this paper, we present a self-supervised multi-scale blind image deblurring method to jointly…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…
Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…
Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we…
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base…
Extending the success of 2D Large Kernel to 3D perception is challenging due to: 1. the cubically-increasing overhead in processing 3D data; 2. the optimization difficulties from data scarcity and sparsity. Previous work has taken the first…
We develop a unified framework for identifying bounds to maximum resonant nonlinear optical susceptibilities, and for "inverse designing" quantum-well structures that can approach such bounds. In special cases (e.g. second-harmonic…
Asgard/NOTT (previously Hi-5) is a European Research Council (ERC)-funded project hosted at KU Leuven and a new visitor instrument for the Very Large Telescope Interferometer (VLTI). Its primary goal is to image the snow line region around…
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…