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Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarisation of light and hence promise great utility in realisation of compact photonic devices. In this paper, we demonstrate a novel chip-scale…
It is well-known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not depend on the size or shape of the filter. These fast algorithms are generally referred to as constant-time or…
A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…
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…
We provide a $O(k^2 \mathrm{log} k)$ vertex kernel for cograph edge editing. This improves a cubic kernel found by Guillemot, Havet, Paul and Perez [1] which involved four reduction rules. We generalize one of their rules, based on packing…
We propose a novel layer-wise parameterization for convolutional neural networks (CNNs) that includes built-in robustness guarantees by enforcing a prescribed Lipschitz bound. Each layer in our parameterization is designed to satisfy a…
Photonic computing chips have made significant progress in accelerating linear computations, but nonlinear computations are usually implemented in the digital domain, which introduces additional system latency and power consumption, and…
Radio-frequency pulses are widespread for the control of quantum bits and the execution of operations in quantum computers. The ability to tune key pulse parameters such as time-dependent amplitude, phase, and frequency is essential to…
We propose to use the family of Mat\'ern kernels for implicit surface reconstruction, building upon the recent success of kernel methods for 3D reconstruction of oriented point clouds. As we show from a theoretical and practical…
In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A…
We generalize cubic norm structures to cubic norm pairs and extend hermitian cubic norm structures to arbitrary commutative unital rings. For the associated ``skew dimension one structurable algebra" of these pairs, we construct a…
Let $X_4\subset\mathbb{P}^{n+1}$ be a quartic hypersurface of dimension $n\geq 4$ over an infinite field $k$. We show that if either $X_4$ contains a linear subspace $\Lambda$ of dimension $h\geq \max\{2,\dim(\Lambda\cap…
It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional…
A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally-polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device, realized with a modified…
In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
The physical spin program at high $p_T$ region and energies $s^{1/2}_{NN} \sim 10 GeV$ is discussed. It's shown that cumulative processes, color transparency problem and polarization phenomenons directly connect with properties new form of…
Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different…