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In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the…
We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…
We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted…
This paper presents a conformal prediction method for classification in highly imbalanced and open-set settings, where there are many possible classes and not all may be represented in the data. Existing approaches require a finite, known…
We obtain a new upper estimate on the Euclidean diameter of the intersection of the kernel of a random matrix with iid rows with a given convex body. The proof is based on a small-ball argument rather than on concentration and thus the…
In this paper we investigate the complex exponential integral means spectra of univalent functions in the unit disk. We show that all integral means spectrum (IMS) functionals for complex exponents on the universal Teichm\"uller space, the…
We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…
We devise a fast and optimal estimator for the amplitude of the bispectrum of clustered Infrared (IR) point-sources. We show how this estimator can account for the cases of partial sky coverage and inhomogeneous noise. Expected detection…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
We report the measurement of a large optical reflection matrix (RM) of a highly disordered medium. Incident optical fields onto a turbid sample are controlled by a spatial light modulator, and the corresponding fields reflected from the…
We use the measurement of the cosmic microwave background taken during the MAXIMA-1 flight to estimate the bispectrum of cosmological perturbations. We propose an estimator for the bispectrum that is appropriate in the flat sky…
We develop a classification of perfectly transmitting resonances occuring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield…
Conformal prediction can yield statistically valid prediction intervals for any regression model, with no model modifications and small computational costs. To assess its practical value, we apply conformal methods to quantify uncertainty…
We prove new unconditional results of sparsity of integral points on orbits under many maps and correspondences in arbitrary dimensions, generalizing theorems of Yasufuku(2015) and others. The main ingredients are new diophantine…
We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$. Under various assumptions we establish the…
Scattering by infinite hexagonal ice prisms is calculated using Maxwell's equations in the discrete dipole approximation for size parameters up to x=400. Birefringence is included in the calculations. Applicability of the geometric optics…
We investigate the asymptotic distribution of integrals of the $j$-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we prove a bound for sums of Kloosterman sums…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…