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Automatic recognition of the historical letters (XI-XVIII centuries) carved on the stoned walls of St.Sophia cathedral in Kyiv (Ukraine) was demonstrated by means of capsule deep learning neural network. It was applied to the image dataset…
We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for an integer d. The proposed procedure can distinguish between integer-integrated time series and…
Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the butterfly algorithm considered here realizes the transfer…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Shearlet systems have so far been only considered as a means to analyze $L^2$-functions defined on $\R^2$, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
Using Fourier series representations of functions on axisymmetric domains, we find weighted Sobolev norms of the Fourier coefficients of a function that yield norms equivalent to the standard Sobolev norms of the function. This…
We present a scheme for finding all roots of an analytic function in a square domain in the complex plane. The scheme can be viewed as a generalization of the classical approach to finding roots of a function on the real line, by first…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with powers $x^n$ for binary encoded numbers $n$. It is shown that polynomial identity testing for…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
A smooth plane curve is said to admit a symmetric determinantal representation if it can be defined by the determinant of a symmetric matrix with entries in linear forms in three variables. We study the local-global principle for the…
Human observers can learn to recognize new categories of images from a handful of examples, yet doing so with artificial ones remains an open challenge. We hypothesize that data-efficient recognition is enabled by representations which make…
The paper presents a new script classification method for the discrimination of the South Slavic medieval labels. It consists in the textural analysis of the script types. In the first step, each letter is coded by the equivalent script…
Photometric data-driven classification of supernovae becomes a challenge due to the appearance of real-time processing of big data in astronomy. Recent studies have demonstrated the superior quality of solutions based on various machine…
We present an end-to-end trainable approach for Optical Character Recognition (OCR) on printed documents. Specifically, we propose a model that predicts a) a two-dimensional character grid (\emph{chargrid}) representation of a document…
We consider radially symmetric capillary surfaces that are described by bounded generating curves. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points…
Most people think that their handwriting is unique and cannot be imitated by machines, especially not using completely new content. Current cursive handwriting synthesis is visually limited or needs user interaction. We show that…