Related papers: Fourier Spectra of Binomial APN Functions
In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
We obtain an algorithm computing explicitly the values of the non solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.
Power functions with low $c$-differential uniformity have been widely studied not only because of their strong resistance to multiplicative differential attacks, but also low implementation cost in hardware. Furthermore, the…
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…
A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.
A divide-and-conquer cryptanalysis can often be mounted against some keystream generators composed of several (nonlinear) independent devices combined by a Boolean function. In particular, any parity-check relation derived from the periods…
We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
Recently, Beierle and Leander found two new sporadic quadratic APN permutations in dimension 9. Up to EA-equivalence, we present a single trivariate representation of those two permutations as $C_u \colon (\mathbb{F}_{2^m})^3 \rightarrow…
Flexible modelling of the autocovariance function (ACF) is central to time-series, spatial, and spatio-temporal analysis. Modern applications often demand flexibility beyond classical parametric models, motivating non-parametric…
We present an algorithm for the numeric calculation of antiferromagnetic resonance frequencies for the non-collinear antiferromagnets of general type. This algorithm uses general exchange symmetry approach \cite{andrmar} and is applicable…
A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…
A natural model of read-once linear branching programs is a branching program where queries are $\mathbb{F}_2$ linear forms, and along each path, the queries are linearly independent. We consider two restrictions of this model, which we…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…
Detector counting rate nonlinearity, though a known problem, is commonly ignored in the analysis of angle resolved photoemission spectroscopy where modern multichannel electron detection schemes using analog intensity scales are used. We…
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…