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In this paper we present a new class of perfect nonlinear %Dembowski-Ostrom polynomials over $\mathbb{F}_{p^{2k}}$ for any odd prime $p$. In addition, we show that the new perfect nonlinear functions are CCZ-inequivalent to all the…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
We give examples of $L^{1}$-functions that are essentially unbounded on every nonempty open subset of their domains of definition. We obtain such functions as limits of weighted sums of functions with the unboundedly increasing number of…
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm…
Let $p$ be an odd prime number. We prove that for $m\equiv1\mod p$, $x^m$ is perfectly nonlinear over $\mathbb{F}_{p^n}$ for infinitely many $n$ if and only if $m$ is of the form $p^l+1$, $l\in\mathbb{N}$. First, we study singularities of…
Random feature model with a nonlinear activation function has been shown to perform asymptotically equivalent to a Gaussian model in terms of training and generalization errors. Analysis of the equivalent model reveals an important yet not…
Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…
The investigation of partially APN functions has attracted a lot of research interest recently. In this paper, we present several new infinite classes of 0-APN power functions over $\mathbb{F}_{2^n}$ by using the multivariate method and…
The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall…
We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary isogeny classes.
Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show…
Recently, a new concept called multiplicative differential cryptanalysis and the corresponding $c$-differential uniformity were introduced by Ellingsen et al.~\cite{Ellingsen2020}, and then some low differential uniformity functions were…
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
The expressivity of Graph Neural Networks (GNNs) is dependent on the aggregation functions they employ. Theoretical works have pointed towards Sum aggregation GNNs subsuming every other GNNs, while certain practical works have observed a…
In a recent paper [Trans. Amer. Math. Soc. 378 (2025), 851-883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The present paper shall extend the study of generalized…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…