Related papers: (Not) weakly regular univariate bent functions

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…

We obtain new nonexistence results for two classes of generalized bent functions from $\mathbb{Z}_{q}^{n}$ to $\mathbb{Z}_{q}$, called type $[n,q]$ generalized bent functions. The first class concerns the case $q=2 p_1^{e_1} p_2^{e_2}$,…

We obtain the following results. For any prime $q$ the minimal Hamming distance between distinct regular $q$-ary bent functions of $2n$ variables is equal to $q^n$. The number of $q$-ary regular bent functions at the distance $q^n$ from the…

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…

The main contribution of this paper is to find a representation of the class $\mathcal{F}_d(p)$ of multivariate Bernoulli distributions with the same mean $p$ that allows us to find its generators analytically in any dimension. We map…

Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…

We introduce the class of semiweak Cullen-regular quaternionic functions by interpreting Cullen-regular functions as solutions to an inhomogeneous PDE in terms of the Fueter operator.

Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how…

Planar functions over finite fields give rise to finite projective planes. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and codebooks. They were originally defined only in finite fields with…

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

This paper is concerned with the approximation of continuously differentiable functions with high-dimensional input by a composition of two functions: a feature map that extracts few features from the input space, and a profile function…

We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…

Let $n$ and $k$ be positive integers, and $f_n(k)$ (resp. $g_n(k)$) be the number of unital subrings (resp. unital irreducible subrings) of $\mathbb{Z}^n$ of index $k$. The numbers $f_n(k)$ are coefficients of certain zeta functions of…

Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $, be a rational function that simultaneously interpolates $ f_0 $ at the origin with order $…

We use a constructive method to obtain all but finitely many p-local representation zeta functions of a family Mn of finitely generated nilpotent groups with maximal nilpotency class. For representation dimensions coprime to all primes p <…

Let $\mathcal{P}$ be the set of the primes. We consider a class of random multiplicative functions $f$ supported on the squarefree integers, such that $\{f(p)\}_{p\in\mathcal{P}}$ form a sequence of $\pm1$ valued independent random…