相关论文: New P$c$N and AP$c$N functions over finite fields

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…

A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…

Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…

We study the approximate fixed point property (AFPP) for continuous single-valued functions and for continuous multivalued functions in digital topology. We extend what is known about these notions and discuss errors that have appeared in…

One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…

Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite…

Let $(\Sigma_A, \sigma)$ be a subshift of finite type and let $M(x)$ be a continuous function on $\Sigma_A$ taking values in the set of non-negative matrices. We extend the classical scalar pressure function to this new setting and prove…

This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ of analytic and univalent functions in the open…

The aim of this study is to examine some numerical tests of Pade approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut and natural boundary. As pointed out by Baker, it was shown…

A recently introduced measure of Boolean functions complexity--disjunc\-tive complexity (DC)--is compared with other complexity measures: the space complexity of streaming algorithms and the complexity of nondeterministic branching programs…

Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using…

Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and…

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…

Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…

In the literature, there are many APN-like functions that generalize the APN properties or are similar to APN functions, e.g. locally-APN functions, 0-APN functions or those with boomerang uniformity 2. In this paper, we study the problem…

Differentially 4-uniform permutations on $\gf_{2^{2k}}$ with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred…

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…

This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods.…