相关论文: Vectorial Negabent Concepts: Similarities, Differe…

We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…

This note introduces a new range of modified gamma and beta $k$ functions. The authors present new modified gamma and beta $k$-functions, first and second summation relations, various functionals, Mellin transforms, and integral…

Convolution plays a crucial role in various applications in signal and image processing, analysis, and recognition. It is also the main building block of convolution neural networks (CNNs). Designing appropriate convolution neural networks…

We show the existence of many infinite classes of permutations over finite fields and bent functions by extending the notion of linear translators, introduced by Kyureghyan [12]. We call these translators Frobenius translators since the…

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…

Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design…

We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta…

Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this…

In this paper, we develop some basic techniques towards the Riemann hypothesis for higher rank non-abelian zeta functions of an integral regular projective curve of genus $g$ over a finite field $\mathbb F_q$. As an application of the…

In this paper, we investigate properties of functions from $\mathbb{Z}_{p}^n$ to $\mathbb{Z}_q$, where $p$ is an odd prime and $q$ is a positive integer divided by $p$. we present the sufficient and necessary conditions for bent-ness of…

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\v{e}k states that by inserting all cyclic permutations of some initial blocks of 2's into the multiple zeta value $ \zeta(1,3,\ldots,1,3) $ and summing, one obtains…

We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function…

The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…

We review some recent observations in theories with eight supercharges. We point out that such theories can be generalized by starting from the equations of motion rather than from an action. We show that vector multiplets constructed in…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…

In this paper, we describe a different approach to the proof of the nonexistence of homogeneous rotation symmetric bent functions. As a result, we obtain some new results which support the conjecture made in this journal, i.e., there are no…

After an elementary derivation of Bell's inequality, several forms of expectation functions for two-valued observables are discussed. Special emphasis is given to hypothetical stronger-than quantum expectation functions which give rise to a…

We propose to view hermitian metrics on trivial holomorphic vector bundles $E\to\Omega$ as noncommutative analogs of functions defined on the base $\Omega$, and curvature as the notion corresponding to the Laplace operator or…

In this paper, we construct the beta function in the functorial formulation of two-dimensional quantum field theories (FQFT). A key feature of this approach is the absence of ultraviolet divergences. We show that, nevertheless, in the FQFT…