相关论文: A new APN function which is not equivalent to a po…
We give a new simple construction for known binary quadratic symmetric bent and almost bent functions. In particular, for even number of variables, they are self-dual and anti-self-dual quadratic bent functions, respectively, which are not…
In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\sqrt{m})$ where $m$ is the size of…
This article presents examples of an application of the finite field method for the computation of the characteristic polynomial of the matching arrangement of a graph. Weight functions on edges of a graph with weights from a finite field…
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
It is well known that constructing codes with good parameters is one of the most important and fundamental problems in coding theory. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes…
We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously…
Using recent results on solving the equation $X^{2^k+1}+X+a=0$ over a finite field $\mathbb{F}_{2^n}$, we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions $x\mapsto…
We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for…
APN functions play a big role as primitives in symmetric cryptography as building blocks that yield optimal resistance to differential attacks. In this note, we consider a recent extension of a biprojective APN family by G\"olo\u{g}lu…
In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers.…
The active power filter (APF) is attracting more and more attention for its outstanding performance in current and voltage ripple compensation. As modern high-energy accelerators are demanding much more stringent current ripple guideline,…
Optimal Power Flow (OPF) is a very traditional research area within the power systems field that seeks for the optimal operation point of electric power plants, and which needs to be solved every few minutes in real-world scenarios.…
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…
A deep neural network for classification tasks is essentially consist of two components: feature extractors and function approximators. They usually work as an integrated whole, however, improvements on any components can promote the…
We investigate the interpolation of power spectra of matter fluctuations using Artificial Neural Network (PkANN). We present a new approach to confront small-scale non-linearities in the power spectrum of matter fluctuations. This…
Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…
Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding in \cite{D} constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar…
We consider image sets of differentially $d$-uniform maps of finite fields. We present a lower bound on the image size of such maps and study their preimage distribution, by extending methods used for planar maps. We apply the results to…