Related papers: Axioms for consensus functions on the n-cube

For functions defined on the $n$-dimensional hypercube $I_n (r) = \{{\bm{x}} \in \mathbb{R}^n ~\vert~ \vert x_i \vert \le r,~ i = 1, 2, \ldots , n\}$ and harmonic therein, we establish certain analogues of Gauss surface and volume…

Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…

In this article we introduce a general definition of the concept of center of an $n$-gon, for $n\geq 3$, generalizing the idea of C. Kimberling for triangle. We define centers associated to functions instead of to geometrical properties. We…

Let $(X,\mathcal{B},\mu, T)$ be a measure preserving system. We prove the pointwise convergence of the averages $$\frac{1}{N^2}\sum_{n,m= 0}^{N-1} f_1(T^nx)f_2(T^mx)f_3(T^{n+m}x)$$ and of similar averages with seven bounded functions.

We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$…

The main aim of this paper is to find a unique common fixed point for six functions in a Menger probabilistic generalized metric space. For this purpose, we have defined the compatibility of three functions and established some required…

The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.

In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…

In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…

The purpose of this work is to introduce a general class of $C_G$-simulation functions and obtained some new coincidence and common fixed points results in metric spaces. Some useful examples are presented to illustrate our theorems.…

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…

The functions satisfying the mean value property for an n-dimensional cube are determined explicitly. This problem is related to invariant theory for a finite reflection group, especially to a system of invariant differential equations.…

Let $(X,\mathcal{B},\mu, T)$ be a measure preserving system. We prove the pointwise convergence of averages along cubes of $2^{k}-1$ bounded and measurable functions for all $k$.

Machine learning (ML) models are often valued by the accuracy of their predictions. However, in some areas of science, the inner workings of models are as relevant as their accuracy. To understand how ML models work internally, the use of…

For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.

Existing interpretation algorithms have found that, even deep models make the same and right predictions on the same image, they might rely on different sets of input features for classification. However, among these sets of features, some…

Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…

Let $(X, \mathcal{B}, \mu)$ be a probability measure space and $T_1$, $T_2$, $T_3$ three not necessarily commuting measure preserving transformations on $(X, \mathcal{B}, \mu)$. We prove that for all bounded functions $f_1$, $f_2$, $f_3$…

A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points…

Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…