Related papers: Quasi-Random Influences of Boolean Functions

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number…

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…

In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent…

This paper studies a class of Koebe-type harmonic quasiconformal functions. It is motivated by the shear construction of Clunie and Sheil-Small [Ann. Acad. Sci. Fenn. Ser. A I Math. 9: 3--25, 1984] and the harmonic quasiconformal Koebe…

We present a regularity lemma for Boolean functions $f:\{-1,1\}^n \to \{-1,1\}$ based on noisy influence, a measure of how locally correlated $f$ is with each input bit. We provide an application of the regularity lemma to weaken the…

In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…

In this article, we first give the characterizations of quasi-homogeneous aggregation functions, which show us that quasi-homogeneous aggregation functions are classified into three classes. We then introduce the concept of triple generator…

In [arXiv 0811.3913] the authors introduced the notion of quasi-polynomial function as being a mapping f: X^n -> X defined and valued on a bounded chain X and which can be factorized as f(x_1,...,x_n)=p(phi(x_1),...,phi(x_n)), where p is a…

We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…

We examine the correspondence between the various notions of quasirandomness for k-uniform hypergraphs and sigma-algebras related to measurable hypergraphs. This gives a uniform formulation of most of the notions of quasirandomness for…

An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasiinvariant curvelinear and analytic functionals intrinsically…

The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is $\varepsilon$-far from having that property. We investigate here several types of properties…

Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting…

In the present paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an…

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension…

We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…

In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic…

We demonstrate that in semiconductor quantum dots wave functions probed by imaging techniques based on local tunneling spectroscopies like STM show characteristic signatures of electron-electron Coulomb correlation. We predict that such…

For the Hamming graph $H(n,q)$, where a $q$ is a constant prime power and $n$ grows, we construct perfect colorings without non-essential arguments such that $n$ depends exponentially on the off-diagonal part of the quotient matrix. In…

The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve…