相关论文: Influential coalitions for Boolean Functions
Binary codes of length $n$ may be viewed as subsets of vertices of the Boolean hypercube $\{0,1\}^n$. The ability of a linear error-correcting code to recover erasures is connected to influences of particular monotone Boolean functions.…
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…
In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect,…
The infinite set of coupled integral nonlinear equations for correlation functions in the case of classical canonical ensemble is considered. Some kind of graph expansions of correlation functions in the density parameter are constructed.…
In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…
It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.
Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial…
Higher-Order Influence Functions (HOIFs) provide a unified theory for constructing rate-optimal estimators for a large class of low-dimensional (smooth) statistical functionals/parameters (and sometimes even infinite-dimensional functions)…
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…
We give a new presentation of the main result of Arunachalam, Bri\"et and Palazuelos (SICOMP'19) and show that quantum query algorithms are characterized by a new class of polynomials which we call Fourier completely bounded polynomials. We…
We generalize a result of Matom\"aki, Radziwi{\l}{\l}, and Tao, by proving an averaged version of a conjecture of Chowla and a conjecture of Elliott regarding correlations of the Liouville function, or more general bounded multiplicative…
The Fourier-Entropy Influence (FEI) Conjecture states that for any Boolean function $f:\{+1,-1\}^n \to \{+1,-1\}$, the Fourier entropy of $f$ is at most its influence up to a universal constant factor. While the FEI conjecture has been…
The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact…
We consider a committee voting on whether to adopt a reform under a quota rule, where members differ in how much they value the reform some supporting it, others opposing it. We examine how members can influence each other's votes through…
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…
We show that on every product probability space, Boolean functions with small total influences are essentially the ones that are almost measurable with respect to certain natural sub-sigma algebras. This theorem in particular describes the…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…
As machine learning is increasingly deployed in the real world, it is paramount that we develop the tools necessary to analyze the decision-making of the models we train and deploy to end-users. Recently, researchers have shown that…
The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning…