Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] showed that shared nonlocal boxes with the CHSH probability greater than 3+ √ 6 6 yields trivial communication complexity. There still exists the gap with the maximum CHSH probability 2+ √ 2 4 achievable by quantum mechanics. It is an interesting open question to determine the exact threshold for the trivial communication complexity. Brassard...

Increasing concern over corporate governance has led to calls for more shareholder influence over corporate decisions, but allowing shareholders to vote on more issues may not affect the quality of governance. We should expect instead that, under current rules, shareholder voting will implement the preferences of the majority of large shareholders and management. This is because majority rule o...

We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone errorcorrecting codes, and show that hardness amplification for NP is essentially equivalent to constructing efficiently locally encodable and locally list-decodable monotone codes. The previous hardness amplification resul...

We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and applicable to several models of computation previously studied. As a first illustration we show how all the results of Evans and Pippenger (SIAM J. Computing,...

values alone capture too little information about relationships between concrete values. For example, consider a system containing a majority voter. The voter's outputs depend on equality relationships among its inputs. If two inputs both have abstract value N, denoting the natural numbers, there is no way to tell from this whether they are equal. To more accurately track relationships between ...

This paper introduces a new and more appropriate ECG signal preprocessing using mediated morphological filters. These filters are based on a particular combination of median operator and classical morphological operators. The proposed method has been applied to adult and fetal ECG signals as an efficient preprocessing task. Accurate numerical descriptions demonstrate better performance quality ...

Noise removal or noise suppression is an important task in image processing. In general, the results of the noise removal have a strong influence on the quality of the following image processing techniques. Several techniques for noise removal are well established in gray value image processing. However, it is not easy to adapt these techniques to color image processing. The median filter is of...

We study approximation of Boolean functions by low-degree polynomials over the ring Z/2kZ. More precisely, given a Boolean function F : {0,1}n {0,1}, define its k-lift to be F : {0,1}n {0,2k-1} by Fk(x) = 2k-F(x) mod 2k$. We consider the fractional agreement (which we refer to as d,k(F)) of Fk(x) with degree d polynomials from Z/2kZ[x1,...,xn]. Our results are the following: 1. Increasing k can...

In this paper, we prove that the quadratic polynomials modulo 3 with the largest correlation with parity are unique up to permutation of variables and constant factors. As a consequence of our result, we completely characterize the smallest MAJ◦ MOD3 ◦ AND2 circuits that compute parity, where a MAJ ◦MOD3 ◦ AND2 circuit is one that has a majority gate as output, a middle layer of MOD3 gates and ...