We show new results about the garden-hose model. Our main results include improved lower bounds based on non-deterministic communication complexity (leading to the previously unknown Θ(n) bounds for Inner Product mod 2 and Disjointness), as well as an O(n · log n) upper bound for the Distributed Majority function (previously conjectured to have quadratic complexity). We show an efficient simula...

Given a Boolean function f , the (Hamming) weight wt(f) and the nonlinearity N(f) are well known to be important in designing functions that are useful in cryptography. The nonlinearity is expensive to compute, in general, so any formulas giving the nonlinearity for particular functions f are significant. The well known majority function has been extensively studied in a cryptographic context f...

This paper describes a new filter for impulse noise reduction in colour images which is aimed at improving the noise reduction capability of the classical vector median filter. The filter is inspired by the application of a vector marginal median filtering process over a selected group of pixels in each filtering window. This selection, which is based on the vector median, along with the applic...

Which is the best, impartially most plausible consensus view to serve as the basis of democratic group decision when voters disagree? Assuming that the judgment aggregation problem can be framed as a matter of judging a set of binary propositions (“issues”), we develop a multi-issue majoritarian approach based on the criterion of supermajority efficiency (SME). SME reflects the idea that smalle...

Experiments exploring the effects of group discussion on attitudes, jury decisions, ethical decisions, judgments, person perceptions, negotiations, and risk taking (other than the choice-dilemmas task) are generally consistent with a "group polarization" hypothesis, derived from the risky-shift literature. Recent attempts to explain the phenomenon fall mostly into one of three theoretical appro...

An improvement of the majority gate algorithm suitable for grey scale morphological operations is presented in this letter. The redundancy of temporal signals led to a simplified hardware implementation. It is shown that max/min operators can be computed by the same circuit. A new pipelined systolic array architecture based on this circuit is illustrated for dilation/erosion operations. 2 Intro...

This paper considers the construction of median unbiased forecasts for near-integrated autoregressive processes. It derives the appropriately scaled limiting distribution of the deviation of the forecast from the true conditional mean. The dependence of the limiting distribution on nuisance parameters precludes the use of the standard asymptotic and bootstrap methods for bias correction. We pro...

Reliability is expected to be a critical challenge in designing future molecular electronic circuits. Using a compact model that captures the essential physics of the device, the effect on digital gate functionality of variations in the device parameters, as well as the improvements afforded by a TMR majority gate structure are quantified. It is shown that the improvement is substantial, showin...