19,403 research outputs found
Simple Dynamics for Plurality Consensus
We study a \emph{Plurality-Consensus} process in which each of anonymous
agents of a communication network initially supports an opinion (a color chosen
from a finite set ). Then, in every (synchronous) round, each agent can
revise his color according to the opinions currently held by a random sample of
his neighbors. It is assumed that the initial color configuration exhibits a
sufficiently large \emph{bias} towards a fixed plurality color, that is,
the number of nodes supporting the plurality color exceeds the number of nodes
supporting any other color by additional nodes. The goal is having the
process to converge to the \emph{stable} configuration in which all nodes
support the initial plurality. We consider a basic model in which the network
is a clique and the update rule (called here the \emph{3-majority dynamics}) of
the process is the following: each agent looks at the colors of three random
neighbors and then applies the majority rule (breaking ties uniformly).
We prove that the process converges in time with high probability, provided that .
We then prove that our upper bound above is tight as long as . This fact implies an exponential time-gap between the
plurality-consensus process and the \emph{median} process studied by Doerr et
al. in [ACM SPAA'11].
A natural question is whether looking at more (than three) random neighbors
can significantly speed up the process. We provide a negative answer to this
question: In particular, we show that samples of polylogarithmic size can speed
up the process by a polylogarithmic factor only.Comment: Preprint of journal versio
Computing Majority with Triple Queries
Consider a bin containing balls colored with two colors. In a -query,
balls are selected by a questioner and the oracle's reply is related
(depending on the computation model being considered) to the distribution of
colors of the balls in this -tuple; however, the oracle never reveals the
colors of the individual balls. Following a number of queries the questioner is
said to determine the majority color if it can output a ball of the majority
color if it exists, and can prove that there is no majority if it does not
exist. We investigate two computation models (depending on the type of replies
being allowed). We give algorithms to compute the minimum number of 3-queries
which are needed so that the questioner can determine the majority color and
provide tight and almost tight upper and lower bounds on the number of queries
needed in each case.Comment: 22 pages, 1 figure, conference version to appear in proceedings of
the 17th Annual International Computing and Combinatorics Conference (COCOON
2011
Sonic Pictures
Winning essay of the American Society for Aesthetics' inaugural Peter Kivy Prize. Extends Kivy's notion of sonic picturing through engagement with recent work in philosophy of perception. Argues that sonic pictures are more widespread and more aesthetically and artistically important than even Kivy envisioned. Topics discussed include: the nature of sonic pictures; the nature of sounds; what we can (and more importantly, cannot) conclude from musical listening; sonic pictures in film; beatboxing as an art of sonic picturing; and cover songs as sonic pictures. To be published in the Journal of Aesthetics and Art Criticism
Interactive color display for multispectral imagery using correlation clustering
A method for processing multispectral data is provided, which permits an operator to make parameter level changes during the processing of the data. The system is directed to production of a color classification map on a video display in which a given color represents a localized region in multispectral feature space. Interactive controls permit an operator to alter the size and change the location of these regions, permitting the classification of such region to be changed from a broad to a narrow classification
High speed multi focal plane optical system
An apparatus for eliminating beamsplitter generated optical aberrations in a pupil concentric optical system providing a plurality of spatially separated images on different focal planes or surfaces is presented. The system employs a buried surface beamsplitter having spherically curved entrance and exit faces which are concentric to a system aperture stop with the entrance face being located in the path of a converging light beam directed there from an image forming objective element which is also concentric to the aperture stop
Finding a non-minority ball with majority answers
Suppose we are given a set of balls each colored
either red or blue in some way unknown to us. To find out some information
about the colors, we can query any triple of balls
. As an answer to such a query we obtain (the
index of) a {\em majority ball}, that is, a ball whose color is the same as the
color of another ball from the triple. Our goal is to find a {\em non-minority
ball}, that is, a ball whose color occurs at least times among the
balls. We show that the minimum number of queries needed to solve this
problem is in the adaptive case and in the
non-adaptive case. We also consider some related problems
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