174,354 research outputs found

    Finding a non-minority ball with majority answers

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    Suppose we are given a set of nn balls {b1,,bn}\{b_1,\ldots,b_n\} 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 {bi1,bi2,bi3}\{b_{i_1},b_{i_2},b_{i_3}\}. 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 n2\frac n2 times among the nn balls. We show that the minimum number of queries needed to solve this problem is Θ(n)\Theta(n) in the adaptive case and Θ(n3)\Theta(n^3) in the non-adaptive case. We also consider some related problems

    Computing Majority with Triple Queries

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    Consider a bin containing nn balls colored with two colors. In a kk-query, kk 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 kk-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

    Factors related to the rejection and/or abandonment of AAC devices

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    More than 3.5 million Americans have such significant communication disability that they cannot rely on their natural speech to meet their communication needs. As a result, these individuals are severely restricted in their participation in all aspects of life, including their education, employment, family, and community. Augmentative and alternative communication strategies offer great potential to enhance the communication of individuals with complex communication needs, and therefore improve their quality of life. Fifty-two ISAAC members that responded to the online survey utilized a 5 point Likert-type scale (strongly agree to strongly disagree) to rate the importance of factors as they relate to the rejection and/or abandonment. The mean values of ratings were calculated to determine which factors were cited as relevant in predicting AAC device rejection and abandonment. Additionally, an independent T-test was utilized to determine if the factors cited varied depending on the role of the person completing the survey. The results of this investigation indicate that it is imperative to consider a complex interaction of factors pertaining to the individuals who use AAC, their conversational partners, settings in which interactions occur, and devices used to interact, when designing an AAC intervention. The statistical analysis revealed no significance difference in how the respondents rated the factors based on their occupation. Based on the results of the study, a checklist of factors that an AAC practitioner might consider addressing in order to foster acceptance of AAC systems initially and later on was constructed

    Group status, minorities and trust

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    We present the results of an experiment that attempts to measure the impact of majority and minority groups, and high status and low status groups, on well-being, cooperation and social capital. In the experiment, group membership is induced artificially, subjects interact with insiders and outsiders in trust games and periodically enter markets where they can trade group membership. We find that trust falls with groups because of discrimination against outsiders. Against this, however, there is evidence that low group status and minority subjects are less satisfied, and that low status subjects trust less other low status subjects
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