1,721,053 research outputs found

    Some applications of Freiman's inverse theorem

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    The celebrated Freiman's inverse theorem in Additive Combinatorics asserts that an additive set of small doubling constant must have additive structure. This thesis contains two applications achieved by combining this theorem with a dyadic pigeonhole principle technique. 1. A finite set A of integers is square-sum-free if no subset of A sums up to a square. In 1986, Erdos posed the problem of determining the largest cardinality of a square-sum-free subset of {1,..., n}. Significantly improving earlier results, we show in Chapter 2 that this maximum cardinality is of order n^{1/3+o(1)}, which is asymptotically tight. 2. A classical result of Littlewood-Offord and Erdos from the 1940s asserts that if the v_i are non-zero, then the concentration probability of the (multi)set V={v_1,...,v_n}, ho(V) := sup_{x} P( v_1 eta_1+ ... + v_n eta_n=x), is of order O(n^{-1/2}), where eta_i are i.i.d. copies of a Bernoulli random variable. Motivated by problems concerning random matrices, Tao and Vu introduced the Inverse Littlewood-Offord problem. In the inverse problem, one would like to give a characterization of the set V, given that ho(V) is relatively large. In Chapter 3, we develop a method to attack the inverse problem. As an application, we strengthen several previous results of Tao and Vu, obtaining an almost optimal characterization for VV. This implies several classical theorems, such as those of Sarkozy-Szemeredi, Halasz, and Stanley.Ph.D.Includes abstractVitaIncludes bibliographical referencesby Hoi H. Nguye

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed

    Variations on the Author

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    “Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship

    Appropriate Similarity Measures for Author Cocitation Analysis

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    We provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis

    Female ornamentation and directional male mate preference in the rock sparrow

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    Albeit there is growing evidence that males prefer to mate with ornamented females, it has been suggested that the production of costly ornaments may reduce female fecundity, hence favoring males with a preference for females with average ornamentation. In the rock sparrow, Petronia petronia, males and females possess a sexually selected patch of yellow feathers on the breast (a carotenoid-based trait). To test whether males prefer females with the largest ornament or average ornamented females, male rock sparrows were simultaneously faced with 3 conspecific females differing in breast patch size and a female house sparrow as a control. We found that the house sparrow and rock sparrow female with the smallest patch were least preferred, and males showed a clear proximity preference for the females with the above average-sized patch. Our results demonstrate that, contrary to theoretical predictions, a directional preference for female ornament was observed. Directional male preference may arise as consequence of a male's sensory bias or may be associated with indirect (genetic) benefits of choosing ornamented females, if ornament size is correlated with female genetic quality. Clearly, more work is necessary to identify the conditions under which directional preference for female ornament arise
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