1,721,008 research outputs found
Two extensions of the Erdis-Szekeres problem
Get PDFAccording to Suk's breakthrough result on the Erdos-Szekeres problem, any point set in general position in the plane, which has no n elements that form the vertex set of a convex n-gon, has at most 2(n)+ O(n(2/3) log n) points. We strengthen this theorem in two ways. First, we show that the result generalizes to convexity structures induced by pseudoline arrangements. Second, we improve the error term. A family of n convex bodies in the plane is said to be in convex position if the convex hull of the union of no n - 1 of its members contains the remaining one. If any three members are in convex position, we say that the family is in general position. Combining our results with a theorem of Dobbins, Holmsen, and Hubard, we significantly improve the best known upper bounds on the following two functions, introduced by Bisztriczky and Fejes Toth and by Pach and Toth, respectively. Let c(n) (and c'(n)) denote the smallest positive integer N with the property that any family of N pairwise disjoint convex bodies in general position (resp., N convex bodies in general position, any pair of which share at most two boundary points) has an n-member subfamily in convex position. We show that c(n) <= c' (n) <= 2(n+O)(root n log n).
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
Disjointness Graphs
No full textThe {\em disjointness graph} of a set of segments in , is a graph whose vertex set is and two vertices are connected by an edge if and only if the corresponding segments are disjoint. We prove that the chromatic number of is bounded by a function of , the clique number of . More precisely, we have . It follows, that has pairwise intersecting or pairwise disjoint elements. Stronger bounds are established for lines in space, instead of segments.
We show that computing and for disjointness graphs of lines in space are NP-complete tasks. However, we can design efficient algorithms to compute proper colorings of in which the number of colors satisfies the above upper bounds.
One cannot expect similar results for sets of continuous arcs, instead of segments, even in the plane. We construct families of arcs whose disjointness graphs are triangle-free (), but whose chromatic numbers are arbitrarily large. Joint work with G\'abor Tardos and G\'eza T\'oth.Non UBCUnreviewedAuthor affiliation: Ecole Polytechnique Federale de LausanneFacult
Towards a theory of geometric graphs
No full textThe early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been successfully applied in other areas of mathematics. However, the same methods were often incapable of providing satisfactory answers to questions arising in geometric applications. In the spirit of Konig, geometric graph theory focuses on combinatorial and geometric properties of graphs drawn in the plane by straight-line edges (or more generally, by edges represented by simple Jordan arcs). It is an emerging discipline that abounds in open problems, but it has already yielded some striking results which have proved instrumental in the solution of several basic problems in combinatorial and computational geometry. The present volume is a careful selection of 25 invited and thoroughly refereed papers, reporting about important recent discoveries on the way Towards a Theory of Geometric Graphs
Geometric intersection patterns and order
No full textTBANon UBCUnreviewedAuthor affiliation: Ecole Polytechnique Federale de LausanneFacult
Incidence results on the plane and distinct distances
No full textNon UBCUnreviewedAuthor affiliation: Ecole Polytechnique Federale de Lausanne and Renyi InstituteResearche
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