1,720,957 research outputs found
Braid groups of J-reflection groups and associated classical and dual Garside structures
No full text57 pages, comments welcome !The family of -reflection groups can be seen as a combinatorial generalisation of irreducible rank two complex reflection groups and was introduced by the author in a previous article. In this article, we define the braid groups associated to -reflection groups, which coincide with the complex braid group when the -reflection group is finite. We show that the isomorphism type of the braid groups only depend on the reflection isomorphism types of the corresponding -reflection groups. Moreover, we show that these braid groups are always abstractly isomorphic to circular groups. At the same time, we show that the center of the braid groups is cyclic and sent onto the center of the corresponding -reflection groups under the natural quotient. Finally, we exhibit two Garside structures for each braid group of -reflection group. These structures generalise the classical and dual Garside structures (when defined) of rank two irreducible complex reflection groups. In particular, the dual Garside structure of -reflection groups provides candidates for dual monoids associated to the irreducible complex reflection groups of rank two which do not already have one
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
Généralisations de groupes de réflexions complexes de rang 2 et structures de Garside associées
No full textThis thesis focuses on the study of -reflection groups, a generalisation of complex reflection groups of rank two. The starting point of this work is an article of Anne-Marie Aubert and Pramod Achar, in which they introduced and studied the family of -groups. In particular, they showed that the family of finite -groups coincides with that of irreducible complex reflection groups of rank two and introduced a representation for each -group. A first family of -groups was later studied by Thomas Gobet, which he called toric reflection groups. The study of this family allows both a combinatorial exploration of infinite groups generalising irreducible complex reflection groups of rank two with one conjugacy class of reflecting hyperplanes, and the extension of a known link between their complex braid groups and certain torus knot groups. The first part of this work consists in extending the notion of toric reflection groups to that of -reflection groups. These groups form a family of -groups which is simultaneously large enough to contain all irreducible complex reflection groups of rank two and small enough to make their study accessible. We obtain presentations by generators and relations for all -reflection groups. In particular, we give a uniform description of the presentations given by Michel Broué, Gunter Malle and Raphaël Rouquier for irreducible complex reflection groups of rank two. We also compute the center of these groups and precisely determine when two -reflection groups are isomorphic. The second part of this work then consists of associating to each -reflection group a -braid group. By construction, whenever the -reflection group is a complex reflection group, its -braid group coincides with its complex braid group. We exhibit a correspondence between -braid groups, circular groups and fundamental groups of complements of links that we call torus necklaces. In particular, this shows that whenever a link group has a non-trivial center, it is a Garside group. The third part of this work is about Garside structures of -braid groups. For each -braid group, we give two Garside structures respectively generalising the classical and dual structures of some complex braid groups of rank two. In particular, the dual structures provide new Garside structures for complex braid groups of rank two with three conjugacy classes of reflecting hyperplanes.Cette thèse porte sur l'étude des -groupes de réflexions, une généralisation des groupes de réflexions complexes de rang deux. Le point de départ de ce travail est un article d'Anne-Marie Aubert et Pramod Achar dans lequel ils ont introduit et étudié la famille des -groupes. Ils ont démontré en particulier que la famille des -groupes finis coïncide avec les groupes de réflexions complexes irréductibles de rang deux, et ont introduit une représentation de chaque -groupe. Une première famille de -groupes fut ensuite étudiée par Thomas Gobet, qu'il a nommés groupes de réflexions toriques. L'analyse de cette famille de groupes permet à la fois une exploration combinatoire de groupes infinis qui généralisent les groupes de réflexions complexes irréductibles de rang deux à une classe de conjugaison d'hyperplans de réflexions, et l'extension d'un lien connu entre les groupes de tresses complexes de ces derniers et certains groupes de nœuds toriques. La première partie de ce travail consiste à étendre la notion de groupes de réflexions toriques à celle de -groupes de réflexions. Ces groupes forment une famille de -groupes simultanément assez grande pour contenir tous les groupes de réflexions complexes irréductibles de rang deux et suffisamment restreinte pour que l'étude en soit accessible. Nous obtenons des présentations par générateurs et relations pour tous les -groupes de réflexions. En particulier, nous donnons une description uniforme des présentations données par Michel Broué, Gunter Malle et Raphaël Rouquier pour les groupes de réflexions complexes irréductibles de rang deux. Nous calculons également le centre de ces groupes et déterminons sous quelles conditions deux -groupes de réflexions sont isomorphes. La deuxième partie de ce travail consiste alors à associer à chaque -groupe de réflexions un -groupe de tresses. Par construction, dès lors que le -groupe de réflexions est un groupe de réflexions complexes, son -groupe de tresses coïncide avec son groupe de tresses complexes. Nous mettons en évidence une correspondance entre les -groupes de tresses, les groupes circulaires et les groupes fondamentaux de compléments des entrelacs que nous appelons pendentifs toriques. Cette correspondance démontre entre autres qu'à chaque fois qu'un groupe d'entrelacs possède un centre non-trivial, c'est un groupe de Garside. Le troisième aspect de ce travail consiste à étudier des structures de Garside des -groupes de tresses. Nous donnons deux structures de Garside pour chaque -groupe de tresses, généralisant respectivement les structures classiques et duales de certains groupes de tresses complexes de rang deux. En particulier, les structures duales fournissent de nouvelles structures de Garside pour les groupes de tresses complexes de rang deux à trois classes de conjugaison d'hyperplans de réflexions
A Combinatorial Generalisation of Rank two Complex Reflection Groups via Generators and Relations
No full textComplex reflection groups of rank two are precisely the finite groups in the family of groups that we call virtual complex reflection groups of rank two. These groups are particular cases of -groups as defined by Achar \& Aubert in ['On rank 2 complex reflection groups', \emph{Comm. Algebra} \textbf{36}(6) (2008), 2092-2132]. Virtual complex reflection groups generalise both complex reflection groups of rank two and toric reflection groups, a family of groups defined and studied by Gobet in ['Toric reflection groups', \emph{Journal of the Australian Mathematical Society} \textbf{116} (2) (2024), 171-199]. We give uniform presentations by generators and relations of virtual complex reflection groups of rank two, which coincide with the presentations given by Broué, Malle and Rouquier in ['Complex reflection groups, braid groups, Hecke algebras', \emph{J. reine angew. Math.} \textbf{500} (1998), 127-190.] when the groups are finite. In particular, these presentations provide uniform presentations for complex reflection groups of rank two where the generators are reflections (however the proof uses the classification of irreducible complex reflection groups). Moreover, we show that the center of virtual complex reflection groups is cyclic, generalising what happens for irreducible complex reflection groups of rank two and toric reflection groups. Finally, we classify virtual complex reflection groups up to reflection isomorphisms
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Généralisations de groupes de réflexions complexes de rang 2 et structures de Garside associées
No full textThis thesis focuses on the study of -reflection groups, a generalisation of complex reflection groups of rank two. The starting point of this work is an article of Anne-Marie Aubert and Pramod Achar, in which they introduced and studied the family of -groups. In particular, they showed that the family of finite -groups coincides with that of irreducible complex reflection groups of rank two and introduced a representation for each -group. A first family of -groups was later studied by Thomas Gobet, which he called toric reflection groups. The study of this family allows both a combinatorial exploration of infinite groups generalising irreducible complex reflection groups of rank two with one conjugacy class of reflecting hyperplanes, and the extension of a known link between their complex braid groups and certain torus knot groups. The first part of this work consists in extending the notion of toric reflection groups to that of -reflection groups. These groups form a family of -groups which is simultaneously large enough to contain all irreducible complex reflection groups of rank two and small enough to make their study accessible. We obtain presentations by generators and relations for all -reflection groups. In particular, we give a uniform description of the presentations given by Michel Broué, Gunter Malle and Raphaël Rouquier for irreducible complex reflection groups of rank two. We also compute the center of these groups and precisely determine when two -reflection groups are isomorphic. The second part of this work then consists of associating to each -reflection group a -braid group. By construction, whenever the -reflection group is a complex reflection group, its -braid group coincides with its complex braid group. We exhibit a correspondence between -braid groups, circular groups and fundamental groups of complements of links that we call torus necklaces. In particular, this shows that whenever a link group has a non-trivial center, it is a Garside group. The third part of this work is about Garside structures of -braid groups. For each -braid group, we give two Garside structures respectively generalising the classical and dual structures of some complex braid groups of rank two. In particular, the dual structures provide new Garside structures for complex braid groups of rank two with three conjugacy classes of reflecting hyperplanes.Cette thèse porte sur l'étude des -groupes de réflexions, une généralisation des groupes de réflexions complexes de rang deux. Le point de départ de ce travail est un article d'Anne-Marie Aubert et Pramod Achar dans lequel ils ont introduit et étudié la famille des -groupes. Ils ont démontré en particulier que la famille des -groupes finis coïncide avec les groupes de réflexions complexes irréductibles de rang deux, et ont introduit une représentation de chaque -groupe. Une première famille de -groupes fut ensuite étudiée par Thomas Gobet, qu'il a nommés groupes de réflexions toriques. L'analyse de cette famille de groupes permet à la fois une exploration combinatoire de groupes infinis qui généralisent les groupes de réflexions complexes irréductibles de rang deux à une classe de conjugaison d'hyperplans de réflexions, et l'extension d'un lien connu entre les groupes de tresses complexes de ces derniers et certains groupes de nœuds toriques. La première partie de ce travail consiste à étendre la notion de groupes de réflexions toriques à celle de -groupes de réflexions. Ces groupes forment une famille de -groupes simultanément assez grande pour contenir tous les groupes de réflexions complexes irréductibles de rang deux et suffisamment restreinte pour que l'étude en soit accessible. Nous obtenons des présentations par générateurs et relations pour tous les -groupes de réflexions. En particulier, nous donnons une description uniforme des présentations données par Michel Broué, Gunter Malle et Raphaël Rouquier pour les groupes de réflexions complexes irréductibles de rang deux. Nous calculons également le centre de ces groupes et déterminons sous quelles conditions deux -groupes de réflexions sont isomorphes. La deuxième partie de ce travail consiste alors à associer à chaque -groupe de réflexions un -groupe de tresses. Par construction, dès lors que le -groupe de réflexions est un groupe de réflexions complexes, son -groupe de tresses coïncide avec son groupe de tresses complexes. Nous mettons en évidence une correspondance entre les -groupes de tresses, les groupes circulaires et les groupes fondamentaux de compléments des entrelacs que nous appelons pendentifs toriques. Cette correspondance démontre entre autres qu'à chaque fois qu'un groupe d'entrelacs possède un centre non-trivial, c'est un groupe de Garside. Le troisième aspect de ce travail consiste à étudier des structures de Garside des -groupes de tresses. Nous donnons deux structures de Garside pour chaque -groupe de tresses, généralisant respectivement les structures classiques et duales de certains groupes de tresses complexes de rang deux. En particulier, les structures duales fournissent de nouvelles structures de Garside pour les groupes de tresses complexes de rang deux à trois classes de conjugaison d'hyperplans de réflexions
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