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Alexander Type Invariants of Tangles, Skew Howe Duality for Crystals and The Cactus Group
No full textThis thesis consists of two parts, the first part is in the setting of algebraic knot theory while the second studies ideas in representation theory.
In the first part of this work, we study generalizations of a classical link invariant--the multivariable Alexander polynomial--to tangles. The starting point is Archibald's tMVA invariant for virtual tangles which lives in the setting of circuit algebras. Using the Hodge star map and restricting to tangles without closed components, we define a reduction of the tMVA to an invariant (rMVA) which is valued in matrices with entries equal to certain Laurent polynomials. We show the rMVA has the structure of a metamonoid morphism and is further equivalent to a tangle invariant defined by Bar-Natan. This invariant also reduces to the Gassner representation on braids and has a partially defined trace operation for closing open strands of a tangle.
In the second part, we look at crystals and the cactus group. The crystals for a finite-dimensional complex reductive Lie algebra \fg encode the structure of its representations, yet can also reveal surprising new structure of their own. In this work, we construct a group J_{\fg}, the ``cactus group'', using the Dynkin diagram of \fg and show that it acts combinatorially on any \fg-crystal via the Sch\"{u}tzenberger involutions. Henriques and Kamnitzer studied J_n=J_{\mgl_n}, and constructed an action of it on -tensor products of \fg-crystals, for any \fg as above. We discuss the crystal corresponding to the \mgl_n \times \mgl_m-representation \Lambda^N(\C^n \otimes \C^m), derive skew Howe duality on the crystal level and show that the two cactus group actions agree in this setting. An application of this result is discussed in studying a family of maximal commutative subalgebras of the universal enveloping algebra, the shift of argument and Gaudin algebras, where an algebraically constructed monodromy action is expected to match that of the cactus group.Ph.D
Alexander Type Invariants of Tangles, Skew Howe Duality for Crystals and The Cactus Group
Get PDFThis thesis consists of two parts, the first part is in the setting of algebraic knot theory while the second studies ideas in representation theory.
In the first part of this work, we study generalizations of a classical link invariant--the multivariable Alexander polynomial--to tangles. The starting point is Archibald's tMVA invariant for virtual tangles which lives in the setting of circuit algebras. Using the Hodge star map and restricting to tangles without closed components, we define a reduction of the tMVA to an invariant (rMVA) which is valued in matrices with entries equal to certain Laurent polynomials. We show the rMVA has the structure of a metamonoid morphism and is further equivalent to a tangle invariant defined by Bar-Natan. This invariant also reduces to the Gassner representation on braids and has a partially defined trace operation for closing open strands of a tangle.
In the second part, we look at crystals and the cactus group. The crystals for a finite-dimensional complex reductive Lie algebra g encode the structure of its representations, yet can also reveal surprising new structure of their own. In this work, we construct a group J g, the "cactus group'', using the Dynkin diagram of g and show that it acts combinatorially on any g-crystal via the Schützenberger involutions. Henriques and Kamnitzer studied Jn = Jg ln, and constructed an action of it on n-tensor products of g-crystals, for any g as above. We discuss the crystal corresponding to the gln × glm-representation Λ N(Cn ⊗ Cm), derive skew Howe duality on the crystal level and show that the two cactus group actions agree in this setting. An application of this result is discussed in studying a family of maximal commutative subalgebras of the universal enveloping algebra, the shift of argument and Gaudin algebras, where an algebraically constructed monodromy action is expected to match that of the cactus group.Ph.D
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
Cacti, Toggles, and Reverse Plane Partitions
No full textThe cactus group acts combinatorially on crystals via partial Schützenberger involutions. This action has been studied extensively in type and described via Bender-Knuth involutions. We prove an analogous result for the family of crystals in type . Our main tools are combinatorial toggles acting on reverse plane partitions of height . As a corollary, we show that the length one and two subdiagram elements generate the full cactus action, addressing conjectures of Dranowski, the second author, Kamnitzer, and Morton-Ferguson.12 page
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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