1,720,960 research outputs found
Dominance Regions for Rank Two Cluster Algebras
Full text linkWe study the polygons defining the dominance order on g-vectors in cluster algebras of rank 2 as in Fig. 1
On Generalized Minors and Quiver Representations
Full text linkThe cluster algebra of any acyclic quiver can be realized as the coordinate ring of a
subvariety of a Kac-Moody group – the quiver is an orientation of its Dynkin diagram, defining a
Coxeter element and thereby a double Bruhat cell. We use this realization to connect representations of
the quiver with those of the group. We show that cluster variables of preprojective (resp. postinjective)
quiver representations are realized by generalized minors of highest-weight (resp. lowest-weight)
group representations, generalizing results of Yang-Zelevinsky in finite type. In type A_n^(1) and finitely
many other affine types, we show that cluster variables of regular quiver representations are realized by
generalized minors of group representations that are neither highest- nor lowest-weight; we conjecture
this holds more generally
Some consequences of categorification
No full textSeveral conjectures on acyclic skew-symmetrizable cluster algebras are proven
as direct consequences of their categorification via valued quivers. These include conjectures
of Fomin–Zelevinsky, Reading–Speyer, and Reading–Stella related to d-vectors, g-vectors,
and F -polynomials
Affine cluster monomials are generalized minors
No full textWe study the realization of acyclic cluster algebras as coordinate rings of Coxeter double Bruhat cells in Kac-Moody groups. We prove that all cluster monomials with g-vector lying in the doubled Cambrian fan are restrictions of principal generalized minors. As a corollary, cluster algebras of finite and affine type admit a complete and non-recursive description via (ind-)algebraic group representations, in a way similar in spirit to the Caldero-Chapoton description via quiver representations. In type A_1^{(1)}, we further show that elements of several canonical bases (generic, triangular, and theta) which complete the partial basis of cluster monomials are composed entirely of restrictions of minors. The discrepancy among these bases is accounted for by continuous parameters appearing in the classification of irreducible level-zero representations of affine Lie groups. We discuss how our results illuminate certain parallels between the classification of representations of finite-dimensional algebras and of integrable weight representations of Kac-Moody algebras
The greedy basis equals the theta basis: A rank two haiku
No full textWe prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy
basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich
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
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
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