1,720,959 research outputs found
Orbit semigroups and the representation type of quivers
No full textAbstractWe show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated
Quivers, long exact sequences and Horn type inequalities
No full textAbstractWe give necessary and sufficient inequalities for the existence of long exact sequences of m finite abelian p-groups with fixed isomorphism types. This problem is related to some generalized Littlewood–Richardson coefficients that we define in this paper. We also show how this problem is related to eigenvalues of Hermitian matrices satisfying certain (in)equalities. When m=3, we recover the Horn type inequalities that solve the saturation conjecture for Littlewood–Richardson coefficients and Horn's conjecture
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
Geometric characterizations of the representation type of hereditary algebras and of canonical algebras
No full textAbstractWe show that a finite connected quiver Q with no oriented cycles is tame if and only if for each dimension vector d and each integral weight θ of Q, the moduli space M(Q,d)θss of θ-semi-stable d-dimensional representations of Q is just a projective space. In order to prove this, we show that the tame quivers are precisely those whose weight spaces of semi-invariants satisfy a certain log-concavity property. Furthermore, we characterize the tame quivers as being those quivers Q with the property that for each Schur root d of Q, the field of rational invariants k(rep(Q,d))GL(d) is isomorphic to k or k(t). Next, we extend this latter description to canonical algebras. More precisely, we show that a canonical algebra Λ is tame if and only if for each generic root d of Λ and each indecomposable irreducible component C of rep(Λ,d), the field of rational invariants k(C)GL(d) is isomorphic to k or k(t). Along the way, we establish a general reduction technique for studying fields of rational invariants on Schur irreducible components of representation varieties
The cone of effective weights for quivers and Horn type problems.
No full textWe study Horn type problems which come from algebraic combinatorics, group theory, linear algebra, and quiver invariant theory. In particular, we give new proofs to a series of problems revolving around the celebrated conjecture of Horn on the possible eigenvalues of sums of Hermitian matrices. Specifically, we find necessary and sufficient conditions for the existence of long exact sequences of finite abelian p-groups and for the existence of Hermitian matrices with positive semi-definite sum of bounded rank. Our approach to these problems is to rephrase them in terms of cones of effective weights for quivers. Finally, using methods from quiver invariant theory we are able to describe these cones by Horn type inequalities.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125041/2/3186595.pd
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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