1,720,988 research outputs found
The Inverse Eigenvalue Problem of a Graph
Full text linkHistorically, matrix theory and combinatorics have enjoyed a powerful, mutually beneficial relationship. Examples include: Perron-Frobenius theory describes the relationship between the combinatorial arrangement of the entries of a nonnegative matrix and the properties of its eigenvalues and eigenvectors (see [53, Chapter 8]). The theory of vibrations (e.g., of a system of masses connected by strings) provides many inverse problems (e.g., can the stiffness of the springs be prescribed to achieve a system with a given set of fundamental vibrations?) whose resolution intimately depends upon the families of matrices with a common graph (see [46, Chapter 7]).
The Inverse Eigenvalue Problem of a graph (IEP-G), which is the focus of this chapter, is another such example of this relationship. The IEP-G is rooted in the 1960s work of Gantmacher, Krein, Parter and Fielder, but new concepts and techniques introduced in the last decade have advanced the subject significantly and catalyzed several mathematically rich lines of inquiry and application. We hope that this chapter will highlight these new ideas, while serving as a tutorial for those desiring to contribute to this expanding area.This is a manuscript of a chapter published as Hogben, Leslie, Jephian C.-H. Lin, and Bryan L. Shader. “The Inverse Eigenvalue Problem of a Graph.” In 50 years of Combinatorics, Graph Theory, and Computing (Fan Chung, Ron Graham, Frederick Hoffman, Leslie Hogben, Ronald C. Mullin, and Douglas B. West, eds.). Boca Raton, FL: CRC Press, Taylor & Francis Group (2019): 239-262. Posted with permission.</p
A Simple Proof of Fiedler's Conjecture Concerning Orthogonal Matrices
No full textWe give a simple proof that an n x n orthogonal matrix with n ≥ 2 which cannot be written as a direct sum has at least 4n-4 nonzero entries
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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