1,720,963 research outputs found
Degrees of Kalman varieties of tensors
Full text linkFunding Information: The idea of this project was conceived during Shahidi's postdoc at Università di Firenze. We thank Giorgio Ottaviani for very useful discussions and encouragement. We thank Jan Draisma for explaining to us a way of deriving the equations in Example 41 . The first author thanks Dr. Alireza Firoozfar and Dr. Mohsen Afsharchi for their support. The second author is partially supported by the Academy of Finland Grant 323416 . During most of the preparation of the manuscript, the third author was a postdoc at Universität Bern, supported by Vici Grant 639.033.514 of Jan Draisma from the Netherlands Organisation for Scientific Research . We thank two anonymous referees for their useful comments and questions that also helped to improve the presentation. Publisher Copyright: © 2022 The Author(s)Kalman varieties of tensors are algebraic varieties consisting of tensors whose singular vector k-tuples lay on prescribed subvarieties. They were first studied by Ottaviani and Sturmfels in the context of matrices. We extend recent results of Ottaviani and the first author to the partially symmetric setting. We describe a generating function whose coefficients are the degrees of these varieties and we analyze its asymptotics, providing analytic results à la Zeilberger and Pantone. We emphasize the special role of isotropic vectors in the spectral theory of tensors and describe the totally isotropic Kalman variety as a dual variety.Peer reviewe
Asymptotics of degrees and ED degrees of Segre products
Full text linkFunding Information: We thank Jay Pantone for very useful conversations. We thank the referees for useful comments. The first two authors are members of INDAM-GNSAGA. The third author would like to thank The Department of Mathematics of Universit? di Firenze, where this project started in June 2018, for the warm hospitality and financial support. The first author is supported by the H2020-MSCA-ITN-2018 project POEMA. The second author is partially supported by the Academy of Finland Grant 323416. The third author is supported by Vici Grant 639.033.514 of Jan Draisma from the Netherlands Organisation for Scientific Research. Publisher Copyright: © 2021 The Author(s)Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product X×Qn, where X is a projective variety and Qn⊂Pn+1 is a smooth quadric hypersurface.Peer reviewe
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
The distance function from a real algebraic variety
No full textFor any (real) algebraic variety X in a Euclidean space V endowed with a nondegenerate quadratic form q, we introduce a polynomial EDpolyX,u(t2) which, for any u∈V, has among its roots the distance from u to X. The degree of EDpolyX,u is the Euclidean Distance degree of X. We prove a duality property when X is a projective variety, namely EDpolyX,u(t2)=EDpolyX∨,u(q(u)−t2) where X∨ is the dual variety of X. When X is transversal to the isotropic quadric Q, we prove that the ED polynomial of X is monic and the zero locus of its lower term is X∪(X∨∩Q)∨.Peer reviewe
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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