1,721,013 research outputs found
An Overview
No full textThe cotangent formula constitutes an intrinsic discretization of the Laplace-Beltrami operator on polyhedral surfaces in a finite-element sense. This note gives an overview of approximation and convergence properties of discrete Laplacians and mean curvature vectors for polyhedral surfaces located in the vicinity of a smooth surface in euclidean 3-space. In particular, we show that mean curvature vectors converge in the sense of distributions, but fail to converge in L 2
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
Discrete zero and constant mean curvature surfaces in Euclidean and Lorentz space and dimer models
No full textWe introduce a new theory of discrete isothermic surfaces and discrete maximal surfaces in Lorentz-Minkowski space ℝ²˒¹. Maximal surfaces are Riemannian surfaces with vanishing mean curvature in ℝ²˒¹, the natural analogue of minimal surfaces in ℝ³. We transfer results known for discrete minimal surfaces in ℝ³ and obtain a correspondence between discrete maximal surfaces in ℝ²˒¹ and hyperbolic orthogonal circle patterns, as well as a discrete Weierstrass type representation and an associated family of a discrete maximal surface in ℝ²˒¹. Our main motivation for introducing this discrete theory in ℝ²˒¹ originates from recent developments in statistical mechanics, in which a surprising connection was found between smooth maximal surfaces in ℝ²˒¹ and models in statistical mechanics. We give an interpretation of this relation in the discrete setting and show how discrete isothermic and discrete maximal surfaces relate to certain graph embeddings studied in the context of the Ising and the dimer model. We provide a geometric interpretation of the statistical parameters that define the corresponding model. Moreover, we define discrete constant mean curvature (cmc) surfaces in ℝ³ and ℝ²˒¹. We show that discrete cmc surfaces can be constructed from spherical and hyperbolic orthogonal ring patterns by introducing a new generalization of classical Koebe polyhedra. Ring patterns can be described by a variational principle, which we use to derive a general construction method for discrete cmc surfaces from given smooth examples. We present discretizations of classical smooth cmc surfaces, discuss the implementation of the general construction scheme, and provide access to the data of the discrete surfaces. Finally, we demonstrate that the theories of discrete minimal surfaces in ℝ³ and discrete maximal surfaces in ℝ²˒¹ can be obtained from the theory of discrete cmc surfaces by considering the limit of vanishing mean curvature.Wir führen eine neue Theorie diskreter Isothermflächen und diskreter Maximalflächen im Lorentz-Minkowski Raum ℝ²˒¹ ein. Maximalflächen sind Riemannsche Flächen in ℝ²˒¹ mit konstanter mittlerer Krümmung Null, das natürliche Gegenstück zu Minimalflächen in ℝ³. Wir übertragen bekannte Ergebnisse aus dem Euklidischen und erhalten eine Korrespondenz zwischen diskreten Maximalflächen in ℝ²˒¹ und hyperbolischen orthogonalen Kreismustern, sowie eine diskrete Weierstraß Darstellung und eine assoziierte Familie einer diskreten Maximalfläche in ℝ²˒¹. Unsere Hauptmotivation für die Einführung dieser diskreten Theorie in ℝ²˒¹ stammt aus aktuellen Entwicklungen in der statistischen Mechanik, in der eine überraschende Verbindung zwischen glatten Maximalflächen in ℝ²˒¹ und Modellen der statistischen Mechanik gefunden wurde. Wir geben eine Interpretation dieser Beziehung im Diskreten und zeigen, wie diskrete Isothermflächen und Maximalflächen mit Einbettungen von Graphen zusammenhängen, die im Zusammenhang mit dem Ising und dem Dimer Modell untersucht wurden. Wir liefern eine geometrische Interpretation der statistischen Parameter, die das entsprechende Modell definieren. Außerdem definieren wir diskrete Flächen konstanter mittlerer Krümmung (cmc) in ℝ³ und ℝ²˒¹. Wir zeigen, dass diskrete cmc Flächen aus sphärischen und hyperbolischen orthogonalen Ringmustern konstruiert werden können, indem wir eine neue Verallgemeinerung klassischer Koebe Polyeder einführen. Ringmuster können durch ein Variationsprinzip beschrieben werden, das wir verwenden, um eine allgemeine Konstruktionsmethode für diskrete cmc Flächen aus gegebenen glatten Beispielen abzuleiten. Wir stellen Diskretisierungen klassischer glatter cmc Flächen vor, beschreiben die Implementierung des allgemeinen Konstruktionsschemas und bieten Zugriff auf die Daten der diskreten Flächen. Schließlich zeigen wir, dass sich die Theorien der diskreten Minimalflächen in ℝ³ und der diskreten Maximalflächen in ℝ²˒¹ aus der Theorie der diskreten cmc Flächen ableiten lassen, indem man den Grenzwert betrachtet, bei dem die mittlere Krümmung verschwindet
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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