1,721,039 research outputs found
On local analysis
Get PDFWe extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these condition numbers around a point.Fil: Cucker, Felipe. City University Of Hong Kong; Hong KongFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
Computing the Homology of Real Projective Sets
Get PDFWe describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on its size and is singly exponential in the number of variables (the dimension of the ambient space) and polynomial in the condition and the degrees of the defining polynomials. In addition, we show that outside of an exceptional set of measure exponentially small in the size of the data, the algorithm takes exponential time.Fil: Cucker, Felipe. City University Of Hong Kong; Hong KongFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Shub, Michael Ira. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina. City University of New York; Estados Unido
A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
Get PDFWe show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.Fil: Cucker, Felipe. University of Hong Kong; ChinaFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Malajovich, Gregorio. Universidade Federal do Rio de Janeiro; BrasilFil: Wschebor, Mario. Universidad de la República; Urugua
Pathwise convergence of numerical schemes for random and stochastic differential equations
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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
Numerische und statistische Aspekte von Tensor-Zerlegungen
No full textIn this work we study numerical and statistical properties of tensor decompositions, namely the canonical-polyadic decomposition— commonly known as tensor-rank decomposition—and the computation of tensor eigenpairs. After a preliminary section, in which we consider tensors and their properties, explain the use of condition numbers in numerical analysis and give a short introduction to random tensors, this work is divided into three parts. In the first part we define a condition number for the tensor-rank decomposition, give an algorithm to compute tensor-rank decompositions and analyze this algorithm by means of the aforementioned condition number. Furthermore, we give an interpretation of the condition number for the tensor-rank decomposition
as an inverse distance to ill-posedness. In the second part we give an introduction to eigenpairs of tensors. Thereafter, we compute the density of an eigenvalue that is chosen uniform at random from all the eigenvalues of a tensor, whose entries are i.i.d. complex Gaussian ran-
dom variables. Furthermore, we construct an efficient (average polynomial-time) homotopy-method to solve for tensor eigenpairs.
Finally, in the third part we investigate the expected number of real eigenpairs for a random real tensor tensor. We consider two random tensor models: The first is the generalization of the real Ginibre ensemble from matrices to tensors; the second is the generalization of the Gaussian Orthogonal Ensemble from symmetric matrices to symmetric tensors.In dieser Arbeit werden numerische und statistische Eigenschaft von Tensor Zerlegungen untersucht. Diese sind die kanonisch-polyadische Zerlegung—auch bekannt als Tensor-Rang Zerlegung—und die Berechnung von Tensor Eigenpaaren. Zunächst stellen wir in einem einleitenden Abschnitt Tensoren und ihre Eigenschaften vor, erklären den Nutzen von Konditionszahlen in der numerischen Analyse und geben eine kurze Einleitung in zufällige Tensoren. Der weitere Teil der Arbeit ist in drei Abschnitte gegliedert. Im ersten Abschnitt definieren wir die Konditionszahl der Tensor-Rang Zerlegung, beschreiben einen Algorithmus um jene zu berechnen und analysieren diesen Algorithmus mit Hilfe der zuvor genannten Konditionszahl. Zudem interpretieren wir die Konditionszahl als inversen Abstand zur ”ill-posedness”. Darauf folgend, im zweiten Teil, geben wir eine Einführung in Tensor Eigenpaare. Im Anschluss berechnen wir die Dichte eines Eigenwertes, der uniform aus allen Eigenwerten eines zufälligen complexen Tensors gezogen wird. Dabei sind die Einträge des Tensors unabhängig und identisch verteilte complex Gauss’sche Zufallsvariablen. Weiterhin beschreiben wir ein effizientes (im Mittel Polynomialzeit) Homotopie-Verfahren um Tensor Eigenpaare zu berechnen. Im dritten und letzten Abschnitt untersuchen wir die erwartete Anzahl reeller Eigenpaare eines reellen zufälligen Tensors. Dabei betrachten wir zwei Modelle eines zufälligen Tensors: Das Erste ist die Verallgemeinerung des reellen Ginibre Ensembles von Matrizen zu Tensoren; das zweite ist die Verallgemeinerung des Gauss’schen Orthogonal Ensembles von symmetrischen Matrizen zu symmetrischen Tensoren.DFG, BU 1371/2-2, Geglättete Analyse von Konditionszahle
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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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