1,720,970 research outputs found
On constructing RAGS via homogeneous splines
Full text linkRecently, a construction of spline spaces suitable for representing smooth parametric surfaces of arbitrary topological genus and arbitrary order of continuity has been proposed. These splines, called RAGS (rational geometric splines), are a direct generalization of bivariate polynomial splines on planar triangulations. In this paper we discuss how to construct parametric splines associated with the three homogeneous geometries (spherical, affine, and hyperbolic) and we also consider a number of related computational issues. We then show how homogeneous splines can be used to obtain RAGS. As examples of RAGS surfaces we consider direct analogs of the Powell-Sabin macro-elements and also spline surfaces of higher degrees and higher orders of continuity obtained by minimizing an energy functional
Modifications of Prony’s Method for the Recovery and Sparse Approximation with Generalized Exponential Sums
No full textCascade Networks, Generalized Neural Networks, and Approximation of Functions
No full textA neural network is a supervised machine learning model based on how the brain acquires and stores knowledge. Due to the availability of large amounts of training data and improvements in computing power, neural networks are increasingly used in a wide range of machine learning problems. While neural networks have produced an abundance of successes in practical applications, the basis of these successes lacks rigorous mathematical analysis. In its most general form, a neural network is a function given by repeatedly applying a fixed function, in general nonlinear, to an affine operator. In this thesis, close analogs to neural networks using the rectified linear unit (ReLU) activation function are introduced. These analogs, called cascade networks, are also functions given by repeatedly applying a fixed function to an affine operator. Cascade networks have a close connection with algorithms used in computer aided geometric design and multiresolution analysis. In particular, the connection between cascade networks, subdivision algorithms, and the cascade algorithm is discussed. Using cascade networks to approximate polynomials and smooth functions, similar results were obtained when compared to the results for ReLU neural networks
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
Approximation of Besov Vectors by Paley–Wiener Vectors in Hilbert Spaces
Full text linkWe develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data representation, compression, denoising and visualization. These tasks are of great importance to machine learning, complex data analysis and computer vision
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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