1,721,042 research outputs found
A canonical thickening of Q and the dynamics of continued fractions
No full textWe construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy of α-continued fractions, thus proving a conjecture of Nakada and Natsui
The bifurcation locus for numbers of bounded type
No full textWe define a family of compact subsets of the unit interval which provides a filtration of the set of numbers whose continued fraction expansion has bounded digits. We study how the set changes as the parameter t ranges in, and see that the family undergoes period-doubling bifurcations and displays the same transition pattern from periodic to chaotic behaviour as the family of real quadratic polynomials. The set of bifurcation parameters is a fractal set of measure zero and Hausdorff dimension. The Hausdorff dimension of varies continuously with the parameter, and we show that the dimension of each individual set equals the dimension of the corresponding section of the bifurcation set
The entropy of alpha-continued fractions: numerical results
No full textWe consider the one-parameter family of interval maps arising from
generalized continued fraction expansions known as -continued fractions.
For such maps, we perform a numerical study of the behaviour of metric
entropy as a function of the parameter. The behaviour of entropy is known
to be quite regular for parameters for which a matching condition on the
orbits of the endpoints holds. We give a detailed description of the set
M where this condition is met: it consists of a countable union of open
intervals, corresponding to dierent combinatorial data, which appear to
be arranged in a hierarchical structure. Our experimental data suggest
that the complement of M is a proper subset of the set of bounded-type
numbers, hence it has measure zero. Furthermore, we give evidence that
the entropy on matching intervals is smooth; on the other hand, we can
construct points outside of M on which it is not even locally monotone
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
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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