1,720,961 research outputs found
A length comparison theorem for geodesic currents
Get PDFWe work with the space of geodesic currents on a closed
surface of negative Euler characteristic. By prior work of the author with
Sebastian Hensel, each filling geodesic current has a unique
length-minimizing metric in Teichm\"uller space. In this paper, we show
that, on so-called thick components of , the geometries of and are
comparable, up to a scalar depending only on and the topology of . We
also characterize thick components of the projection using only the length
function of .Comment: 46 pages, 29 figures. Added results on identifying short curves,
thick subsurfaces of projectio
An extension of the Thurston metric to projective filling currents
Get PDFWe study the geometry of the space of projectivized filling geodesic currents
. Bonahon showed that Teichm\"uller space,
embeds into . We extend the
symmetrized Thurston metric from to the entire (projectivized)
space of filling currents, and we show that is isometrically
embedded into the bigger space. Moreover, we show that there is no
quasi-isometric projection back down to . Lastly, we study the
geometry of a length-minimizing projection from to defined previously by Hensel and the author.Comment: 16 pages, 3 figures. Updated to cite theorems from previous pape
Counting geodesics on expander surfaces
Get PDFWe study properties of typical closed geodesics on expander surfaces of high
genus, i.e. closed hyperbolic surfaces with a uniform spectral gap of the
Laplacian. Under an additional systole lower bound assumption, we show almost
every geodesic of length much greater than is non-simple. And
we prove almost every closed geodesic of length much greater than is filling, i.e. each component of the complement of the geodesic is a
topological disc. Our results apply to Weil-Petersson random surfaces, random
covers of a fixed surface, and Brooks-Makover random surfaces, since these
models are known to have uniform spectral gap asymptotically almost surely.
Our proof technique involves adapting Margulis' counting strategy to work at
low length scales.Comment: 55 pages, 7 figures. Minor modification
A projection from filling currents to Teichm\"uller space
Get PDFLet be a closed, genus surface. The space of geodesic currents on
encompasses the set of closed curves up to homotopy, as well as Teichm\"uller
space, and many other spaces of structures on . We show that one can define
a mapping class group equivariant, length-minimizing projection from the set of
filling geodesic currents down to Teichm\"uller space, and prove some basic
properties of this projection to show that it is well-behaved.Comment: 13 page
Simple vs non-simple loops on random regular graphs
Get PDFIn this note we solve the ``birthday problem'' for loops on random regular
graphs. Namely, for fixed , we prove that on a random -regular graph
with vertices, as approaches infinity, with high probability:
(i) almost all primitive non-backtracking loops of length
are simple, i.e. do not self-intersect,
(ii) almost all primitive non-backtracking loops of length
self-intersect.Comment: 20 Pages, 1 Figur
Coarse density of subsets of
Get PDFLet be the moduli space of genus Riemann surfaces. We
show that an algebraic subvariety of is coarsely dense with
respect to the Teichm\"uller metric (or Thurston metric) if and only if it is
all of . We apply this to projections of
-orbit closures in the space of abelian
differentials. Moreover, we determine which strata of abelian differentials
have coarsely dense projection to .Comment: 12 pages, 1 figur
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
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