1,720,969 research outputs found
The Martin compactification of the Cartesian product of two hyperbolic spaces
No full textConsider H_m × H_n the Cartesian product of two hyperbolic spaces with dimensions m and n respectively. It carries the product Riemannian structure and corresponding Laplace-Beltrami operator Δ=Δ_m x Δ_n, the sum of the Laplace Beltrami operators on the two factors. It is well known that there exist positive functions h on H_m × H_n which satisfy Δh=λh if and only if λ≥λ_0, where λ_0=-((m-1)/2)^2-((n-1)/2)^2 is the bottom of the positive spectrum
Brownian motion and harmonic functions on Sol(p,q)
No full textThe Lie group Sol(p, q) is the semidirect product induced by the action of R on R-2 which is given by (x, y) bar right arrow (e(pz)x, e(-qz)y), z is an element of R. Viewing Sol(p, q) as a three-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and compute the rate of escape. Also, we introduce the natural geometric compactification of Sol(p, q) and explain how Brownian motion converges almost surely to the boundary in the resulting topology. We also study all positive harmonic functions for the Laplacian with drift, and determine explicitly all minimal harmonic functions. All these are carried out with a strong emphasis on understanding and using the geometric features of Sol(p, q), and, in particular, the fact that it can be described as the horocyclic product of two hyperbolic planes with curvatures -p(2) and -q(2), respectively
Brownian motion on treebolic space: escape to infinity
No full textTreebolic space is an analog of the Sol geometry, namely, it is the horocylic product of the hyperbolic upper half plane H and the homogeneous tree T = T-p, with degree p + 1 >= 3, the latter seen as a one-complex. Let h be the Busemann function of T with respect to a fixed boundary point. Then for real q > 1 and integer p >= 2, treebolic space HT(q, p) consists of all pairs (z = x + iy, w) is an element of H x T with h(w) = log(q) y. It can also be obtained by glueing together horizontal strips of Elf in a tree-like fashion. We explain the geometry and metric of HT and exhibit a locally compact group of isometries (a horocyclic product of affine groups) that acts with compact quotient. When q = p, that group contains the amenable Baumslag-Solitar group BS(p) as a co-compact lattice, while when q not equal p, it is amenable, but non-unimodular. HT(q, p) is a key example of a strip complex in the sense of [4].
Relying on the analysis of strip complexes developed by the same authors in [4], we consider a family of natural Laplacians with "vertical drift" and describe the associated Brownian motion. The main difficulties come from the singularities which treebolic space (as any strip complex) has along its bifurcation lines. In this first part, we obtain the rate of escape and a central limit theorem, and describe how Brownian motion converges to the natural geometric boundary at infinity. Forthcoming work will be dedicated to positive harmonic functions
Brownian motion on treebolic space : positive harmonic functions
Full text linkThis paper studies potential theory on treebolic space, that is,
the horocyclic product of a regular tree and hyperbolic upper half plane. Relying
on the analysis on strip complexes developed by the authors, a family of Laplacians
with “vertical drift” parameters is considered. We investigate the positive harmonic
functions associated with those Laplacians
The heat semigroup and Brownian motion on strip complexes
No full textAbstractWe introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing “strips” along their natural boundaries according to a given graph structure. The most familiar example is the one-dimensional complex classically associated with a graph, in which case the strips are simply copies of the unit interval (our setup actually allows for variable edge length). A leading key example is treebolic space, a geometric object studied in a number of recent articles, which arises as a horocyclic product of a metric tree with the hyperbolic plane. In this case, the graph is a regular tree, the strips are [0,1]×R, and each strip is equipped with the hyperbolic geometry of a specific strip in upper half plane. We consider natural families of Dirichlet forms on a general strip complex and show that the associated heat kernels and harmonic functions have very strong smoothness properties. We study questions such as essential self-adjointness of the underlying differential operator acting on a suitable space of smooth functions satisfying a Kirchhoff type condition at points where the strip complex bifurcates. Compatibility with projections that arise from proper group actions is also considered
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
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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