1,721,045 research outputs found
Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups
No full textWe describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author (Duke Math. J., 2010) and are the lamplighter groups F integral Z where F is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type F-n for any n.ungraded113sciescopu
Large Scale Geometry of Nilpotent-By-Cyclic Groups
No full textWe show quasi-isometric rigidity for a class of finitely generated, non-polycyclic nilpotent-by-cyclic groups. Specifically, let Gamma(1), Gamma(2) be ascending HNN extensions of finitely generated nilpotent groups N-1 and N-2, such that Gamma(1) is irreducible (see Definition 1.1). If Gamma(1) and Gamma(2) are quasi-isometric to each other then N-1 and N-2 are virtual lattices in a common simply connected nilpotent Lie group (N) over tilde. As a consequence, we show the class of irreducible ascending HNN extensions of finitely generated nilpotent groups is quasi-isometrically rigid.X1122sciescopu
Coarse differentiation and quasi-isometries of a class of solvable Lie groups II
No full textIn this paper, we continue with the results in [12] and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member of the subclass has to be polycyclic and is virtually a lattice in an abelian-by-abelian solvable Lie group. We also give an example of a unimodular solvable Lie group that is not quasi-isometric to any finitely generated group, as well deduce some quasi-isometric rigidity results.X1173sciescopu
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
Assouad-Nagata dimension of connected Lie groups
No full textWe prove that the asymptotic Assouad-Nagata dimension of a connected Lie group G equipped with a left-invariant Riemannian metric coincides with its topological dimension of G/C where C is a maximal compact subgroup. To prove it we will compute the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometrically embedded into any cocompact lattice on a connected Lie group.X1111sciescopu
Signed frames and Hadamard products of Gram matrices
No full textThis paper concerns (redundant) representations in a Hilbert space H of the form f = (j)Sigma c(j) Phi (j) For Allf is an element of H . These are more general than those obtained from a tight frame, and we develop a general theory based on what are called signed frames. We are particularly interested in the cases where the scaling factors cj are unique and the geometric interpretation of negative cj. This is related to results about the invertibility of certain Hadamard products of Gram matrices which are of independent interest, e.g., we show for almost every nu(1).....,nu(n) is an element of C-d rank ([ (r) (s)]) = min {((r+d-1)(d-1))((s+d-1)(d-1)).n}, r, s greater than or equal to 0. Applications include the construction of tight frames of bivariate Jacobi polynomials on a triangle which preserve symmetries, and numerical results and conjectures about the class of tight signed frames in a finite-dimensional space. (C) 2002 Elsevier Science Inc. All rights reserved.X1112sciescopu
Bilipschitz maps of boundaries of certain negatively curved homogeneous spaces
No full textIn this paper we study certain groups of bilipschitz maps of the boundary minus a point of a negatively curved space of the form R x M R-n, where M is a matrix whose eigenvalues all lie outside of the unit circle. The case where M is diagonal was previously studied by Dymarz (Geom Funct Anal (GAFA) 19:1650-1687, 2009). As an application, combined with work of Eskin-Fisher-Whyte and Peng, we provide the last steps in the proof of quasi-isometric rigidity for a class of lattices in solvable Lie groups.X1178sciescopu
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
- …
