1,720,986 research outputs found
SICs and the elements of order three in the Clifford group
No full textFor over a decade, there has been intensive work on the numerical and analytic construction of SICs (d(2) equiangular lines in C-d) as an orbit of the Heisenberg group. The Clifford group, which consists of the unitary matrices which normalise the Heisenberg group, plays a key role in these constructions. All of the known fiducial (generating) vectors for such SICs are eigenvectors of symplectic operations in the Clifford group with canonical order 3. Here we describe the Clifford group and the subgroup of symplectic operations in terms of a natural set of generators. From this, we classify all its elements of canonical order three. In particular, we show (contrary to prior claims) that there are symplectic operations of canonical order 3 for d 6 mod 9, which are not conjugate to the Zauner matrix. It is as yet unknown whether these give rise to SICs
The Construction of Complex and Quaternionic Spherical Designs
No full textThe existence of a spherical (t, t)-design with a small number of vectors is of
interest to mathematical researchers. In this thesis, I discuss how to construct a
spherical design of higher order from the union of spherical designs. Furthermore,
by finding the harmonic Molien series for some finite subgroups of unitary actions,
I show under what conditions all orbits of these groups are spherical (t, t)-design.
These techniques provide some examples of spherical (t, t)-design with a small number
of vectors. Finally, I show the decomposition of complex-valued multivariate
quaternion polynomials into irreducible unitarily invariant subspaces
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
A generalised beta integral and the limit of the Bernstein--Durrmeyer operator with Jacobi weights
No full textWe give a generalisation of the multivariate beta integral. This is used to show that the (multivariate) Bernstein--Durrmeyer operator for a Jacobi weight has a limit as the weight becomes singular. The limit is an operator previously studied by Goodman and Sharma. From the elementary proof given, it follows that this operator inherits many properties of the Bernstein--Durrmeyer operator in a natural way. In particular, we determine its eigenstructure and give a differentiation formula for it
On Bernstein's comparison theorem, Peano kernels of constant sign and near-minimax approximation
No full textSome basic properties of what are called `B(ernstein)-monotone' seminorms are investigated. These lie between the classes of monotone and sign-monotone seminorms. It is seen that these seminorms arise naturally in Bernstein's comparison theorem, the description of Peano kernels of constant sign, and in near-minimax approximations. A number of new results are obtained including some sufficient conditions for a projection to be near-minimax which are easily seen to be satisfied by all the known examples, and a characterisation of the Peano kernels of constant sign where derivatives are replaced by divided difference
Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials
No full textA sharp pointwise error estimate is given for multivariate positive linear operators which reproduce the linear polynomials. This quantitative Korovkin--type theorem generalises a known univariate result. It is applied to a number of operators including the multivariate Bernstein operators, and the recently introduced Bernstein--Schoenberg type operators of Dahmen, Micchelli and Seidel
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