1,720,983 research outputs found
Long shortest vectors in low dimensional lattices
No full textFor coprime integers , with , we define the set We study which parameters generate point sets with long shortest distances between the points of the set in dependence of and relate such sets to lattices of a particular form. As a main result, we present an infinite family of such lattices with the property that the normalised norm of the shortest vector of each lattice converges to the square root of the Hermite constant . We obtain a similar result for the generalisation of our construction to 4 and 5 dimensions.<br/
On the expected L2-discrepancy of stratified samples from parallel lines
No full textWe study the expected -discrepancy of stratified samples
generated from special equi-volume partitions of the unit square. The
partitions are defined via parallel lines that are all orthogonal to the
diagonal of the square. It is shown that the expected discrepancy of stratified
samples derived from these partitions is a factor 2 smaller than the expected
discrepancy of the same number of i.i.d uniformly distributed random points in
the unit square. We conjecture that this is best possible among all partitions
generated from parallel lines.Comment: 22 pages, 8 figures, several inaccuracies correcte
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
Uniformly distributed sequences in the orthogonal group and on the Grassmannian manifold
No full textWe construct and implement a uniformly distributed sequence in the orthogonal group O(n). From this sequence we obtain a uniformly distributed sequence on the Grassmannian manifold G(n,k), which we use to approximate integral-geometric formulas. We show that our algorithm compares well with classical random constructions which motivates various directions for future research.</p
Greedy energy minimization can count in binary: point charges and the van der Corput sequence
No full textThis paper establishes a connection between a problem in Potential Theory and Mathematical Physics, arranging points so as to minimize an energy functional, and a problem in Combinatorics and Number Theory, constructing ’well-distributed’ sequences of points on [0, 1). Let f:[0,1]→R be (1) symmetric f(x)=f(1−x), (2) twice differentiable on (0, 1), and (3) such that f′′(x)>0 for all x∈(0,1). We study the greedy dynamical system, where, given an initial set {x0,…,xN−1}⊂[0,1), the point xN is obtained as xN=argminx∈[0,1)∑k=0N−1f(|x−xk|). We prove that if we start this construction with the single element x0=0, then all arising constructions are permutations of the van der Corput sequence (counting in binary and reflected about the comma): greedy energy minimization recovers the way we count in binary. This gives a new construction of the classical van der Corput sequence. The special case f(x)=1−log(2sin(πx)) answers a question of Steinerberger. Interestingly, the point sets we derive are also known in a different context as Leja sequences on the unit disk
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
Long shortest vectors in low dimensional lattices
No full textFor coprime integers , with , we define the set We study which parameters generate point sets with long shortest distances between the points of the set in dependence of and relate such sets to lattices of a particular form. As a main result, we present an infinite family of such lattices with the property that the normalised norm of the shortest vector of each lattice converges to the square root of the Hermite constant . We obtain a similar result for the generalisation of our construction to 4 and 5 dimensions.<br/
An Accurate Heuristic for a Problem of Shparlinski
No full textIn this note, we apply classical results from number theory to give an affirmative, but heuristic, answer to the question of Shparlinski (Japanese J. Math., 2012) whether there exist infinitely many primes p of the form p = k2 + lk + 1, with integers k, l, such that k > 0 and 0 ≤ 1 < 2√k + 1. Based on a heuristic argument, we provide a formula for the number of such primes, which is surprisingly accurate as computations show.</p
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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