1,720,959 research outputs found
On the Number of Flats Tangent to Convex Hypersurfaces in Random Position
Get PDFMotivated by questions in real enumerative geometry (Borcea et al., in Discrete Comput Geom 35(2):287–300, 2006; Bürgisser and Lerario, in J Reine Angew Math, https://doi.org/10.1515/crelle-2018-0009, 2018; Megyesi and Sottile, in Discrete Comput Geom 33(4):617–644, 2005; Megyesi et al., in Discrete Comput Geom 30(4):543–571, 2003; Sottile and Theobald, in Trans Am Math Soc 354(12):4815–4829, 2002; Proc Am Math Soc 133(10):2835–2844, 2005; in: Goodman et al., in Surveys on discrete and computational geometry. AMS, Providence, 2008) we investigate the problem of the number of flats simultaneously tangent to several convex hypersurfaces in real projective space from a probabilistic point of view (here by “convex hypersurfaces” we mean that these hypersurfaces are boundaries of convex sets). More precisely, we say that smooth convex hypersurfaces X1,...,Xdk,n⊂RPn, where dk,n= (k+ 1) (n- k) , are in random position if each one of them is randomly translated by elements g1,...,gdk,n sampled independently from the orthogonal group with the uniform distribution. Denoting by τk(X1,...,Xdk,n) the average number of k-dimensional projective subspaces (k-flats) which are simultaneously tangent to all the hypersurfaces we prove that τk(X1,...,Xdk,n)=δk,n·∏i=1dk,n|Ωk(Xi)||Sch(k,n)|,where δk,n is the expected degree from [6] (the average number of k-flats incident to dk,n many random (n- k- 1) -flats), | Sch (k, n) | is the volume of the Special Schubert variety of k-flats meeting a fixed (n- k- 1) -flat (computed in [6]) and | Ω k(X) | is the volume of the manifold Ω k(X) ⊂ G(k, n) of all k-flats tangent to X. We give a formula for the evaluation of | Ω k(X) | in terms of some curvature integral of the embedding X↪ RP n and we relate it with the classical notion of intrinsic volumes of a convex set: |Ωk(∂C)||Sch(k,n)|=4Vn-k-1(C),k=0,...,n-1.As a consequence we prove the universal upper bound: τk(X1,...,Xdk,n)≤δk,n·4dk,n.Since the right hand side of this upper bound does not depend on the specific choice of the convex hypersurfaces, this is especially interesting because already in the case k= 1 , n= 3 for every m> 0 we can provide examples of smooth convex hypersurfaces X1, ... , X4 such that the intersection Ω 1(X1) ∩ ⋯ ∩ Ω 1(X4) ⊂ G(1 , 3) is transverse and consists of at least m lines. Finally, we present analogous results for semialgebraic hypersurfaces (not necessarily convex) satisfying some nondegeneracy assumptions
Random spectrahedra
Get PDFSpectrahedra are affine-linear sections of the cone Pn of positive semidefinite symmetric n × n-matrices. We consider random spectrahedra that are obtained by intersecting Pn with the affine-linear space 1 + V , where 1 is the identity matrix and V is an `-dimensional linear space that is chosen from the unique orthogonally invariant probability measure on the Grassmanian of `-planes in the space of n × n real symmetric matrices (endowed with the Frobenius inner product). Motivated by applications, for ` = 3 we relate the average number Eσn of singular points on the boundary of a three-dimensional spectrahedron to the volume of the set of symmetric matrices whose two smallest eigenvalues coincide. In the case of quartic spectrahedra (n = 4) we show that Eσ4 = 6 − √43 . Moreover, we prove that the average number E ρn of singular points on the real variety of singular matrices in 1 + V is n(n − 1). This quantity is related to the volume of the variety of real symmetric matrices with repeated eigenvalues. Furthermore, we compute the asymptotics of the volume and the volume of the boundary of a random spectrahedron
Minimality of tensors of fixed multilinear rank
No full textWe discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of the fixed multilinear rank form a minimal submanifold of the Euclidean space of tensors endowed with the Frobenius inner product. We also establish the absence of local extrema for linear functionals restricted to the submanifold of rank-one tensors, finding application in statistics
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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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