1,720,960 research outputs found
Periodic triangulations of Zn
Get PDFWe consider in this work triangulations of Z n that are periodic along Z n . They generalize the triangulations obtained from Delaunay tessellations of lattices. In certain cases we impose additional restrictions on such triangulations such as regularity or invariance under central symmetry with respect to the origin; both properties hold for Delaunay tessellations of lattices. Full enumeration of such periodic triangulations is obtained for dimension at most 4 . In dimension 5 several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension 4 ) and a given simplex has a priori infinitely many possible adjacent simplices. We found 950 periodic triangulations in dimension 5 but finiteness of the whole family is unknown
On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5
Get PDFIn a recent paper, Garber, Gavrilyuk, and Magazinov [Discrete Comput. Geom., 53 (2015), pp. 245--260] proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all 5-dimensional Voronoi parallelohedra. Consequently, the Voronoi conjecture in holds if and only if every 5-dimensional parallelohedron is combinatorially Voronoi. Here, by saying that a parallelohedron is combinatorially Voronoi, we mean that is combinatorially equivalent to a Dirichlet--Voronoi polytope for some lattice , and this combinatorial equivalence is naturally translated into equivalence of the tiling by copies of with the Voronoi tiling of . We also propose a new condition which, if satisfied by a parallelohedron , is sufficient to infer that is affinely Voronoi. The condition is based on the new notion of the Venkov complex associated with a parallelohedron and cohomologies of this complex
Stable Betti numbers of (partial) toroidal compactifications of the moduli space of Abelian varieties
No full textWe present an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification ofA g satisfying certain additivity and finiteness properties, in terms of the combinatorics of the corresponding toric fans. In particular, the algorithm determines the stable cohomology of the matroidal partial compactification A Matrg , in terms of simple regular matroids that are irreducible with respect to the 1-sum operation, and their automorphism groups. The algorithm also applies to compute the stable Betti numbers in close to top degree for the perfect cone toroidal compactification APerf g. This suggests the existence of an algebra structure on H top−kstable (A Perfg , Q)
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
The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices
Get PDFThis paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check
VORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF FOR AND THE TRIVIALITY OF
No full textWe enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups and for , using quotient sublattices techniques for and linear programming methods for higher dimensions. These enumerations allow us to compute some cohomology of these groups and prove that , providing new knowledge on the Kummer-Vandiver conjecture.IDEX UG
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
VORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF FOR AND THE TRIVIALITY OF
No full textWe enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups and for , using quotient sublattices techniques for and linear programming methods for higher dimensions. These enumerations allow us to compute some cohomology of these groups and prove that , providing new knowledge on the Kummer-Vandiver conjecture.IDEX UG
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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