1,720,986 research outputs found
Buchberger-Weispfenning theory for effective associative rings
Get PDFWe present here a new approach for computing Groebner bases for bilateral modules over an effective ring. Our method is based on Weispfenning notion of restricted Groebner bases and related multiplication
Buchberger-Zacharias Theory of multivariate Ore extensions
Get PDFFollowing the recent survey on Buchberger-Zacharias Theory for monoid rings R[S] over a unitary effective ring R and an effective monoid S, we propose here a presentation of Buchberger Zacharias Theory and related Grobner basis computation algorithms for multivariate Ore extensions of rings presented as modules over a principal ideal domain, using Moller-Pritchard lifting theorem
A general framework for Noetherian well ordered polynomial reductions
Get PDFPolynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly established. This paper presents a definition of the generic concept of polynomial reduction structure, studies its features and highlights the aspects needed in order to grant and to efficiently test the main properties (Noetherianity, confluence, ideal membership). The most significant aspect of this analysis is a negative reappraisal of the role of the notion of term ordering which is usually considered a central and crucial tool in the theory. In fact, as it was already established in the computer science context in relation with termination of algorithms, most of the properties can be obtained simply considering a well founded order, while the classical requirement that it be preserved by multiplication is irrelevant. The last part of the paper shows how the polynomial basis concepts present in literature are interpreted in our language and their properties are consequences of the general results established in the first part of the paper
HELP: a sparse error locator polynomial for BCH codes
Get PDFIn 1990 Cooper suggested to use Groebner bases’ computations to decode
cyclic codes and his idea gave rise to many research papers. In particular, as proved
by Sala-Orsini, once defined the polynomial ring whose variables are the syndromes,
the locations and the error values and considered the syndrome ideal, only one polynomial of a lexicographical Groebner basis for such ideal is necessary to decode (the
general error locator polynomial, a.k.a. GELP). The decoding procedure only consists
in evaluating this polynomial in the syndromes and computing its roots: the roots are
indeed the error locations. A possible bottleneck in this procedure may be the evaluation part, since a priori the GELP may be dense.
In this paper, focusing on binary cyclic codes with length n = 2^m − 1, correcting up to
two errors, we give a Groebner-free, sparse analog of the GELP, the half error locator polynomial (HELP). In particular, we show that it is not necessary to compute the
whole Groebner basis for getting such kind of locator polynomial and we construct
the HELP, studying the quotient algebra of the polynomial ring modulo the syndrome
ideal by a combinatorial point of view. The HELP turns out to be computable with
quadratic complexity and it has linear growth in the length n of the code: O( (n+1)/2)
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
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