1,721,050 research outputs found
Hilbert's Nullstellensatz is in the Polynomial Hierarchy
No full textWe show that if the Generalized Riemann Hypothesis is true, the problem of deciding whether a system of polynomial equations in several complex variables has a solution is in the second level of the polynomial hierarchy. In fact, this problem is in AM, the "Arthur-Merlin" class (recall that NP ` AM ` RP NP ` \Pi 2 ). The best previous bound was PSPACE. An earlier version of this paper was distributed as NeuroCOLT Technical Report 96-44. The present paper includes in particular a new lower bound for unsatisfiable systems, and remarks on the ArthurMerlin class. 1 A part of this work was done when the author was visiting DIMACS at Rutgers University. 1 Introduction In its weak form, Hilbert's Nullstellensatz states that a system f 1 (x) = 0; : : : ; f s (x) = 0 (1) of polynomial equations in n unknowns has no solution over C if and only if there are polynomials g 1 ; : : : ; g s 2 C [X 1 ; : : : ; X n ] such that P s i=1 f i g i = 1. For this reason, the problem of deciding whethe..
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
Elimination of Constants from Machines over Algebraically Closed Fields
No full textLet K be an algebraically closed field of characteristic 0. We show that constants can be removed efficiently from any machine over K solving a problem which is definable without constants. This gives a new proof of the transfer theorem of Blum, Cucker, Shub & Smale for the problem P ? = NP. We have similar results in positive characteristic for non-uniform complexity classes. We also construct explicit and correct test sequences (in the sense of Heintz and Schnorr) for the class of polynomials which are easy to compute. An earlier version of this paper appeared as NeuroCOLT Technical Report 96-43. The present paper contains in particular a new bound for the size of explicit correct test sequences. 1 A part of this work was done when the author was visiting DIMACS at Rutgers University. 1 Introduction As in discrete complexity theory, the problem P ? = NP is a major open problem in the Blum-Shub-Smale model of computation over the reals [3]. It has been possible to show that P..
Closed-form Analytic Maps in One and Two Dimensions Can Simulate Turing Machines
No full textWe show closed-form analytic functions consisting of a finite number of trigonometric terms can simulate Turing machines, with exponential slowdown in one dimension or in real time in two or more. 1 A part of this author's work was done when he was visiting DIMACS at Rutgers University. 1 Introduction Various authors have independently shown [9, 12, 4, 14, 1] that finite-dimensional piecewise-linear maps and flows can simulate Turing machines. The construction is simple: associate the digits of the x and y coordinates of a point with the left and right halves of a Turing machine's tape. Then we can shift the tape head by halving or doubling x and y, and write on the tape by adding constants to them. Thus two dimensions suffice for a map, or three for a continuous-time flow. These systems can be thought of as billiards or optical ray tracing in three dimensions, recurrent neural networks, or hybrid systems. However, piecewise-linear functions are not very realistic from a physical p..
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
Definability of Geometric Properties in Algebraically Closed Fields
No full textWe prove that there exists no sentence F of the language of rings with an extra binary predicat I 2 satisfying the following property: for every definable set X ` C 2 , X is connected if and only if (C; X) j= F where I 2 is interpreted by X . We conjecture that the same result holds for the closed subsets of C 2 . We prove some results motivated by this conjecture. Keywords: definability, constraint databases, model theory, algebraically closed fields. R'esum'e On montre qu'il n'existe pas d"enonc'e F dans le langage des anneaux muni d'un pr'edicat binaire suppl'ementaire I 2 satisfaisant la propri'et'e suivante: pour tout ensemble d'efinissable X ` C 2 , X est connexe si et seulement si (C; X) j= F (I 2 est interpr'et'e par X dans l"enonc'e F ). Nous conjecturons que le meme r'esultat est vrai pour les ferm'ees de C 2 . Nous d'emontrons 'egalement quelques r'esultats motiv'es par cette conjecture. Mots-cl'es: d'efinissabilit'e, bases de donn'ees contraintes, th'eorie des m..
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