Complex networks analysis of manual and machine translations

Complex networks have been increasingly used in text analysis, including in connection with natural language processing tools, as important text features appear to be captured by the topology and dynamics of the networks. Following previous works that apply complex networks concepts to text quality measurement, summary evaluation, and author characterization, we now focus on machine translation (MT). In this paper we assess the possible representation of texts as complex networks to evaluate cross-linguistic issues inherent in manual and machine translation. We show that different quality translations generated by NIT tools can be distinguished from their manual counterparts by means of metrics such as in-(ID) and out-degrees (OD), clustering coefficient (CC), and shortest paths (SP). For instance, we demonstrate that the average OD in networks of automatic translations consistently exceeds the values obtained for manual ones, and that the CC values of source texts are not preserved for manual translations, but are for good automatic translations. This probably reflects the text rearrangements humans perform during manual translation. We envisage that such findings could lead to better NIT tools and automatic evaluation metrics.

Paleomagnetic data and K-Ar ages from Mesozoic units of the Santa Marta massif: A preliminary interpretation for block rotation and translations

We report 6 K-Ar ages and paleomagnetic data from 28 sites collected in Jurassic, Lower Cretaceous and Paleocene rocks of the Santa Marta massif, to test previous hypothesis of rotations and translations of this massif, whose rock assemblage differs from other basement-cored ranges adjacent to the Guyana margin. Three magnetic components were identified in this study. A first component has a direction parallel to the present magnetic field and was uncovered in all units (D 352, I = 25.6, k = 57.35, a95 = 5.3, N = 12). A second component was isolated in Cretaceous limestone and Jurassic volcaniclastic rocks (D = 8.8, I = 8.3, k = 24.71, a95 = 13.7, N = 6), and it was interpreted as of Early Cretaceous age. In Jurassic sites with this component, Early Cretaceous K-Ar ages obtained from this and previous studies are interpreted as reset ages. The third component was uncovered in eight sites of Jurassic volcaniclastic rocks, and its direction indicates negative shallow to moderate inclinations and northeastward declinations. K-Ar ages in these sites are of Early (196.5 +/- 4.9 Ma) to early Late Jurassic age (156.6 +/- 8.9 Ma). Due to local structural complexity and too few Cretaceous outcrops to perform a reliable unconformity test, we only used two sites with (1) K-Ar ages, (2) less structural complexity, and (3) reliable structural data for Jurassic and Cretaceous rocks. The mean direction of the Jurassic component is (D = 20.4, I = -18.2, k = 46.9, a95 = 5.1, n = 18 specimens from two sites). These paleomagnetic data support previous models of northward along-margin translations of Grenvillian-cored massifs. Additionally, clockwise vertical-axis rotation of this massif, with respect to the stable craton, is also documented; the sense of rotation is similar to that proposed for the Perija Range and other ranges of the southern Caribbean margin. More data is needed to confirm the magnitudes of rotations and translations. (C) 2009 Elsevier Ltd. All rights reserved.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.