On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

GEOCHEMISTRY AND U-PB ZIRCON AGE OF THE INTERNAL OSSA-MORENA ZONE OPHIOLITE SEQUENCES: A REMNANT OF RHEIC OCEAN IN SW IBERIA

The Early Paleozoic geodynamic evolution in SW Iberia is believed to have been dominated by the opening of the Rheic Ocean. The Rheic Ocean is generally accepted to have resulted from the drift of peri-Gondwanan terranes such as Avalonia from the northern margin of Gondwana during Late Cambrian-Early Ordovician times. The closure of the Rheic Ocean was the final result of a continent-continent collision between Gondwana and Laurussia that produced the Variscan orogen. The Ossa-Morena Zone is a peri-Gondwana terrane, which preserves spread fragments of ophiolites - the Internal Ossa-Morena Zones Ophiolite Sequences (IOMZOS). The final patchwork of the IOMZOS shows a complete oceanic lithospheric sequence with geochemical characteristics similar to the ocean-floor basalts, without any orogenic fingerprint and/or crustal contamination. The IOMZOS were obducted and imbricated with high pressure lithologies. Based on structural, petrological and whole-rock geochemical data, the authors argue that the IOMZOS represent fragments of the oceanic lithosphere from the Rheic Ocean. Zircon SHRIMP U-Pb geochronological data on metagabbros point to an age of ca. 480 Ma for IOMZOS, providing evidence of a well-developed ocean in SW Iberia during this period, reinforcing the interpretation of the Rheic Ocean as a wide ocean among the peri-Gondwanan terranes during Early Ordovician times.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

A note on tilting sequences

We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.