Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly Influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network Sampling Therefore, it becomes critical to devise effective means for sound estimation of net work topological and dynamical properties will le avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential IS Illustrated with respect to two real-world networks. namely bone canals and air transportation (C) 2009 Elsevier B.V. All rights reserved.

Major shear zones of southern Brazil and Uruguay: escape tectonics in the eastern border of Rio de La plata and Paranapanema cratons during the Western Gondwana amalgamation

The Mantiqueira Province represents a series of supracrustal segments of the South-American counterpart formed during the Gondwana Supercontinent agglutination. In this crustal domain, the process of escape tectonics played a conspicuous role, generating important NE-N-S-trending lineaments. The oblique component of the motions of the colliding tectonic blocks defined the transpressional character of the main suture zones: Lancinha-Itariri, Cubato-Arcadia-Areal, Serrinha-Rio Palmital in the Ribeira Belt and Sierra Ballena-Major Gercino in the Dom Feliciano Belt. The process as a whole lasted for ca. 60 Ma, since the initial collision phase until the lateral escape phase predominantly marked by dextral and subordinate sinistral transpressional shear zones. In the Dom Feliciano Belt, southern Brazil and Uruguay, transpressional event at 630-600 Ma is recognized and in the Ribeira Belt, despite less coevally, the transpressional event occurred between 590 and 560 Ma in its northern-central portion and between ca. 625 and 595 Ma in its central-southern portion. The kinematics of several shear zones with simultaneous movement in opposite directions at their terminations is explained by the sinuosity of these lineaments in relation to a predominantly continuous westward compression.

The basement of the Punta del Este Terrane (Uruguay): an African Mesoproterozoic fragment at the eastern border of the South American Rio de La Plata craton

The Punta del Este Terrane (eastern Uruguay) lies in a complex Neoproterozoic (Brasiliano/Pan-African) orogenic zone considered to contain a suture between South American terranes to the west of Major Gercino-Sierra Ballena Suture Zone and eastern African affinities terranes. Zircon cores from Punta del Este Terrane basement orthogneisses have U-Pb ages of ca. 1,000 Ma, which indicate an lineage with the Namaqua Belt in Southwestern Africa. U-Pb zircon ages also provide the following information on the Punta del Este terrane: the orthogneisses containing the ca. 1,000 Ma inheritance formed at ca. 750 Ma; in contrast to the related terranes now in Africa, reworking of the Punta del Este Terrane during Brasiliano/Pan-African orogenesis was very intense, reaching granulite facies at ca. 640 Ma. The termination of the Brasiliano/Pan-African orogeny is marked by formation of acid volcanic and volcanoclastic rocks at ca. 570 Ma (Sierra de Aguirre Formation), formation of late sedimentary basins (San Carlos Formation) and then intrusion at ca. 535 Ma of post-tectonic granitoids (Santa Teresa and Jos, Ignacio batholiths). The Punta del Este Terrane and unrelated western terranes represented by the Dom Feliciano Belt and the Rio de La Plata Craton were in their present positions by ca. 535 Ma.

Unraveling an antique subduction process from metamorphic basement around Medellin city, Central Cordillera of Colombian Andes

In the surroundings of Caldas and El Retiro cities (Colombia) metamorphic rocks derived from basic and pelitic protoliths comprise the Caldas amphibole schist and the Ancon schist respectively. Subordinated metamorphosed granite bodies (La Miel gneiss) are associated to these units, and The El Retiro amphibolites, migmatites and granulites crops out eastwards of these units, separated by shear zones. The Caldas amphibole schist and the Ancon schist protoliths could have been formed in a distal marine reduced environment and amalgamated to the South American continent in an apparent Triassic subduction event. The El Retiro rocks are akin to a continental basement and possible include impure metasediments of continental margin, whose metamorphism originated granulite facies rocks and migmatites as a result of the anatexis of quartz-feldspathic rocks. The metamorphism was accompanied by intense deformation, which has juxtaposed both migmatites and granulite blocks. Afterward, heat and fluid circulation associated with the emplacement of minor igneous intrusions resulted in intense fluid-rock interaction, variations in the grain size of the minerals and, especially, intense retrograde metamorphic re-equilibrium. Thermobarometric estimations for the Caldas amphibole schist indicate metamorphism in the Barrovian amphibolite fades. The metamorphic path is counter-clockwise, but retrograde evolution could not be precisely defined. The pressures of the metamorphism in these rocks range from 6.3 to 13.5 kbar, with narrow temperature ranging from 550 to 630 degrees C. For the Ancon schist metapelites the P-T path is also counter-clockwise, with a temperature increase evidenced by the occurrence of sillimanite and the cooling by later kyanite. The progressive metamorphism event occurred at pressures of 7.6-7.2 kbar and temperatures of 645-635 degrees C for one sample and temperature between 500 and 600 degrees C under constant pressure of 6 kbar. The temperature estimated for these rocks varies between 400 and 555 degrees C at pressures of 5-6 kbar in the retrograde metamorphic path. The El Retiro rocks evidence strong decompression with narrow variation in temperature, showing pressure values between 8.7 and 2.7 kbar at temperatures of 740-633 degrees C. These metamorphic fragments of the basement in the Central Cordillera of the Colombian Andes could represent a close relationship with an antique subduction zone. (C) 2011 Elsevier Ltd. All rights reserved.