MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

Reaction microtextures of monazite: Correlation between chemical and age domains in the Nazare Paulista migmatite, SE Brazil

Back-scattered imaging, X-ray element mapping and electron microprobe analyzer (EMPA) chemical dating reveal complex compositional and age zoning in monazite crystals from different layers and textural positions in a garnet-bearing migmatite in SE Brazil. Y-rich (variable Y(2)O(3), averaging 2.5 wt.%) relict cores are preserved in mesosome and melanosome monazite, and correspond to 793 +/- 6 Ma inherited crystals possibly generated in a previous metamorphic event. These cores are overgrown and widely replaced by two generations of monazite, which are present in all migmatite layers. The first, also Y-rich (average 2.5 wt.% Y(2)O(3)), was produced at similar to 635 Ma during prograde metamorphism under subsolidus conditions, while the second has an Y-poor (<1.5 wt.% Y(2)O(3)), low Th/U signature, and precipitated from low Y and HREE anatectic melts produced by reactions in which garnet was inert. Quartz-rich trondhjemitic leucosome represents lower temperature melt (bearing some subsolidus quartz and garnet with included monazite) formed at temperatures below muscovite breakdown; its Y-poor monazite indicates an age of 617 +/- 6 Ma. Granitic leucosomes formed close to peak metamorphic conditions (T>750 degrees C) above muscovite breakdown have their slightly younger character confirmed by a 609 +/- 7 Ma low-Y monazite age. A similar 606 +/- 5 Ma age was obtained for low-Y monazite rims and domains in mesosome and melanosome, and reflects the time of monazite saturation in interstitial granitic melt that was trapped in these layers. Our results confirm that inherited monazite crystals can be preserved during partial melting at temperatures above muscovite breakdown. Moreover, careful textural control aided by X-ray chemical mapping may allow monazite generated at different stages in a similar to 25 Myr prograde metamorphic path to be identified and dated using an electron microprobe. (C) 2008 Elsevier B.V. All rights reserved.

Microgranitic Enclaves as Products of Self-mixing Events: a Study of Open-system Processes in the Maua Granite, Sao Paulo, Brazil, Based on in situ Isotopic and Trace Elements in Plagioclase

Felsic microgranular enclaves with structures indicating that they interacted in a plastic state with their chemically similar host granite are abundant in the Maua Pluton, SE Brazil. Larger plagioclase xenocrysts are in textural disequilibrium with the enclave groundmass and show complex zoning patterns with partially resorbed An-rich cores (locally with patchy textures) surrounded by more sodic rims. In situ laser ablation-(multi-collector) inductively coupled plasma mass spectrometry trace element and Sr isotopic analyses performed on the plagioclase xenocrysts indicate open-system crystallization; however, no evidence of derivation from more primitive basic melts is observed. The An-rich cores have more radiogenic initial Sr isotopic ratios that decrease towards the outermost part of the rims, which are in isotopic equilibrium with the matrix plagioclase. These profiles may have been produced by either (1) diffusional re-equilibration after rim crystallization from the enclave-forming magma, as indicated by relatively short calculated residence times, or (2) episodic contamination with a decrease of the contaminant ratio proportional to the extent to which the country rocks were isolated by the crystallization front. Profiles of trace elements with high diffusion coefficients would require unrealistically long residence times, and can be modeled in terms of fractional crystallization. A combination of trace element and Sr isotope data suggests that the felsic microgranular enclaves from the Maua Pluton are the products of interaction between end-member magmas that had similar compositions, thus recording `self-mixing` events.

U-Pb-Hf-trace element systematics and geochronology of zircon from a granulite-facies metamorphosed mafic-ultramafic layered complex in Central Brazil

Zircon recrystallization is a common process during high-grade metamorphism and promotes partial or complete resetting of the original isotopic and chemical characteristics of the mineral and thus complicates U-Pb geochronological interpretation. In Central Brazil, this complexity may be illustrated by three composite mafic-ultramafic intrusions metamorphosed under amphibolite-to-granulite conditions. Their ages of emplacement and metamorphic ages have been a matter of controversy for the last thirty years. The Serra da Malacacheta and Barro Alto complexes make up the southernmost of these layered bodies and four samples from distinct rock types were investigated in order to verify the consequences of metamorphic alteration of zircon for U-Pb dating. Cathodoluminescent imaging reveals internal features which are typical of concomitant dissolution-reprecipitation processes, such as convolute zoning and inward-moving recrystallization fronts, even in samples in which partially preserved igneous textures are observed. Due to this extensive alteration, LA-ICPMS U-Pb isotopic analysis yielded inconclusive data. However, in situ Hf isotopic and trace-element analyses help to clarify the real meaning of the geochronological data. Low Lu/Hf (<0.004) and homogeneous (176)Hf/(177)Hf(t) values imply that the zircon populations within individual samples have crystallized in a single episode, despite the observed variations in age values. Trace element signatures of zircon grains from garnet-bearing samples reveal that they were unreactive to the development of the peak metamorphism mineral assemblage and, thus, the main chemical feature in such grains is attributed to a coupled dissolution-reprecipitation process. However, in the Cafelandia amphibolite an additional alteration process is identified, probably related to the influx of late-stage fluids. Combined isotopic and geochemical investigation on zircon grains allowed the distinction of two magmatic events. The first corresponds to the crystallization of the Serra da Malacacheta Complex and characterizes a juvenile magmatism at similar to 1.3 Ga. The younger episode, recognized in the Barro Alto Complex, is dated at ca. 800 Ma and is represented by mafic and ultramafic rocks showing intense contamination with continental crust, implying that the emplacement took place, most likely, in a continental back-arc setting. Altered zircon domains as well as titanite grains date the metamorphic event at ca. 760-750 Ma. (C) 2011 Elsevier B.V. All rights reserved.

Dating coeval mafic magmatism and ultrahigh temperature metamorphism in the Anapolis-Itaucu Complex, Central Brazil

Dating granulites has always been of great interest because they represent one of the most extreme settings of an orogen. Owing to the resilience of zircon, even in such severe environments, the link between P-T conditions and geological time is possible. However, a challenge to geochronologists is to define whether the growth of new zircon is related to pre- or post-P-T peak conditions and which processes might affect the (re) crystallization. In this context, the Anapolis-Itaucu Complex, a high-grade complex in central Brazil with ultrahigh temperature (UHT) granulites, may provide valuable information within this topic. The Anapolis-Itaucu Complex (AIC) includes ortho- and paragranulites, locally presenting UHT mineral assemblages, with igneous zircon ages varying between 760 and 650 Ma and metamorphic overgrowths dated at around 650-640 Ma. Also common in the Anapolis-Itaucu Complex are layered mafic-ultramafic complexes metamorphosed under high-grade conditions. This article presents the first geological and geochronological constraints of three of these layered complexes within the AIC, the Damolandia, Taquaral and Goianira-Trindade complexes. U-Pb (LA-MC-ICPMS, SHRIMP and ID-TIMS) zircon analyses reveal a spread of concordant ages spanning within an age interval of similar to 80 Ma with an ""upper"" intercept age of similar to 670 Ma. Under cathodoluminescence imaging, these crystals show partially preserved primary sector zoning, as well as internal textures typical of alteration during high-grade metamorphism, such as inward-moving boundaries. Zircon grains reveal homogeneous initial (176)Hf/(177)Hf values in distinct crystal-scale domains in all samples. Moreover. Hf isotopic ratios show correlation neither with U-Pb ages nor with Th/U ratios, suggesting that zircon grains crystallized during a single growth event. It is suggested, therefore, that the observed spread of concordant U-Pb ages may be related to a memory effect due to coupled dissolution-reprecipitation process during high grade metamorphism. Therefore, understanding the emplacement and metamorphism of this voluminous mafic magmatism is crucial as it may represent an additional heat source for the development of the ultrahigh temperature paragenesis recorded in the paragranulites. (C) 2010 Elsevier B.V. All rights reserved.