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.

Effects of competition on sexual and clonal reproduction of a tunicate: the importance of competitor identity

Individual fitness and the structure of marine communities are strongly affected by spatial competition. Among the most common space holders are the colonial ascidians, which have the ability to monopolize large areas of hard substrate, overgrowing most other competitors. The effects of competition on colony growth and on gonad production of the ascidian Didemnum perlucidum were studied in southeastern Brazil by experimentally removing surrounding competitors. Colonies of D, perlucidum competing for space exhibited a growth rate 9 times less than that of colonies that were competitor free. Among the colonies subject to competition, growth rates were unrelated to the percentage of colony border that was free of competitors. However, the identity of the competitor was important in the outcome of border contacts. At the beginning of the experiment, most border encounters of D. perlucidum were with solitary organisms, which in most cases were overgrown. These were progressively replaced by colonial ascidians and bryozoans, resulting mostly in stand-off interactions. Besides reducing asexual growth, spatial competition also affected female gonad production. Colonies free of competitors had a significantly higher proportion of zooids with ovaries. Thus, our findings show that spatial competition reduces both ascidian colony size and gonad production.

Basement depths in the Parecis Basin (Amazon) with receiver functions from small local earthquakes in the Porto dos Gauchos seismic zone

Receiver functions from small local earthquakes were used to determine sediment thicknesses in Porto dos Gauchos seismic zone (PGSZ), Parecis basin, Amazonian craton, Brazil. The high velocity contrast between basement and sediments (P-wave velocities of 6.1 and 3.0 km/s, respectively) favors the generation of clear P-to-S converted phases (Ps) seen in the radial component, and also S-to-P conversions (Sp) seen in the vertical component. A reference 10 velocity model determined with shallow refraction experiment in PGSZ helped to convert Ps P time differences to basement depths at 15 stations deployed for aftershocks studies. The results of receiver function integrated with the shallow refraction reveal that the basement depths in the PGSZ increases from the basin border in the north up to about 600 m depth in the south. The basement topography, however, does not vary smoothly and a basement high with a steep topography was detected near the epicentral area. A 400 m elevation difference within 1.7 km distance suggests a possible border fault of a buried graben. This feature seems to be oriented roughly WSW-ENE and could indicate basement structures related to the seismicity of the Porto dos Gauchos Seismic Zone. (C) 2011 Elsevier Ltd. All rights reserved.