k-core organization of complex networks

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure

The interplay of university and industry through the FP5 network

To improve the quality of life in a modern society it is essential to reduce the distance between basic research and applications, whose crucial roles in shaping today's society prompt us to seek their understanding. Existing studies on this subject, however, have neglected the network character of the interaction between university and industry. Here we use state-of-the-art network theory methods to analyze this interplay in the so-called Framework Programme--an initiative which sets out the priorities for the European Union's research and technological development. In particular we study in the 5th Framework Programme (FP5) the role played by companies and scientific institutions and how they contribute to enhance the relationship between research and industry. Our approach provides quantitative evidence that while firms are size hierarchically organized, universities and research organizations keep the network from falling into pieces, paving the way for an effective knowledge transfer.Comment: 21 pages (including Appendix), 8 figures. Published online at http://stacks.iop.org/1367-2630/9/18

Low-field microwave absorption and magnetoresistance in iron nanostructures grown by electrodeposition on n-type lightly-doped silicon substrates

In this study we investigate magnetic properties, surface morphology and crystal structure in iron nanoclusters electrodeposited on lightly-doped (100) n-type silicon substrates. Our goal is to investigate the spin injection and detection in the Fe/Si lateral structures. The samples obtained under electric percolation were characterized by magnetoresistive and magnetic resonance measurements with cycling the sweeping applied field in order to understand the spin dynamics in the as-produced samples. The observed hysteresis in the magnetic resonance spectra, plus the presence of a broad peak in the non-saturated regime confirming the low field microwave absorption (LFMA), were correlated to the peaks and slopes found in the magnetoresistance curves. The results suggest long range spin injection and detection in low resistive silicon and the magnetic resonance technique is herein introduced as a promising tool for analysis of electric contactless magnetoresistive samples.Comment: 12 pages, 5 figure

Scaling Behaviour of Developing and Decaying Networks

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve according to the following rules: (i) Each instant a new site is added, the probability of its connection to old sites is proportional to their connectivities. (ii) In addition, (a) new links between some old sites appear with probability proportional to the product of their connectivities or (b) some links between old sites are removed with equal probability.Comment: 7 pages (revtex

Diluted antiferromagnet in a ferromagnetic enviroment

The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic interactions is investigated. After examing the static properties of the quenched version (in respect to the random antiferromagnetic interactions) of the model, the persistence of the magnetization is analysed also in the annealed approximation, and the difference in the results are discussed

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.Comment: 7 pages, 3 figure

Potencial agronômico de híbridos de cenoura de verão no Distrito Federal.

O programa de melhoramento de cenoura da Embrapa Hortaliças mantem seu foco em desenvolver cultivares adaptadas ao cultivo de verão e com resistência a queima-das-folhas, principal doença da cultura. Assim, o objetivo deste trabalho foi avaliar o potencial agronômico de híbridos experimentais de cenoura de verão no Distrito Federal