Hierarchical Spatial Organization of Geographical Networks

In this work we propose the use of a hirarchical extension of the polygonality index as a means to characterize and model geographical networks: each node is associated with the spatial position of the nodes, while the edges of the network are defined by progressive connectivity adjacencies. Through the analysis of such networks, while relating its topological and geometrical properties, it is possible to obtain important indications about the development dynamics of the networks under analysis. The potential of the methodology is illustrated with respect to synthetic geographical networks.Comment: 3 page, 3 figures. A wokring manuscript: suggestions welcome

Network centrality: an introduction

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A Mathematical modeling approach" by Springe

A Field Approach to 3D Gene Expression Pattern Characterization

We present a vector field method for obtaining the spatial organization of 3D patterns of gene expression based on gradients and lines of force obtained by numerical integration. The convergence of these lines of force in local maxima are centers of gene expression, providing a natural and powerful framework to characterize the organization and dynamics of biological structures. We apply this novel methodology to analyze the expression pattern of the Enhanced Green Fluorescent Protein (EGFP) driven by the promoter of light chain myosin II during zebrafish heart formation.Comment: 9 pages, 2 figures, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.or

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barab\'asi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks

Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcome

Replication of submicrometric organized structures of block copolymer from coordination-polymer templates

This paper presents fabrication of a submicrometric template obtained from self-organized well-ordered pattern of nanostructured (poly(styrene)-b-poly(ethene-co-butene)-b-poly(styrene) (SEBS) copolymer. The SEBS ordered structure was formed on mica substrate, in which a thin liquid film of SEBS/Toluene solution was deposited by dip-coating procedure, and after the solvent evaporation, SEBS droplets are spontaneously displayed in a hexagonal arrangement. The molding template was made of PDMS by a soft lithography process and replicas of epoxy forming the original hexagonal pattern with reasonable accuracy. All structures were studied by AFM images, using quantitative computational analyses: hexagonality index and radial distribution functions. The computational analyses showed that the high spacial order in the SEBS nanostructures was followed by the produced mold although and the replica. Also we observed that the original pattern presented 1.7% of dislocation defects (from the hexagonality), while the replica reached 5% showing the success of soft lithography process of nano templates