L. da F. Costa

Characterization of complex networks : A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

Estimating crowd density with Minkowski fractal dimension

The estimation of the number of people in an area under surveillance is very important for the problem of crowd monitoring. When an area reaches an occupation level greater than the projected one, peoples safety can be in danger. This paper describes a new technique for crowd density estimation based on Minkowski fractal dimension. The fractal dimension has been widely used to characterize data texture in a large number of physical and biological sciences. The results of our experiments show that fractal dimension can also be used to characterize levels of people congestion in images of crowds. The proposed technique is compared with a statistical and a spectral technique, in a test study of nearly 300 images of a specific area of the Liverpool Street Railway Station, London, UK. Results obtained in this test study are presented.

A graph-based approach for multiscale shape analysis

Abstract This paper presents two shape descriptors, multiscale fractal dimension and contour saliences, using a graph-based approach— the image foresting transform. It introduces a robust approach to locate contour saliences from the relation between contour and skeleton. The contour salience descriptor consists of a vector, with salience location and value along the contour, and a matching algorithm. We compare both descriptors with fractal dimension, Fourier descriptors, moment invariants, Curvature Scale Space and Beam Angle Statistics regarding to their invariance to object characteristics that belong to a same class (compact-ability) and to their ability to separate objects of distinct classes (separability).

Neurodevelopmental and neuropsychiatric disorders represent an interconnected molecular system

Many putative genetic factors that confer risk to neurodevelopmental disorders such as autism spectrum disorders (ASDs) and X-linked intellectual disability (XLID), and to neuropsychiatric disorders including attention deficit hyperactivity disorder (ADHD) and schizophrenia (SZ) have been identified in individuals from diverse human populations. Although there is significant aetiological heterogeneity within and between these conditions, recent data show that genetic factors contribute to their comorbidity. Many studies have identified candidate gene associations for these mental health disorders, albeit this is often done in a piecemeal fashion with little regard to the inherent molecular complexity. Here, we sought to abstract relationships from our knowledge of systems level biology to help understand the unique and common genetic drivers of these conditions. We undertook a global and systematic approach to build and integrate available data in gene networks associated with ASDs, XLID, ADHD and SZ. Complex network concepts and computational methods were used to investigate whether candidate genes associated with these conditions were related through mechanisms of gene regulation, functional protein–protein interactions, transcription factor (TF) and microRNA (miRNA) binding sites. Although our analyses show that genetic variations associated with the four disorders can occur in the same molecular pathways and functional domains, including synaptic transmission, there are patterns of variation that define significant differences between disorders. Of particular interest is DNA variations located in intergenic regions that comprise regulatory sites for TFs or miRNA. Our approach provides a hypothetical framework, which will help discovery and analysis of candidate genes associated with neurodevelopmental and neuropsychiatric disorders.

Caste development and reproduction: a genome-wide analysis of hallmarks of insect eusociality

The honey bee queen and worker castes are a model system for developmental plasticity. We used established expressed sequence tag information for a Gene Ontology based annotation of genes that are differentially expressed during caste development. Metabolic regulation emerged as a major theme, with a caste‐specific difference in the expression of oxidoreductases vs. hydrolases. Motif searches in upstream regions revealed group‐specific motifs, providing an entry point to cis‐regulatory network studies on caste genes. For genes putatively involved in reproduction, meiosis‐associated factors came out as highly conserved, whereas some determinants of embryonic axes either do not have clear orthologs (bag of marbles, gurken, torso), or appear to be lacking (trunk) in the bee genome. Our results are the outcome of a first genome‐based initiative to provide an annotated framework for trends in gene regulation during female caste differentiation (representing developmental plasticity) and reproduction.

Multiscale skeletons by image foresting transform and its application to neuromorphometry

Abstract The image foresting transform (IFT) reduces optimal image partition problems based on seed pixels to a shortest-path forest problem in a graph, whose solution can be obtained in linear time. Such a strategy has allowed a unified and efficient approach to the design of image processing operators, such as edge tracking, region growing, watershed transforms, distance transforms, and connected filters. This paper presents a fast and simple method based on the IFT to compute multiscale skeletons and shape reconstructions without border shifting. The method also generates one-pixel-wide connected skeletons and the skeleton by influence zones, simultaneously, for objects of arbitrary topologies. The results of the work are illustrated with respect to skeleton quality, execution time, and its application to neuromorphometry.

Strong correlations between text quality and complex networks features

Concepts of complex networks have been used to obtain metrics that were correlated to text quality established by scores assigned by human judges. Texts produced by high-school students in Portuguese were represented as scale-free networks (word adjacency model), from which typical network features such as the in/outdegree, clustering coefficient and shortest path were obtained. Another metric was derived from the dynamics of the network growth, based on the variation of the number of connected components. The scores assigned by the human judges according to three text quality criteria (coherence and cohesion, adherence to standard writing conventions and theme adequacy/development) were correlated with the network measurements. Text quality for all three criteria was found to decrease with increasing average values of outdegrees, clustering coefficient and deviation from the dynamics of network growth. Among the criteria employed, cohesion and coherence showed the strongest correlation, which probably indicates that the network measurements are able to capture how the text is developed in terms of the concepts represented by the nodes in the networks. Though based on a particular set of texts and specific language, the results presented here point to potential applications in other instances of text analysis.

Shape characterization with the wavelet transform

We present a new approach to the problem of two-dimensional multiscale shape representation and analysis, based on the one-dimensional continuous wavelet transform (CWT). The shape is represented by the complex signal that describes its boundary, and the CWT is applied to this signal, leading to the so-called W-representation. Wavelet theory provides the W-representation with several properties that are generally required from shape representation frameworks. In addition, we introduce algorithms for extracting meaningful information about the shape from its W-representation, for instance, detection of dominant points and shape partitioning, natural scales analysis, and fractal-based analysis. The algorithms that accomplish these tasks are tested on shapes obtained from synthetic and real images. Thus the W-representation yields a unified approach to a number of important problems of shape characterization for purposes of machine vision

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 Barabasi-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.

A generalized approach to complex networks

Abstract.This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.