Signatures of small-world and scale-free properties in large computer programs

Exploring Spatio-temporal Dynamics of Cellular Automata for Pattern Recognition in Networks

Network science is an interdisciplinary field which provides an integrative approach for the study of complex systems. In recent years, network modeling has been used for the study of emergent phenomena in many real-world applications. Pattern recognition in networks has been drawing attention to the importance of network characterization, which may lead to understanding the topological properties that are related to the network model. In this paper, the Life-Like Network Automata (LLNA) method is introduced, which was designed for pattern recognition in networks. LLNA uses the network topology as a tessellation of Cellular Automata (CA), whose dynamics produces a spatio-temporal pattern used to extract the feature vector for network characterization. The method was evaluated using synthetic and real-world networks. In the latter, three pattern recognition applications were used: (i) identifying organisms from distinct domains of life through their metabolic networks, (ii) identifying online social networks and (iii) classifying stomata distribution patterns varying according to different lighting conditions. LLNA was compared to structural measurements and surpasses them in real-world applications, achieving improvement in the classification rate as high as 23%, 4% and 7% respectively. Therefore, the proposed method is a good choice for pattern recognition applications using networks and demonstrates potential for general applicability.

Probing the topological properties of complex networks modeling short written texts

In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on textual stylistic analysis. The most common approach to treat texts as networks has simply considered either large pieces of texts or entire books. This approach has certainly worked well—many informative discoveries have been made this way—but it raises an uncomfortable question: could there be important topological patterns in small pieces of texts? To address this problem, the topological properties of subtexts sampled from entire books was probed. Statistical analyses performed on a dataset comprising 50 novels revealed that most of the traditional topological measurements are stable for short subtexts. When the performance of the authorship recognition task was analyzed, it was found that a proper sampling yields a discriminability similar to the one found with full texts. Surprisingly, the support vector machine classification based on the characterization of short texts outperformed the one performed with entire books. These findings suggest that a local topological analysis of large documents might improve its global characterization. Most importantly, it was verified, as a proof of principle, that short texts can be analyzed with the methods and concepts of complex networks. As a consequence, the techniques described here can be extended in a straightforward fashion to analyze texts as time-varying complex networks.

A bridge role metric model for nodes in software networks

A bridge role metric model is put forward in this paper. Compared with previous metric models, our solution of a large-scale object-oriented software system as a complex network is inherently more realistic. To acquire nodes and links in an undirected network, a new model that presents the crucial connectivity of a module or the hub instead of only centrality as in previous metric models is presented. Two previous metric models are described for comparison. In addition, it is obvious that the fitting curve between the Bre results and degrees can well be fitted by a power law. The model represents many realistic characteristics of actual software structures, and a hydropower simulation system is taken as an example. This paper makes additional contributions to an accurate understanding of module design of software systems and is expected to be beneficial to software engineering practices.

Chaotic phase synchronization in scale-free networks of bursting neurons

There is experimental evidence that the neuronal network in some areas of the brain cortex presents the scale-free property, i.e., the neuron connectivity is distributed according to a power law, such that neurons are more likely to couple with other already well-connected ones. From the information processing point of view, it is relevant that neuron bursting activity be synchronized in some weak sense. A coherent output of coupled neurons in a network can be described through the chaotic phase synchronization of their bursting activity. We investigated this phenomenon using a two-dimensional map to describe neurons with spiking-bursting activity in a scale-free network, in particular the dependence of the chaotic phase synchronization on the coupling properties of the network as well as its synchronization with an externally applied time-periodic signal.

Graph theoretic modeling of large-scale semantic networks

During the past several years, social network analysis methods have been used to model many complex real-world phenomena, including social networks, transportation networks, and the Internet. Graph theoretic methods, based on an elegant representation of entities and relationships, have been used in computational biology to study biological networks; however they have not yet been adopted widely by the greater informatics community. The graphs produced are generally large, sparse, and complex, and share common global topological properties. In this review of research (1998-2005) on large-scale semantic networks, we used a tailored search strategy to identify articles involving both a graph theoretic perspective and semantic information. Thirty-one relevant articles were retrieved. The majority (28, 90.3%) involved an investigation of a real-world network. These included corpora, thesauri, dictionaries, large computer programs, biological neuronal networks, word association networks, and files on the Internet. Twenty-two of the 28 (78.6%) involved a graph comprised of words or phrases. Fifteen of the 28 (53.6%) mentioned evidence of small-world characteristics in the network investigated. Eleven (39.3%) reported a scale-free topology, which tends to have a similar appearance when examined at varying scales. The results of this review indicate that networks generated from natural language have topological properties common to other natural phenomena. It has not yet been determined whether artificial human-curated terminology systems in biomedicine share these properties. Large network analysis methods have potential application in a variety of areas of informatics, such as in development of controlled vocabularies and for characterizing a given domain.

The Cytomatrix as a Cooperative System of Macromolecular and Water Networks

Water was called by Szent-Gyorgi "life's mater and matrix, mother and medium." This chapter considers both aspects of his statement. Many astrobiologists argue that some, if not all, of Earth's water arrived during cometary bombardments. Amorphous water ices of comets possibly facilitated organization of complex organic molecules, kick-starting prebiotic evolution. In Gaian theory, Earth retains its water as a consequence of biological activity. The cell cytomatrix is a proteinaceous matrix/lattice incorporating the cytoskeleton, a pervasive, holistic superstructural network that integrates metabolic pathways. Enzymes of metabolic pathways are ordered in supramolecular clusters (metabolons) associated with cytoskeleton and/or membranes. Metabolic intermediates are microchanneled through metabolons without entering a bulk aqueous phase. Rather than being free in solution, even major signaling ions are probably clustered in association with the cytomatrix. Chloroplasts and mitochondria, like bacteria and archaea, also contain a cytoskeletal lattice, metabolons, and channel metabolites. Eukaryotic metabolism is mathematically a scale-free or small-world network. Enzyme clusters of bacterial origin are incorporated at a pathway level that is architecturally archaean. The eucaryotic cell may be a product of serial endosymbiosis, a chimera. Cell cytoplasm is approximately 80% water. Water is indisputably a conserved structural element of proteins, essential to their folding, specificity, ligand binding, and to enzyme catalysis. The vast literature of organized cell water has long argued that the cytomatrix and cell water are an entire system, a continuum, or gestalt. Alternatives are offered to mainstream explanations of cell electric potentials, ion channel, enzyme, and motor protein function, in terms of high-order cooperative systems of ions, water, and macromolecules. This chapter describes some prominent concepts of organized cell water, including vicinal water network theory, the association-induction hypothesis, wave-cluster theory, phase-gel transition theories, and theories of low- and high-density water polymorphs.

Properties of dense partially random graphs

We study the properties of random graphs where for each vertex a neighborhood has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbors or not, as happens in small-world graphs (SWG's). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWG's, which are sparse). This allows us to calculate the mean distance and clustering, which are qualitatively similar (although not in such a dramatic scale range) to the case of SWG's. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.

Bug propagation and debugging in asymmetric software structures

We address the issue of how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Because of the functional form of the incoming link distribution of software dependence network, software is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failure only affects its nearest neighbors, while it is hard if it propagates further.