Distributed Dynamics on Networks and their Applications in Network Communities, Sensor Networks and EEG's

Coupled neural networks, the Internet, World Wide Web, social networks and interacting biological networks are few examples of systems which consist of a large number of interacting dynamical units. Collective behavior of such systems is a consequence of the network structure as well as their dynamic properties. In this thesis, we study some aspects of structural properties of complex networks. We use the term "complex networks" informally to mean large networks without regular structure. Furthermore, we have exploited complex dynamical networks in order to solve three important distinct problems. The first problem that is tackled in two different ways is community detection in complex networks. This problem has recently attracted many researchers whereas many advantageous potential applications can be launched by knowing the community structure of the networks of interest. In our first work, we proposed to modify the network such that the performance of the existing community detection algorithms would be enhanced. More precisely, we have argued that a convenient weighting scheme improves the intrinsic drawbacks of the modularity measure, i.e. resolution limit and extreme degeneracies, and consequently; suitably weighting the network prior to applying a modularity optimization based community detection algorithm improves the overall performance. Then, we proposed a proper weighting scheme to verify our claim. The algorithm shows good results on a variety of networks. We have also extended our proposal for weighted networks . In our second work on community detection, we proposed a general appropriate graph-generative-model based likelihood function so that the actual community structure of the graph maximizes this function. Then, a dynamics based algorithm is proposed for optimizing this function. Indeed, we map a network into a dynamical network to disclose its community structure. This algorithm is very fast and accurate. In addition, it delivers the overlapping communities as well as the hierarchical structure. The second problem that is addressed in this thesis is finding abnormalities of neural synchronization patterns in different regions of the cortex for Alzheimer's disease patients. In fact, we study the interdependencies within the time series of the sources of electroencephalography (EEG) and give the relevant specific maps for patients suffering from Alzheimer's disease. In order to find the sources of EEG in the cortex, the LAURA inverse solution method is exploited. The synchronization within multivariate time series of EEG sources is estimated to capture the collective coherent spatiotemporal activity of neuronal populations. The results shows that the main effect of Alzheimer's disease progression type was clearly visible in the left hemisphere and mainly limited to the higher EEG frequencies. Finally, the last problem that is studied is fire forest surveillance using wireless sensor networks. We have proposed two algorithms to a