Spatially explicit modeling on networks: understanding patterns & describing processes - Miranda, Gisele Helena Barboni (2019)
In contrast to established approaches that analyze networks based on their structural properties, networks can also be studied by investigating the patterns that are evolved by a discrete dynamical system built upon them, such as cellular automata (CAs). Combined with networks these tools can be used to map the relationship between the network architecture and its impact on the patterns evolved by the governing spatially discrete dynamical system. This thesis focuses on the investigation of discrete spatially explicit models (SEMs), among which are CAs, for network analysis and characterization. The relationship between network architecture and its dynamic aspects concerning pattern formation is studied. Additionally, this work aims at the development of evolutionary methods that can be employed for extracting features from such patterns and then be used as network descriptors. In order to achieve this goal, methods that integrate the network structure with the SEMs were proposed, implemented and analyzed. The proposed family of network automata is characterized by birth-survival dynamics that results in different categories of spatio-temporal patterns. Such patterns were quantitatively assessed and used to characterize different network topologies and perform classification tasks in the context of pattern recognition. Inspired by the classic Life-like CA, the proposed Life-like Network Automata (LLNA) illustrate how such tasks can be performed in real-world applications. In addition, the rock-paper-scissors (RPS) model, normally implemented on square lattices, was investigated by defining it on networks. The obtained results confirm the potential of the proposed quantitative analysis of the spatio-temporal patterns for network classification. This quantitative analysis was performed for a set of different pattern recognition tasks and for the majority of them, the classification performance improved. In addition, the reliability of LLNA as a general tool for pattern recognition applications was demonstrated in a diverse scope of classification tasks. The applicability of structural network descriptors was also highlighted in the context of shape characterization in computer vision. Through the proposed approach, the link between these network descriptors and the shape properties, such as angle and curvature, was illustrated. Moreover, when chosen adequately, the network descriptors led to a better classification performance for different shape recognition tasks. Regarding the RPS model, we demonstrated that the presence of long-range correlations in some networks directly influence the RPS dynamics. Finally, it was shown how a commuter network can be used to predict influenza outbreaks. All the proposed methods use different aspects of network analysis and contribute to the study of CAs and other SEMs on irregular tessellations, in contrast to the commonly used regular topologies. In addition, new insights were obtained concerning pattern recognition in networks through the use of spatio-temporal patterns as network descriptors.