This dissertation focuses on a comparative study of small-world characteristics in geographical, epidemic, and virtual spaces. Small-world network is the major component of the “new science of networks” that emerged recently in research related to complex networks. It has shown a great potential to model the complex networks encountered in geographical studies. This dissertation, in an attempt to understand the emergence of small-world phenomenon in spatial networks, has investigated the smallworld properties in aforementioned three spaces. Specifically, this dissertation has studied roadway transportation networks at national, metropolitan, and intra-city scales via network autocorrelation methods to investigate the distance effect on the emergence of small-world properties. This dissertation also investigated the effect of small-world network properties on the epidemic diffusion and different control strategies through agent-based simulation on social networks. The ASLevel Internet in the contiguous U.S. has been studied in its relation between local and global connections, and its correspondence with small-world characteristics. Through theoretical simulations and empirical studies on spatial networks, this dissertation has contributed to network science with a new method – network autocorrelation, and better understanding from the perspective of the relation between local and global connections and the distance effect in networks. A small-world phenomenon results from the interplay between the dynamics occurring on networks and the structure of networks; when the influencing distance of the dynamics reaches to the threshold of the network, the network will logically emerge as a small-world network. With the aid of numerical simulation a small-world network has a large number of local connections and a small number of global links. It is also found that the epidemics will take shorter time period to reach largest size on a small-world network and only particular control strategy, such as targeted control strategy, will be effective on smallworld networks. This dissertation bridges the gap between new science of networks and the network study in geography. It potentially contributes to GIScience with new modeling strategy for representing, analyzing, and modeling complexity in hazards prevention, landscape ecology, and sustainability science from a network-centric perspective.

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Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Socially-based networks are of particular interest amongst the variety of communication networks arising in reality. They are distinguished by having small average path length and high clustering coefficient, and so are examples of small-world networks. This thesis studies both real examples and theoretical models of small-world networks, with particular attention to average path length. Existing models of small-world networks, due to Watts and Strogatz (1998) and Newman and Watts (1999a), impose boundary conditions on a one dimensional lattice, and rewire links locally and probabilistically in the former or probabilistically adding extra links in the latter. These models are investigated and compared with real-world networks. We consider a model in which randomness is provided by the Erdos-Rényi random network models superposed on a deterministic one dimensional structured network. We reason about this model using tools and results from random graph theory. Given a disordered network C(n, p) formed by adding links randomly with probability p to a one dimensional network C(n). We improve the analytical result regarding the average path length by showing that the onset of smallworld behaviour occurs if pn is bounded away from zero. Furthermore, we show that when pn tends to zero, C(n, p) is no longer small-world. We display that the average path length in this case approaches infinity with the network order. We deduce that at least εn (where ε is a constant bigger than zero) random links should be added to a one dimensional lattice to ensure average path length of order log n. / AFRIKAANSE OPSOMMING: Sosiaal-baseerde netwerke is van besondere belang onder die verskeidenheid kommunikasie netwerke. Hulle word onderskei deur ’n klein gemiddelde skeidingsafstand en hoë samedrommingskoëffisiënt, en is voorbeelde van kleinwêreld netwerke. Hierdie verhandeling bestudeer beide werklike voorbeelde en teoretiese modelle van klein-wêreld netwerke, met besondere aandag op die gemiddelde padlengte. Bestaande modelle van klein-wêreld netwerke, te danke aan Watts en Strogatz (1998) en Newman en Watts (1999a), voeg randvoorwaardes by tot eendimensionele roosters, en herbedraad nedwerkskakels gebaseer op lokale kennis in die eerste geval en voeg willekeurig ekstra netwerkskakels in die tweede. Hierdie modelle word ondersoek en vergelyk met werklike-wêreld netwerke. Ons oorweeg ’n prosedure waarin willekeurigheid verskaf word deur die Erdös- Renyi toevalsnetwerk modelle wat op ’n een-dimensionele deterministiese gestruktureerde netwerk geimposeer word. Ons redeneer oor hierdie modelle deur gebruik te maak van gereedskap en resultate toevalsgrafieke teorie. Gegewe ’n wanordelike netwerk wat gevorm word deur skakels willekeurig met waarskynlikheid p tot ‘n een-dimensionele netwerk C(n) toe te voeg, verbeter ons die analitiese resultaat ten opsigte van die gemiddelde padlengte deur te wys dat die aanvang van klein-wêreld gedrag voorkom wanneer pn weg van nul begrens is. Verder toon ons dat, wanneer pn neig na nul, C(n, p) nie meer klein-wêreld is nie. Ons toon dat die gemiddelde padlengte in hierdie geval na oneindigheid streef saam met die netwerk groote. Ons lei af dat ten minste εn (waar εn n konstante groter as nul is) ewekansige skakels bygevoeg moet word by ’n een-dimensionele rooster om ‘n gemiddelde padlengte van orde log n te verseker.

Background: Biological systems adapt to changing environments by reorganizing their cellula r and physiological program with metabolites representing one important response level. Different stresses lead to both conserved and specific responses on the metabolite level which should be reflected in the underl ying metabolic network. Methodology/Principal Findings: Starting from experimental data obtained by a GC-MS based high-throughput metabolic profiling technology we here develop an approach that: (1) extracts network representations from metabolic conditiondependent data by using pairwise correlations, (2) determines the sets of stable and condition-dependent correlations based on a combination of statistical significance and homogeneity tests, and (3) can identify metabolites related to the stress response, which goes beyond simple ob servation s about the changes of metabolic concentrations. The approach was tested with Escherichia colias a model organism observed under four different environmental stress conditions (cold stress, heat stress, oxidative stress, lactose diau xie) and control unperturbed conditions. By constructing the stable network component, which displays a scale free topology and small-world characteristics, we demonstrated that: (1) metabolite hubs in this reconstructed correlation networks are significantly enriched for those contained in biochemical networks such as EcoCyc, (2) particular components of the stable network are enriched for functionally related biochemical path ways, and (3) ind ependently of the response scale, based on their importance in the reorganization of the cor relation network a set of metabolites can be identified which represent hypothetical candidates for adjusting to a stress-specific response. Conclusions/Significance: Network-based tools allowed the identification of stress-dependent and general metabolic correlation networks. This correlation-network-ba sed approach does not rely on major changes in concentration to identify metabolites important for st ress adaptation, but rather on the changes in network properties with respect to metabolites. This should represent a useful complementary technique in addition to more classical approaches.

abstract: This dissertation explores how practices and interactions of actors at different scales structure social networks and lead to the emergence of social complexity in middle range societies. To investigate this process, I apply a complex adaptive systems approach and a methodology that combines network science with analytical tools from economics to the three sub-periods of the Prehistoric Bronze Age (The Philia Phase, PreBA 1 and PreBA 2) on Cyprus, a transformational period marked by social and economic changes evident in the material record. Using proxy data representative of three kinds of social interactions or facets of social complexity, the control of labor, participation in trade networks, and access to resources, at three scales, the community, region and whole island, my analysis demonstrates the variability in and non-linear trajectory for the emergence of social complexity in middle range society. The results of this research indicate that complexity emerges at different scales, and times in different places, and only in some facets of complexity. Cycles of emergence are apparent within the sub-periods of the PreBA, but a linear trajectory of increasing social complexity is not evident through the period. Further, this research challenges the long-held notion that Cyprus' involvement in the international metal trade lead to the emergence of complexity. Instead, I argue based on the results presented here, that the emergence of complexity is heavily influenced by endogenous processes, particularly the social interactions that limited participation in an on-island exchange system that flourished on the island during the Philia Phase, disintegrated along the North Coast during the PreBA 1 and was rebuilt across the island by the end of the period. Thus, the variation seen in the emergence of social complexity on Cyprus during the PreBA occurred as the result of a bottom-up process in which the complex and unequal interactions and relationships between social actors structured and restructured social networks across scales differently over time and space. These results speak more broadly about the variability of middle range societies and the varying conditions under which social complexity can emerge and add to our understanding of this phenomenon. / Dissertation/Thesis / Doctoral Dissertation Anthropology 2017

Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population that is mixing homogeneously at random. For a population with structure determined by social interactions, Prisoner's Dilemma brings to light certain requirements for the altruistic strategy to become established. Monte Carlo simulations of Prisoner's Dilemma are carried out using both simulated social networks and a dataset of a real social network. In both scenarios we confirm the requirements for the persistence of altruism in a population.

Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population that is mixing homogeneously at random. For a population with structure determined by social interactions, Prisoner's Dilemma brings to light certain requirements for the altruistic strategy to become established. Monte Carlo simulations of Prisoner's Dilemma are carried out using both simulated social networks and a dataset of a real social network. In both scenarios we confirm the requirements for the persistence of altruism in a population.

With the transition from single-core to multi-core computing and CMOS technology reaching its physical limits, new computing architectures which are scalable, robust, and low-power are required. A promising alternative to conventional computing architectures are Cellular Automata (CA) networks and Random Boolean Networks (RBN), where simple computational nodes combine to form a network that is capable of performing a larger computational task. It has previously been shown that RBNs can offer superior characteristics over mesh networks in terms of robustness, information processing capabilities, and manufacturing costs while the locally connected computing elements of a CA network provide better scalability and low average interconnect length. This study presents a low level hardware analysis of these architectures using a framework which generates the HDL code and netlist of these networks for various network parameters. The HDL code and netlists are then used to simulate these new computing architectures to estimate the latency, area and power consumed when implemented on silicon and performing a pre-determined computation. We show that for RBNs, information processing is faster compared to a CA network, but CA networks are found to a have lower and better distribution of power dissipation than RBNs because of their regular structure. A well-established task to determine the latency of operation for these architectures is presented for a good understanding of the effect of non-local connections in a network. Programming the nodes for this purpose is done externally using a novel self-configuration algorithm requiring minimal hardware. Configuration for RBNs is done by sending in configuration packets through a randomly chosen node. Logic for identifying the topology for the network is implemented for the nodes in the RBN network to enable compilers to analyze and generate the configuration bit stream for that network. On the other hand, the configuration of the CA network is done by passing in configuration data through the inputs on one of the sides of the cell array and shifting it into the network. A study of the overhead of the network configuration and topology identification mechanisms are presented. An analysis of small-world networks in terms of interconnect power and information propagation capability has been presented. It has been shown that small-world networks, whose randomness lies between that of completely regular and completely irregular networks, are realistic while providing good information propagation capability. This study provides valuable information to help designers make decisions for various performance parameters for both RBN and CA networks, and thus to find the best design for the application under consideration.

It has been observed that real-world random networks like the WWW, Internet, social networks, citation networks, etc., organize themselves into closely-knit groups that are locally dense and globally sparse. These closely-knit groups are termed communities. Nodes within a community are similar in some aspect. For example in a WWW network, communities might consist of web pages that share similar contents. Mining these communities facilitates better understanding of their evolution and topology, and is of great theoretical and commercial significance. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network, whereas community identification is the problem of identifying the community, to which, a given set of nodes belong. We make a comparative study of various existing community-discovery algorithms. We then propose a new algorithm based on bibliographic metrics, which addresses the drawbacks in existing approaches. Bibliographic metrics are used to study similarities between publications in a citation network. Our algorithm classifies nodes in the network based on the similarity of their neighborhoods. One of the drawbacks of the current community-discovery algorithms is their computational complexity. These algorithms do not scale up to the enormous size of the real-world networks. We propose a hash-table-based technique that helps us compute the bibliometric similarity between nodes in O(m ?) time. Here m is the number of edges in the graph and ?, the largest degree. Next, we investigate different centrality metrics. Centrality metrics are used to portray the importance of a node in the network. We propose an algorithm that utilizes centrality metrics of the nodes to compute the importance of the edges in the network. Removal of the edges in ascending order of their importance breaks the network into components, each of which represent a community. We compare the performance of the algorithm on synthetic networks with a known community structure using several centrality metrics. Performance was measured as the percentage of nodes that were correctly classified. As an illustration, we model the ucf.edu domain as a web graph and analyze the changes in its properties like densification power law, edge density, degree distribution, diameter, etc., over a five-year period. Our results show super-linear growth in the number of edges with time. We observe (and explain) that despite the increase in average degree of the nodes, the edge density decreases with time.

In this dissertation, the critical scaling behavior of magnetic Ising models with long range interactions is studied. These long range interactions, when imposed in addition to interactions on a regular lattice, lead to small-world graphs. By using large-scale Monte Carlo simulations, together with finite-size scaling, the critical behavior of a number of different models is obtained. The Ising models studied in this dissertation include the z-model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bonds superimposed on a square lattice. From the scaling results of the Binder 4th order cumulant, the order parameter, and the susceptibility, the long-range interaction is found to drive the systems behavior from Ising-like to mean field, and drive the critical point to a higher temperature. It is concluded that with a large amount of strong long-range connections (compared to the interactions on regular lattices), so the long-range connection density is non-vanishing, systems have mean field behavior. With a weak interaction that vanishes for an infinite system size or for vanishing density of long-range connections the systems have Ising-like critical behavior. The crossover from Ising-like to meanield behavior due to weak long-range interactions for systems with a large amount of long-range connections is also discussed. These results provide further evidence to support the existence of physical (quasi-) small-world nanomaterials.