Master thesis deals with the design of network topologies with multiple redundant links for investor’s local area network. The objective of the thesis is to design more topology proposals according to investor’s requirements and applied technologies. Design is based on an analysis of the current state, which describes current topology of investor’s network. The main part of the thesis proposes a solution based on currently available network redundancy protocols. The functionality of the proposed solutions is tested in laboratory conditions. Finally, the individual variants are compared and their individual benefits evaluated.

In many network applications, such as the Internet and infrastructure networks, nodes fail or get congested dynamically, but tracking this information about all the nodes in a network where some dynamical processes are taking place is a fundamental problem. In this work, we study the problem of inferring the complete set of failed nodes, when only a sample of the node failures are known---we will be referring to this particular problem as prob{} . We consider the setting in which there exists correlations between node failures in networks, which has been studied in the case of many infrastructure networks. We formalize the prob{} problem using the Minimum Description Length (MDL) principle and we show that, in general, finding solutions that minimize the MDL cost is hard, and develop efficient algorithms with rigorous performance guarantees for finding near-optimal MDL cost solutions. We evaluate our methods on both synthetic and real world datasets, which includes the one from WAZE. WAZE is a crowd-sourced road navigation tool, that collects and presents the traffic incident reports. We found that the proposed greedy algorithm for this problem is able to recover $80%$, on average, of the failed nodes in a network for a given partial sample of input failures, which are sampled from the true set of failures at some predefined rate. Furthermore, we have also proved that this algorithm will find a solution that has MDL cost with an additive approximation guarantee of log(n) from the optimal. / Master of Science

Highway bridges are among the most vulnerable and expensive components in transportation networks. In response, the Government of Ontario has allocated $26 billion in the next 10 years to address issues pertaining to aging bridge and deteriorating highway infrastructure in the province. Although several approaches have been developed to guide their rehabilitation, most bridge rehabilitation approaches are focused on the component level (individual bridge) in a relative isolation of other bridges in the network. The current study utilizes a complex network theoretic approach to quantify the topological characteristics of the Ontario Bridge Network (OBN) and subsequently evaluate the OBN robustness and vulnerability characteristics. These measures are then integrated in the development of a Multi Scale Bridge Classification (MSBC) approach—an innovative classification approach that links the OBN component level data (i.e., Bridge Condition Index and year of construction, etc.) to the corresponding dynamic network-level measures. The novel approach calls for a paradigm shift in the strategy governing classifying and prioritizing bridge rehabilitation projects based on bridge criticality within the entire network, rather than only the individual bridge’s structural conditions. The model was also used to identify the most critical bridges in the OBN under different disruptions to facilitate rapid implementation of the study results. / Thesis / Master of Applied Science (MASc)

A reconfiguration algorithm for electrical distribution system to reduce system losses is presented. The algorithm determines the switching patterns as a function of time. Either seasonal or daily time studies may be performed. Both manual and automatic switches are used to reconfigure the system for seasonal studies, whereas only automatic switches are considered for daily studies. An algorithm for load estimation is developed. The load estimation algorithm provides load information for each time point to be analyzed. The load estimation algorithm can incorporate any or all of the following: spot loads, circuit measurements, and customer time-varying diversified load characteristics. Voltage dependency of loads is considered at the circuit level. It is shown that switching at the system peak can reduce losses but may cause a marginal increase in system peak. Voltage and current constraints are incorporated in the reconfiguration algorithm. Data base tables and data structures used in the algorithm are described. Example problems are provided to illustrate results. / Ph. D.

Critical infrastructure systems are essential for the continuous functionality of modern global societies. Some examples of these systems include electric energy, potable water, oil and gas, telecommunications, and the internet. Different topologies underline the structure of these networked systems. Each topology (i.e., physical layout) conditions the way in which networks transmit and distribute their flow. Also, their ability to absorb unforeseen natural or intentional disruptions depends on complex relations between network topology and optimal flow patterns. Most of the current research on large networks is focused on understanding their properties using statistical physics, or on developing advanced models to capture network dynamics. Despite these important research efforts, almost all studies concentrate on specific networks. This network-specific approach rules out a fundamental phenomenon that may jeopardize the performance predictions of current sophisticated models: network response is in general interdependent, and its performance is conditioned on the performance of additional interacting networks. Although there are recent conceptual advances in network interdependencies, current studies address the problem from a high-level point of view. For instance, they discuss the problem at the macro-level of interacting industries, or utilize economic input-output models to capture entire infrastructure interactions. This study approaches the problem of network interdependence from a more fundamental level. It focuses on network topology, flow patterns within the networks, and optimal interdependent system performance. This approach also allows for probabilistic response characterization of interdependent networked systems when subjected to disturbances of internal nature (e.g., aging, malfunctioning) or disruptions of external nature (e.g., coordinated attacks, seismic hazards). The methods proposed in this study can identify the role that each network element has in maintaining interdependent network connectivity and optimal flow. This information is used in the selection of effective pre-disaster mitigation and post-disaster recovery actions. Results of this research also provide guides for growth of interacting infrastructure networks and reveal new areas for research on interdependent dynamics. Finally, the algorithmic structure of the proposed methods suggests straightforward implementation of interdependent analysis in advanced computer software applications for multi-hazard loss estimation.

Network failures can originate from or be located in any one of several network layers as described by the OSI model. This investigation focuses on the role of physical topological design parameters in determining network reliability and performance as can be expected from the point of view of a typical client-server based connection in an Ethernet local area network. This type of host-to-host IP connection is found in many commercial, military and industrial network based systems. Using Markov modelling techniques reliability and performability models are developed for common network topologies based on the redundancy mechanism provided by IEEE spanning tree protocols. The models are tested and validated using the OPNET network simulation environment. The reliability and performability metrics calculated from the derived models for different topologies are compared leading to the following conclusions. The reliability of the entry-nodes into a redundant network is a determining factor in connection availability. Redundancy mechanisms must be extended from the entry-node to the connecting hosts to gain a significant benefit from redundant network topologies as network availability remains limited to three-nines. The hierarchical mesh network offers the highest availability (sevennines) and performability. Both these metrics can be accurately predicted irrespective of the position of the entry-node in the mesh. Ring networks offer high availability (five to sevennines) and performability if the ring remains small to medium sized, however for larger rings (N≥32) the availability is highly dependant on the relative position of the entry-node in the ring. Performability also degrades significantly as the ring size increases. Although star networks offer predictable and high performability the availability is low (four-nines) because of the lack of redundancy. The star should therefore not be used in IP networked systems requiring more than four-nines availability. In all the topologies investigated the reliability and performability can be increased significantly by introducing redundant links instead of single links interconnecting the various nodes, with the star topology availability increasing from four-nines to seven-nines and performance doubling. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

Network failures can originate from or be located in any one of several network layers as described by the OSI model. This investigation focuses on the role of physical topological design parameters in determining network reliability and performance as can be expected from the point of view of a typical client-server based connection in an Ethernet local area network. This type of host-to-host IP connection is found in many commercial, military and industrial network based systems. Using Markov modelling techniques reliability and performability models are developed for common network topologies based on the redundancy mechanism provided by IEEE spanning tree protocols. The models are tested and validated using the OPNET network simulation environment. The reliability and performability metrics calculated from the derived models for different topologies are compared leading to the following conclusions. The reliability of the entry-nodes into a redundant network is a determining factor in connection availability. Redundancy mechanisms must be extended from the entry-node to the connecting hosts to gain a significant benefit from redundant network topologies as network availability remains limited to three-nines. The hierarchical mesh network offers the highest availability (sevennines) and performability. Both these metrics can be accurately predicted irrespective of the position of the entry-node in the mesh. Ring networks offer high availability (five to sevennines) and performability if the ring remains small to medium sized, however for larger rings (N≥32) the availability is highly dependant on the relative position of the entry-node in the ring. Performability also degrades significantly as the ring size increases. Although star networks offer predictable and high performability the availability is low (four-nines) because of the lack of redundancy. The star should therefore not be used in IP networked systems requiring more than four-nines availability. In all the topologies investigated the reliability and performability can be increased significantly by introducing redundant links instead of single links interconnecting the various nodes, with the star topology availability increasing from four-nines to seven-nines and performance doubling. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.

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: Schizophrenia manifests as a constellation of both psychotic symptoms (eg. hallucinations, delusions) and so-called negative symptoms. The latter includes anhedonia, avolition, amotivation and they are the strongest predictors of disability. Resting state fMRI (rsfMRI) has demonstrated that the brain is organized into low-dimensional number (7-17) brain networks and this allowed visualization of the relationship between symptom severity and large-scale brain network organization. Traditional rsfMRI analyses have assumed that the spatial organization of these networks are spatially invariant between individuals. This dogma has recently been overturned with the observation that the spatial organization of these brain networks shows significant variation between individuals. We sought to determine if previously observed relationships between symptom severity and network connectivity are actually due to individual differences in spatial organization. METHODS: 44 participants diagnosed with schizophrenia underwent rsfMRI scans and clinical assessment. A multivariate pattern analysis was used to examine how each participant’s whole brain functional connectivity correlates with ‘negative’ symptom severity. RESULTS: Brain connectivity to a region of the right dorso-lateral pre-frontal cortex (r DLPFC) correlates with symptom severity. The result is explained by the individual differences in the topographic distribution of two brain networks: the default mode network (DMN) and the task positive network (TPN). Both networks demonstrate strong (r~0.49) and significant (p<0.001) relationships between topography and symptom severity. For individuals with low symptom severity, this critical region is a part of the DMN. In highly symptomatic individuals, this region is a part of the TPN. CONCLUSIONS: Previously overlooked individual variation in brain organization is tightly linked to individual variation in schizophrenia symptom severity. The recognition of critical links between network topology and pathological symptomology may serve as a guide for future interventions aimed at establishing causal relationships between certain critical regions of the brain and cognitive and behavioral phenotypes. Thus, fMRI and network topology may be translated to a clinical setting as a viable, individual-centered treatment option. / 2020-06-17T00:00:00Z