Ion channel models are related to non-equilibrium statistical physics, fluid mechanics and electromagnetism. Some classes of ordinary differential equations that model ion channels can be seen as a limit of finite state-space continuous-time Markov chains. The purpose of this thesis is to qualitatively investigate the numerical results of systems of equations that incorporate ion channels modeled by such Markov chains and an electrical circuit model of a single neuron with isopotential extracellular space. This may be useful for making more detailed micro-physical simulations of neurons. A subset of the Rallpack benchmarks is conducted in order to evaluate the accuracy of the electrical circuit model of the transmembrane voltage propagation. In order to test the tau-leap method employed to simulate the Markov-chain based ion channel models a cylindrical geometry is implemented. Convergence properties are presented in terms of mean interspike intervals of the transmembrane voltages for different time- and spatial discretisations. Accuracy of the tau-leap method is presented in relation to the deterministic versions of the ion channel models. The results show that the method used to simulate the transmembrane voltages is accurate and that while the tau-leap method is convergent in the mean interspike interval sense, it is not conclusive how accurate it is compared to the corresponding ordinary differential equations or how efficient it is.

Continuous time Markov chains are often used in the literature to model the dynamics of a system with low species count and uncertainty in transitions. In this paper, we investigate three particular algorithms that can be used to numerically simulate continuous time Markov chain models (a stochastic simulation algorithm, explicit and implicit tau-leaping algorithms). To compare these methods, we used them to analyze two stochastic infection models with different level of complexity. One of these models describes the dynamics of Vancomycin-Resistant Enterococcus (VRE) infection in a hospital, and the other is for the early infection of Human Immunodeficiency Virus (HIV) within a host. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have similar computational efficiency for the VRE model due to the low number of species and small number of transitions. However, we found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

In recent years, infrastructure renewal has been a focus of attention in North America and around the world. Municipal and federal authorities are increasingly recognizing the need for life cycle cost analysis of infrastructure projects in order to facilitate proper prioritization and budgeting of maintenance operations. Several reports have highlighted the need to increase budgets with the goal of overcoming the backlog in maintaining infrastructure facilities. This situation is apparent in the case of bridge networks, which are considered vital links in the road network infrastructure. Because of harsh environments and increasing traffic volumes, bridges are deteriorating rapidly, rendering the task of managing this important asset a complex endeavour. While several bridge management systems (BMS) have been developed at the commercial and research level, they still have serious drawbacks, particularly in integrating bridge-level and network-level decisions, and handling extremely large optimization problems. To overcome these problems, this study presents an innovative bridge management framework that considers network-level and bridge-level decisions. The initial formulation of the proposed framework was limited to bridge deck management. The model has unique aspects: a deterioration model that uses optimized Markov chain matrices, a life cycle cost analysis that considers different repair strategies along the planning horizon, and a system that considers constraints, such as budget limits and desirable improvement in network condition. To optimize repair decisions for large networks that mathematical programming optimization are incapable of handling, four state-of-the art evolutionary algorithms are used: Genetic algorithms, shuffled frog leaping, particle swarm, and ant colony. These algorithms have been used to experiment on different problem sizes and formulations in order to determine the best optimization setup for further developments. Based on the experiments using the framework for the bridge deck, an expanded framework is presented that considers multiple bridge elements (ME-BMS) in a much larger formulation that can include thousands of bridges. Experiments were carried out in order to examine the framework???s performance on different numbers of bridges so that system parameters could be set to minimize the degradation in the system performance with the increase in numbers of bridges. The practicality of the ME-BMS was enhanced by the incorporation of two additional models: a user cost model that estimates the benefits gained in terms of the user cost after the repair decisions are implemented, and a work zone user cost model that minimizes user cost in work zones by deciding the optimal work zone strategy (nighttime shifts, weekend shifts, and continuous closure), also, decides on the best traffic control plan that suits the bridge configuration. To verify the ability of the developed ME-BMS to optimize repair decisions on both the network and project levels, a case study obtained from a transportation municipality was employed. Comparisons between the decisions provided by the ME-BMS and the municipality policy for making decisions indicated that the ME-BMS has great potential for optimizing repair decisions for bridge networks and for structuring the planning of the maintenance of transportation systems, thus leading to cost savings and more efficient sustainability of the transportation infrastructure.

Increasing population, diminishing supplies and variable climatic conditions can cause difficulties in meeting water demands. When this long range water supply plan is developed to cope with future water demand changes, accuracy and reliability are the two most important factors. To develop an accurate model, the water supply system has become more complicated and comprehensive structures. Future uncertainty also has been considered to improve system reliability as well as economic feasibility.In this study, a general large-scale water supply system that is comprised of modular components was developed in a dynamic simulation environment. Several possible scenarios were simulated in a realistic hypothetical system. In addition to water balances and quality analyses, construction and operation of system components costs were estimated for each scenario. One set of results demonstrates that construction of small-cluster decentralized wastewater treatment systems could be more economical than a centralized plant when communities are spatially scattered or located in steep areas.The Shuffled Frog Leaping Algorithm (SFLA), then, is used to minimize the total system cost of the general water supply system. Decisions are comprised of sizing decisions - pipe diameter, pump design capacity and head, canal capacity, and water/wastewater treatment capabilities - and flow allocations over the water supply network. An explicit representation of energy consumption cost for the operation is incorporated into the system in the optimization process of overall system cost. Although the study water supply systems included highly nonlinear terms in the objective function and constraints, a stochastic search algorithm was applied successfully to find optimal solutions that satisfied all the constraints for the study networks.Finally, a robust optimization approach was introduced into the design process of a water supply system as a framework to consider uncertainties of the correlated future data. The approach allows for the control of the degree of conservatism which is a crucial factor for the system reliabilities and economical feasibilities. The system stability is guaranteed under the most uncertain condition and it was found that the water supply system with uncertainty can be a useful tool to assist decision makers to develop future water supply schemes.

In recent years, infrastructure renewal has been a focus of attention in North America and around the world. Municipal and federal authorities are increasingly recognizing the need for life cycle cost analysis of infrastructure projects in order to facilitate proper prioritization and budgeting of maintenance operations. Several reports have highlighted the need to increase budgets with the goal of overcoming the backlog in maintaining infrastructure facilities. This situation is apparent in the case of bridge networks, which are considered vital links in the road network infrastructure. Because of harsh environments and increasing traffic volumes, bridges are deteriorating rapidly, rendering the task of managing this important asset a complex endeavour. While several bridge management systems (BMS) have been developed at the commercial and research level, they still have serious drawbacks, particularly in integrating bridge-level and network-level decisions, and handling extremely large optimization problems. To overcome these problems, this study presents an innovative bridge management framework that considers network-level and bridge-level decisions. The initial formulation of the proposed framework was limited to bridge deck management. The model has unique aspects: a deterioration model that uses optimized Markov chain matrices, a life cycle cost analysis that considers different repair strategies along the planning horizon, and a system that considers constraints, such as budget limits and desirable improvement in network condition. To optimize repair decisions for large networks that mathematical programming optimization are incapable of handling, four state-of-the art evolutionary algorithms are used: Genetic algorithms, shuffled frog leaping, particle swarm, and ant colony. These algorithms have been used to experiment on different problem sizes and formulations in order to determine the best optimization setup for further developments. Based on the experiments using the framework for the bridge deck, an expanded framework is presented that considers multiple bridge elements (ME-BMS) in a much larger formulation that can include thousands of bridges. Experiments were carried out in order to examine the framework’s performance on different numbers of bridges so that system parameters could be set to minimize the degradation in the system performance with the increase in numbers of bridges. The practicality of the ME-BMS was enhanced by the incorporation of two additional models: a user cost model that estimates the benefits gained in terms of the user cost after the repair decisions are implemented, and a work zone user cost model that minimizes user cost in work zones by deciding the optimal work zone strategy (nighttime shifts, weekend shifts, and continuous closure), also, decides on the best traffic control plan that suits the bridge configuration. To verify the ability of the developed ME-BMS to optimize repair decisions on both the network and project levels, a case study obtained from a transportation municipality was employed. Comparisons between the decisions provided by the ME-BMS and the municipality policy for making decisions indicated that the ME-BMS has great potential for optimizing repair decisions for bridge networks and for structuring the planning of the maintenance of transportation systems, thus leading to cost savings and more efficient sustainability of the transportation infrastructure.

In this paper, we investigate three particular algorithms: A sto- chastic simulation algorithm (SSA), and explicit and implicit tau-leaping al- gorithms. To compare these methods, we used them to analyze two infection models: A Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunode ciency Virus (HIV) within host in- fection model. While the rst has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative effciency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational effciency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modication of tau-Leaping methods are preferred.

Finding optimal configuration of power distribution systems topology is an NP-hard combinatorial optimization problem. It becomes more complex when time varying nature of loads in large-scale distribution systems is taken into account. In the second chapter of this dissertation, a systematic approach is proposed to tackle the computational burden of the procedure. To solve the optimization problem, a novel adaptive fuzzy based parallel genetic algorithm (GA) is proposed that employs the concept of parallel computing in identifying the optimal configuration of the network. The integration of fuzzy logic into GA enhances the efficiency of the parallel GA by adaptively modifying the migration rates between different processors during the optimization process. A computationally efficient graph encoding method based on Dandelion coding strategy is developed which automatically generates radial topologies and prevents the construction of infeasible radial networks during the optimization process. The main shortcoming of the proposed algorithm in Chapter 2 is that it identifies only one single solution. It means that the system operator will not have any option but relying on the found solution. That is why a novel hybrid optimization algorithm is proposed in the third chapter of this dissertation that determines Pareto frontiers, as candidate solutions, for multi-objective distribution network reconfiguration problem. Implementing this model, the system operator will have more flexibility in choosing the best configuration among the alternative solutions. The proposed hybrid optimization algorithm combines the concept of fuzzy Pareto dominance (FPD) with shuffled frog leaping algorithm (SFLA) to recognize non-dominated suboptimal solutions identified by SFLA. The local search step of SFLA is also customized for power systems applications so that it automatically creates and analyzes only the feasible and radial configurations in its optimization procedure which significantly increases the convergence speed of the algorithm. In the fourth chapter, the problem of optimal network reconfiguration is solved for the case in which the system operator is going to employ an optimization algorithm that is automatically modifying its parameters during the optimization process. Defining three fuzzy functions, the probability of crossover and mutation will be adaptively tuned as the algorithm proceeds and the premature convergence will be avoided while the convergence speed of identifying the optimal configuration will not decrease. This modified genetic algorithm is considered a step towards making the parallel GA, presented in the second chapter of this dissertation, more robust in avoiding from getting stuck in local optimums. In the fifth chapter, the concentration will be on finding a potential smart grid solution to more high-quality suboptimal configurations of distribution networks. This chapter is considered an improvement for the third chapter of this dissertation for two reasons: (1) A fuzzy logic is used in the partitioning step of SFLA to improve the proposed optimization algorithm and to yield more accurate classification of frogs. (2) The problem of system reconfiguration is solved considering the presence of distributed generation (DG) units in the network. In order to study the new paradigm of integrating smart grids into power systems, it will be analyzed how the quality of suboptimal solutions can be affected when DG units are continuously added to the distribution network. The heuristic optimization algorithm which is proposed in Chapter 3 and is improved in Chapter 5 is implemented on a smaller case study in Chapter 6 to demonstrate that the identified solution through the optimization process is the same with the optimal solution found by an exhaustive search.

The bull was a potent symbol of power, strength, and, to a lesser degree, fertility to the peoples of the ancient Near East from the twelfth century until 330 BCE. This symbolism was manifested in several iconographic motifs. These motifs reveal the bull as a manifestation of divine characteristics and as an expression of the power of man, and particularly the authority of the king. The use of these iconographic motifs was not consistent across the entire area of the ancient Near East; some differed in appearance and use in the different areas of the region, and many changed over time even in the same area. In all areas and during all periods the basic core symbolism stayed the same, and the bull was always held in a special respect. / Old Testament and Ancient Near Eastern Studies / M.A. (Ancient Near Eastern Studies)

The bull was a potent symbol of power, strength, and, to a lesser degree, fertility to the peoples of the ancient Near East from the twelfth century until 330 BCE. This symbolism was manifested in several iconographic motifs. These motifs reveal the bull as a manifestation of divine characteristics and as an expression of the power of man, and particularly the authority of the king. The use of these iconographic motifs was not consistent across the entire area of the ancient Near East; some differed in appearance and use in the different areas of the region, and many changed over time even in the same area. In all areas and during all periods the basic core symbolism stayed the same, and the bull was always held in a special respect. / Old Testament and Ancient Near Eastern Studies / M.A. (Ancient Near Eastern Studies)