<p>Neural networks are mathematical formulations that can be "trained" to perform certain functions. One particular application of these networks of interest in this thesis is to "model" a physical system using only input-output information. The physical system and the neural network are subjected to the same inputs. The neural network is then trained to produce an output which is the same as the physical system for any input. This neural network model so created is essentially a "blackbox" representation of the physical system. This approach has been used at the University of Saskatchewan to model a load sensing pump (a component which is used to create a constant flow rate independent of variations in pressure downstream of the pump). These studies have shown the versatility of neural networks for modeling dynamic and non-linear systems; however, these studies also indicated challenges associated with the morphology of neural networks and the algorithms to train them. These challenges were the motivation for this particular research.</p> <p>Within the Fluid Power Research group at the University of Saskatchewan, a "global" objective of research in the area of load sensing pumps has been to apply dynamic neural networks (DNN) in the modeling of loads sensing systems.. To fulfill the global objective, recurrent generalized neural network (RGNN) morphology along with a non-gradient based training approach called the complex algorithm (CA) were chosen to train a load sensing pump neural network model. However, preliminary studies indicated that the combination of recurrent generalized neural networks and complex training proved ineffective for even second order single-input single-output (SISO) systems when the initial synaptic weights of the neural network were chosen at random.</p> <p>Because of initial findings the focus of this research and its objectives shifted towards understanding the capabilities and limitations of recurrent generalized neural networks and non-gradient training (specifically the complex algorithm). To do so a second-order transfer function was considered from which an approximate recurrent generalized neural network representation was obtained. The network was tested under a variety of initial weight intervals and the number of weights being optimized. A definite trend was noted in that as the initial values of the synaptic weights were set closer to the "exact" values calculated for the system, the robustness of the network and the chance of finding an acceptable solution increased. Two types of training signals were used in the study; step response and frequency based training. It was found that when step response and frequency based training were compared, step response training was shown to produce a more generalized network.</p> <p>Another objective of this study was to compare the use of the CA to a proven non-gradient training method; the method chosen was genetic algorithm (GA) training. For the purposes of the studies conducted two modifications were done to the GA found in the literature. The most significant change was the assurance that the error would never increase during the training of RGNNs using the GA. This led to a collapse of the population around a specific point and limited its ability to obtain an accurate RGNN.</p> <p>The results of the research performed produced four conclusions. First, the robustness of training RGNNs using the CA is dependent upon the initial population of weights. Second, when using GAs a specific algorithm must be chosen which will allow the calculation of new population weights to move freely but at the same time ensure a stable output from the RGNN. Third, when the GA used was compared to the CA, the CA produced more generalized RGNNs. And the fourth is based upon the results of training RGNNs using the CA and GA when step response and frequency based training data sets were used, networks trained using step response are more generalized in the majority of cases.</p>

<p>Neural networks are mathematical formulations that can be "trained" to perform certain functions. One particular application of these networks of interest in this thesis is to "model" a physical system using only input-output information. The physical system and the neural network are subjected to the same inputs. The neural network is then trained to produce an output which is the same as the physical system for any input. This neural network model so created is essentially a "blackbox" representation of the physical system. This approach has been used at the University of Saskatchewan to model a load sensing pump (a component which is used to create a constant flow rate independent of variations in pressure downstream of the pump). These studies have shown the versatility of neural networks for modeling dynamic and non-linear systems; however, these studies also indicated challenges associated with the morphology of neural networks and the algorithms to train them. These challenges were the motivation for this particular research.</p> <p>Within the Fluid Power Research group at the University of Saskatchewan, a "global" objective of research in the area of load sensing pumps has been to apply dynamic neural networks (DNN) in the modeling of loads sensing systems.. To fulfill the global objective, recurrent generalized neural network (RGNN) morphology along with a non-gradient based training approach called the complex algorithm (CA) were chosen to train a load sensing pump neural network model. However, preliminary studies indicated that the combination of recurrent generalized neural networks and complex training proved ineffective for even second order single-input single-output (SISO) systems when the initial synaptic weights of the neural network were chosen at random.</p> <p>Because of initial findings the focus of this research and its objectives shifted towards understanding the capabilities and limitations of recurrent generalized neural networks and non-gradient training (specifically the complex algorithm). To do so a second-order transfer function was considered from which an approximate recurrent generalized neural network representation was obtained. The network was tested under a variety of initial weight intervals and the number of weights being optimized. A definite trend was noted in that as the initial values of the synaptic weights were set closer to the "exact" values calculated for the system, the robustness of the network and the chance of finding an acceptable solution increased. Two types of training signals were used in the study; step response and frequency based training. It was found that when step response and frequency based training were compared, step response training was shown to produce a more generalized network.</p> <p>Another objective of this study was to compare the use of the CA to a proven non-gradient training method; the method chosen was genetic algorithm (GA) training. For the purposes of the studies conducted two modifications were done to the GA found in the literature. The most significant change was the assurance that the error would never increase during the training of RGNNs using the GA. This led to a collapse of the population around a specific point and limited its ability to obtain an accurate RGNN.</p> <p>The results of the research performed produced four conclusions. First, the robustness of training RGNNs using the CA is dependent upon the initial population of weights. Second, when using GAs a specific algorithm must be chosen which will allow the calculation of new population weights to move freely but at the same time ensure a stable output from the RGNN. Third, when the GA used was compared to the CA, the CA produced more generalized RGNNs. And the fourth is based upon the results of training RGNNs using the CA and GA when step response and frequency based training data sets were used, networks trained using step response are more generalized in the majority of cases.</p>

In recent decades, scientific data has become available in increasing sizes and precision. Therefore techniques to analyze and summarize the ever increasing datasets are of vital importance. A common form of scientific data, resulting from simulations as well as observational sciences, is in the form of scalar-valued function on domains of interest. The Morse-Smale complex is a topological data-structure used to analyze and summarize the gradient behavior of such scalar functions. This thesis deals with efficient parallel algorithms to compute the Morse-Smale complex as well as its application to datasets arising from cosmological sciences as well as structural biology. The first part of the thesis discusses the contributions towards efficient computation of the Morse-Smale complex of scalar functions de ned on two and three dimensional datasets. In two dimensions, parallel computation is made possible via a paralleizable discrete gradient computation algorithm. This algorithm is extended to work e ciently in three dimensions also. We also describe e cient algorithms that synergistically leverage modern GPUs and multi-core CPUs to traverse the gradient field needed for determining the structure and geometry of the Morse-Smale complex. We conclude this part with theoretical contributions pertaining to Morse-Smale complex simplification. The second part of the thesis explores two applications of the Morse-Smale complex. The first is an application of the 3-dimensional hierarchical Morse-Smale complex to interactively explore the filamentary structure of the cosmic web. The second is an application of the Morse-Smale complex for analysis of shapes of molecular surfaces. Here, we employ the Morse-Smale complex to determine alignments between the surfaces of molecules having similar surface architecture.

The ability to efficiently analyze changing data is a key requirement of many real-time analytics applications. Traditional approaches to this problem were developed around the notion of Incremental View Maintenance (IVM), and are based either on the materialization of subresults (to avoid their recomputation) or on the recomputation of subresults (to avoid the space overhead of materialization). Both techniques are suboptimal: instead of materializing results and subresults, one may also maintain a data structure that supports efficient maintenance under updates and from which the full query result can quickly be enumerated. In two previous articles, we have presented algorithms for dynamically evaluating queries that are easy to implement, efficient, and can be naturally extended to evaluate queries from a wide range of application domains. In this paper, we discuss our algorithm and its complexity, explaining the main components behind its efficiency. Finally, we show experiments that compare our algorithm to a state-of-the-art (Higher-order) IVM engine, as well as to a prominent complex event recognition engine. Our approach outperforms the competitor systems by up to two orders of magnitude in processing time, and one order in memory consumption.