In this thesis, we explore the use of double auction markets as a general approach to tackle resource allocation problems in large-scale distributed systems, which are traditionally solved using optimization techniques. Prevalently adopted in real-world markets, double auctions have the power of arbitrating mappings between participating players and trading commodities in a decentralized fashion, with every player trying to maximize her own utility selfishly. Through the design of prefetching strategies in peer-assisted video-on-demand systems, we show how the problem of minimizing server bandwidth costs by reallocating media contents can be solved by double auction markets gracefully. However, not every resource allocation problem satisfies requirements of double auctions. We illustrate the limitation of double auctions with an example of virtual machine migration in container-based datacenters, which is then modeled into a Nash bargaining game and solved by a Nash bargaining solution.

In this thesis, we explore the use of double auction markets as a general approach to tackle resource allocation problems in large-scale distributed systems, which are traditionally solved using optimization techniques. Prevalently adopted in real-world markets, double auctions have the power of arbitrating mappings between participating players and trading commodities in a decentralized fashion, with every player trying to maximize her own utility selfishly. Through the design of prefetching strategies in peer-assisted video-on-demand systems, we show how the problem of minimizing server bandwidth costs by reallocating media contents can be solved by double auction markets gracefully. However, not every resource allocation problem satisfies requirements of double auctions. We illustrate the limitation of double auctions with an example of virtual machine migration in container-based datacenters, which is then modeled into a Nash bargaining game and solved by a Nash bargaining solution.

Kernel machines such as Support Vector Machines (SVMs) have been widely used in various data mining applications with good generalization properties. Performance of SVMs for solving nonlinear problems is highly affected by kernel functions. The complexity of SVMs training is mainly related to the size of a training dataset. How to design a powerful kernel, how to speed up SVMs training and how to train SVMs with millions of examples are still challenging problems in the SVMs research. For these important problems, powerful and flexible kernel trees called Evolutionary Granular Kernel Trees (EGKTs) are designed to incorporate prior domain knowledge. Granular Kernel Tree Structure Evolving System (GKTSES) is developed to evolve the structures of Granular Kernel Trees (GKTs) without prior knowledge. A voting scheme is also proposed to reduce the prediction deviation of GKTSES. To speed up EGKTs optimization, a master-slave parallel model is implemented. To help SVMs challenge large-scale data mining, a Minimum Enclosing Ball (MEB) based data reduction method is presented, and a new MEB-SVM algorithm is designed. All these kernel methods are designed based on Granular Computing (GrC). In general, Evolutionary Granular Kernel Machines (EGKMs) are investigated to optimize kernels effectively, speed up training greatly and mine huge amounts of data efficiently.

Current research suggests that a high level of confidence and a low level of anxiety are predictive of higher math achievement. Compared to students from other provinces, previous research has found that Saskatchewan students have a higher level of confidence and a lower level of anxiety for learning math, but still tend to achieve lower math scores compared to students in other provinces. The data suggest that there may be unique factors effecting math learning for students in Saskatchewan. The purpose of the study is to determine the factors that may affect Saskatchewan students math achievement. Exploratory factor analyses and regression methods were employed to investigate possible traits that aid students in achieving higher math scores. Results from a 2007 math assessment administered to grade 5 students in Saskatchewan were used for the current study. The goal of the study was to provide a better understanding of the factors and trends unique to students for mathematic achievements in Saskatchewan.<p> Using results from a province-wide math assessment and an accompanying questionnaire administered to students in grade five across public school in Saskatchewan (n=11,279), the present study found statistical significance in three factors that have been supported by previous studies to influence math achievement differences, specifically in (1) confidence in math, (2) parental involvement in math and (3) extracurricular participation in math. The three aforementioned factors were found to be related to math achievement as predicted by the Assessment for Learning (AFL) program in Saskatchewan, although there were reservations to the findings due to a weak amount of variances accounted for in the regression model (r2 =.084). Furthermore, a multivariate analysis of variance indicated gender and locations of schools to have effects on students math achievement scores. Although a high amount of measurement errors in the questionnaire (and subsequently a low variance accounted for by the regression model) limited the scope and implications of the model, future implications and improvements are discussed

In this thesis we describe the generation and analysis of hydrodynamical simulations of galaxy clusters and their intracluster medium (ICM), using large cosmological boxes to generate large samples, in conjunction with individual cluster computations. The main focus is the exploration of the non-thermal processes in the ICM and the effect they have on the interpretation of observations used for cosmological constraints. We provide an introduction to the cosmological structure formation framework for our computations and an overview of the numerical simulations and observations of galaxy clusters. We explore the cluster magnetic field observables through radio relics, extended entities in the ICM characterized by their of diffuse radio emission. We show that statistical quantities such as radio relic luminosity functions and rotation measure power spectra are sensitive to magnetic field models. The spectral index of the radio relic emission provides information on structure formation shocks, {\it e.g.}, on their Mach number. We develop a coarse grained stochastic model of active galaxy nucleus (AGN) feedback in clusters and show the impact of such inhomogeneous feedback on the thermal pressure profile. We explore variations in the pressure profile as a function of cluster mass, redshift, and radius and provide a constrained fitting function for this profile. We measure the degree of the non-thermal pressure in the gas from internal cluster bulk motions and show it has an impact on the slope and scatter of the Sunyaev-Zel'dovich (SZ) scaling relation. We also find that the gross shape of the ICM, as characterized by scaled moment of inertia tensors, affects the SZ scaling relation. We demonstrate that the shape and the amplitude of the SZ angular power spectrum is sensitive to AGN feedback, and this affects the cosmological parameters determined from high resolution ACT and SPT cosmic microwave background data. We compare analytic, semi-analytic, and simulation-based methods for calculating the SZ power spectrum, and characterize their differences. All the methods must rely, one way or another, on high resolution large-scale hydrodynamical simulations with varying assumptions for modelling the gas of the sort presented here. We show how our results can be used to interpret the latest ACT and SPT power spectrum results. We provide an outlook for the future, describing follow-up work we are undertaking to further advance the theory of cluster science.

In this thesis we describe the generation and analysis of hydrodynamical simulations of galaxy clusters and their intracluster medium (ICM), using large cosmological boxes to generate large samples, in conjunction with individual cluster computations. The main focus is the exploration of the non-thermal processes in the ICM and the effect they have on the interpretation of observations used for cosmological constraints. We provide an introduction to the cosmological structure formation framework for our computations and an overview of the numerical simulations and observations of galaxy clusters. We explore the cluster magnetic field observables through radio relics, extended entities in the ICM characterized by their of diffuse radio emission. We show that statistical quantities such as radio relic luminosity functions and rotation measure power spectra are sensitive to magnetic field models. The spectral index of the radio relic emission provides information on structure formation shocks, {\it e.g.}, on their Mach number. We develop a coarse grained stochastic model of active galaxy nucleus (AGN) feedback in clusters and show the impact of such inhomogeneous feedback on the thermal pressure profile. We explore variations in the pressure profile as a function of cluster mass, redshift, and radius and provide a constrained fitting function for this profile. We measure the degree of the non-thermal pressure in the gas from internal cluster bulk motions and show it has an impact on the slope and scatter of the Sunyaev-Zel'dovich (SZ) scaling relation. We also find that the gross shape of the ICM, as characterized by scaled moment of inertia tensors, affects the SZ scaling relation. We demonstrate that the shape and the amplitude of the SZ angular power spectrum is sensitive to AGN feedback, and this affects the cosmological parameters determined from high resolution ACT and SPT cosmic microwave background data. We compare analytic, semi-analytic, and simulation-based methods for calculating the SZ power spectrum, and characterize their differences. All the methods must rely, one way or another, on high resolution large-scale hydrodynamical simulations with varying assumptions for modelling the gas of the sort presented here. We show how our results can be used to interpret the latest ACT and SPT power spectrum results. We provide an outlook for the future, describing follow-up work we are undertaking to further advance the theory of cluster science.

This dissertation deals with the problem of scheduling in wireless MIMO (Multiple-Input Multiple-Output) downlink systems. The focus is on the large-scale systems when the number of subscribers is large. In part one, the problem of user selection in MIMO Broadcast channel is studied. An efficient user selection algorithm is proposed and is shown to achieve the sum-rate capacity of the system asymptotically (in terms of the number of users), while requiring (i)~low-complexity precoding scheme of zero-forcing beam-forming at the base station, (ii)~low amount of feedback from the users to the base station, (iii)~low complexity of search. Part two studies the problem of MIMO broadcast channel with partial Channel State Information (CSI) at the transmitter. The necessary and sufficient conditions for the amount of CSI at the transmitter (which is provided to via feedback links from the receivers) in order to achieve the sum-rate capacity of the system are derived. The analysis is performed in various singnal to noise ratio regimes. In part three, the problem of sum-rate maximization in a broadcast channel with large number of users, when each user has a stringent delay constraint, is studied. In this part, a new definition of fairness, called short-term fairness is introduced. A scheduling algorithm is proposed that achieves: (i) Maximum sum-rate throughput and (ii) Maximum short-term fairness of the system, simultaneously, while satisfying the delay constraint for each individual user with probability one. In part four, the sum-rate capacity of MIMO broadcast channel, when the channels are Rician fading, is derived in various scenarios in terms of the value of the Rician factor and the distribution of the specular components of the channel.

This dissertation deals with the problem of scheduling in wireless MIMO (Multiple-Input Multiple-Output) downlink systems. The focus is on the large-scale systems when the number of subscribers is large. In part one, the problem of user selection in MIMO Broadcast channel is studied. An efficient user selection algorithm is proposed and is shown to achieve the sum-rate capacity of the system asymptotically (in terms of the number of users), while requiring (i)~low-complexity precoding scheme of zero-forcing beam-forming at the base station, (ii)~low amount of feedback from the users to the base station, (iii)~low complexity of search. Part two studies the problem of MIMO broadcast channel with partial Channel State Information (CSI) at the transmitter. The necessary and sufficient conditions for the amount of CSI at the transmitter (which is provided to via feedback links from the receivers) in order to achieve the sum-rate capacity of the system are derived. The analysis is performed in various singnal to noise ratio regimes. In part three, the problem of sum-rate maximization in a broadcast channel with large number of users, when each user has a stringent delay constraint, is studied. In this part, a new definition of fairness, called short-term fairness is introduced. A scheduling algorithm is proposed that achieves: (i) Maximum sum-rate throughput and (ii) Maximum short-term fairness of the system, simultaneously, while satisfying the delay constraint for each individual user with probability one. In part four, the sum-rate capacity of MIMO broadcast channel, when the channels are Rician fading, is derived in various scenarios in terms of the value of the Rician factor and the distribution of the specular components of the channel.

Current research suggests that a high level of confidence and a low level of anxiety are predictive of higher math achievement. Compared to students from other provinces, previous research has found that Saskatchewan students have a higher level of confidence and a lower level of anxiety for learning math, but still tend to achieve lower math scores compared to students in other provinces. The data suggest that there may be unique factors effecting math learning for students in Saskatchewan. The purpose of the study is to determine the factors that may affect Saskatchewan students math achievement. Exploratory factor analyses and regression methods were employed to investigate possible traits that aid students in achieving higher math scores. Results from a 2007 math assessment administered to grade 5 students in Saskatchewan were used for the current study. The goal of the study was to provide a better understanding of the factors and trends unique to students for mathematic achievements in Saskatchewan.<p> Using results from a province-wide math assessment and an accompanying questionnaire administered to students in grade five across public school in Saskatchewan (n=11,279), the present study found statistical significance in three factors that have been supported by previous studies to influence math achievement differences, specifically in (1) confidence in math, (2) parental involvement in math and (3) extracurricular participation in math. The three aforementioned factors were found to be related to math achievement as predicted by the Assessment for Learning (AFL) program in Saskatchewan, although there were reservations to the findings due to a weak amount of variances accounted for in the regression model (r2 =.084). Furthermore, a multivariate analysis of variance indicated gender and locations of schools to have effects on students math achievement scores. Although a high amount of measurement errors in the questionnaire (and subsequently a low variance accounted for by the regression model) limited the scope and implications of the model, future implications and improvements are discussed

The focus of this study is to examine the mechanisms involved in the interactions among large-scale atmospheric circulation patterns and how they are related to surface air temperature anomalies in the North American Arctic. Historical temperature data sets of Fairbanks, Alaska and Montreal, Quebec have been analyzed with respect to large-scale atmospheric circulation index data sets to investigate surface temperature anomalies in winter during the period 1960 to 2002.