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In the given work the problem of quality of generating of random numbers is studied. The purpose of work - to find out opportunities and qualitative characteristics of various generators of random numbers; to test their work; to compare and estimate quality of most often used generators. Work consists of three basic parts: The first part is devoted to questions of generating of random numbers, namely: what is the random number where sequences of random numbers are used, what ways of their reception. The big attention is given a question of qualitative characteristics of generators of random numbers, their classification is resulted. The greatest attention is given program gauges pseudo random numbers, and the information on hardware devices of generating of casual sequences has fact-finding character. In the second part it is spoken about testing generators of random numbers. In this part the basic methods of testing are considered, the most interesting sets of statistical tests are described. The third part - research. The purpose of researches - to allocate from the most popular program generators of random numbers (standard functions of various programming languages: Basic, Pascal, Delphi, C ++), the generator with as much as possible high quality of generating. In the end of work conclusions about the executed researches are given. Texts of the used programs, full the table of data, schedules and diagrams are presented in appendices.

The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, k-cores and their properties have been extensively investigated in random graphs and hypergraphs, with the determination of the threshold for the emergence of a giant k-core, due to Pittel, Spencer and Wormald, as one of the most prominent results. In this thesis, we obtain an asymptotic formula for the number of 2-connected graphs, as well as 2-edge-connected graphs, with given number of vertices and edges in the sparse range by exploiting properties of random 2-cores. Our results essentially cover the whole range for which asymptotic formulae were not described before. This is joint work with G. Kemkes and N. Wormald. By defining and analysing a core-type structure for uniform hypergraphs, we obtain an asymptotic formula for the number of connected 3-uniform hypergraphs with given number of vertices and edges in a sparse range. This is joint work with N. Wormald. We also examine robustness aspects of k-cores of random graphs. More specifically, we investigate the effect that the deletion of a random edge has in the k-core as follows: we delete a random edge from the k-core, obtain the k-core of the resulting graph, and compare its order with the original k-core. For this investigation we obtain results for the giant k-core for Erdős-Rényi random graphs as well as for random graphs with minimum degree at least k and given number of vertices and edges.

Discriminant analysis and random forests are used to create models for classification. The number of variables to be tested for inclusion in a model can be large. The goal of this work was to create an efficient and effective selection program. The first method used was based on the work of others. The resulting models were underperforming, so another approach was adopted. Models were built by adding the variable that maximized new-model accuracy. The two programs were used to generate discriminant-analysis and random forest models for three data sets. An existing software package was also used. The second program outperformed the alternatives. For the small number of runs produced in this study, it outperformed the method that inspired this work. The data sets were studied to identify determinants of performance. No definite conclusions were reached, but the results suggest topics for future study.

Animal movement patterns provide a rich source of information for examining a wide range of ecological interactions that span ecological scales from foraging behaviors of individuals to the spread of populations across landscapes. I investigated the causes and consequences of consumer movement, from the localized movements of individuals to the patterns of spread of populations across landscapes, using a series of complimentary microcosm experiments with a model consumer-resource system. In chapter one, I conducted a series of experiments designed to test differences in the fine-scale movement characteristics of swimming rotifers under experimental manipulations of local resource and conspecific abundance. Individual turn frequencies increased in resource-rich environments but were unaffected by competitor density. In contrast, individual swimming speeds increased at high competitor densities but were unaffected by resources. I demonstrated how these contrasting behaviors could be integrated to form predictions of population spread under different ecological scenarios. In chapter two, I tested the predictions established in chapter one by directly measuring the rates of spread of many replicate populations of rotifers in one-dimensional environments. Experimental treatments included a wide range of resource and conspecific densities, and starved versus sated rotifers in the presence versus absence of predator chemical cues. Rates of population spread were negatively correlated with resource abundance, especially when conspecific density was high, and rates of spread of both starved and risk-exposed populations were significantly lower than controls. In chapter three, I tested the effect of resource patchiness, conspecific density, and their interaction, on population spread through a two dimensional landscape. I found that rates of population spread decayed over time indicative of a sub-diffusive movement processes explained by positive density-dependent movement responses. Neither the rate of spread nor the magnitude of its decay differed between patchy and evenly distributed resource treatments, despite observed rotifer preferences for patches. These findings suggest that under certain ecological circumstances resource distribution may be less crucial in predicting population spread than density-dependence. Overall, my research demonstrates mechanistic links between the behavioural responses of individuals to their environment and the resulting larger scale phenomena of population-level movement patterns.

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This work utilizes zero-beta CAPM to derive an alternative form dubbed the ZCAPM. The ZCAPM posits that asset prices are a function of market risk composed of two components: average market returns and cross-sectional market volatility. Market risk associated with average market returns in the CAPM market model is known as beta risk. We refer to market risk related to cross-sectional market volatility as zeta risk. Using U.S. stock returns from January 1965 to December 2010, out-of-sample cross-sectional asset pricing tests show that the ZCAPM better predicts stock returns than popular three- and four-factor models. These and other empirical tests lead us to conclude that the ZCAPM holds promise as a robust asset pricing model.

Network topologies play a vital role in chip design; they largely determine the cost of the network and significantly impact performance in many-core architectures. We propose a novel set of on-chip networks, dodecs, and illustrate how they reduce network diameter with randomized low-radix router connections. In addition, we design an adaptive routing algorithm for dodec networks to achieve high throughput. By introducing randomness, dodec networks exhibit more uniform message latency. By using low-radix routers, dodec networks simplify the router microarchitecture and attain 20% area and 22% power reduction compared to mesh routers while delivering the same overall application performance for PARSEC. We compare our dodec network to alternative low-radix network topologies and show that at the same cost, dodec networks increase the throughput up to 50% while reducing average latency by 10% compared to a mesh.

The state of the art of modeling fluid flow in shale gas reservoirs is dominated by dual porosity models that divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano- pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual porosity models and Darcy’s Law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of complex flow mechanisms occurring in these reservoirs. Through the use of a unique simulator, this research work establishes a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three separate porosity systems: organic matter (mainly kerogen); inorganic matter; and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In the organic matter or kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of smaller pores (mainly nanopores and picopores) and larger pores (mainly micropores and nanopores) in kerogen are incorporated in the simulator. The separate inorganic sub-blocks mainly contribute to the ability to better model dynamic water behavior. The multiple porosity model is built upon a unique tool for simulating general multiple porosity systems in which several porosity systems may be tied to each other through arbitrary transfer functions and connectivities. This new model will allow us to better understand complex flow mechanisms and in turn to extend simulation to the reservoir scale including hydraulic fractures through upscaling techniques

We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, independent ensembles of the three real models of random matrices which we consider, namely real Ginibre matrices, Gaussian orthogonal matrices, and real Wishart matrices, are asymptotically second-order free. These ensembles do not satisfy the complex definition of second-order freeness satisfied by their complex analogues. This definition may be used to calculate the asymptotic fluctuations of products of matrices in terms of the fluctuations of each ensemble. We use a combinatorial approach to the matrix calculations similar to genus expansion, but in which nonorientable surfaces appear, demonstrating the commonality between the real ensembles and the distinction from their complex analogues, motivating this distinct definition. We generalize the description of graphs on surfaces in terms of the symmetric group to the nonorientable case. In the real case we find, in addition to the terms appearing in the complex case corresponding to annular spoke diagrams, an extra set of terms corresponding to annular spoke diagrams in which the two circles of the annulus are oppositely oriented, and in which the matrix transpose appears. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-09-09 11:07:37.414