Flag varieties of reductive Lie groups and their subvarieties play a central role in representation theory. In the early 1980s, V. Deodhar introduced a decomposition of the flag variety which was then used to study the Kazdan-Lusztig polynomials. A Deodhar-type decomposition of the product of the flag variety with itself, referred to as the double flag variety, was introduced in 2007 by B. Webster and M. Yakimov, and each piece of the decomposition was shown to be coisotropic with respect to a naturally defined Poisson structure on the double flag variety. The work of Webster and Yakimov was partially motivated by the theory of cluster algebras in which Poisson structures play an important role. The Deodhar decomposition of the flag variety is better understood in terms of a cell decomposition of Bott-Samelson varieties, which are resolutions of Schubert varieties inside the flag variety. In the thesis, double Bott-Samelson varieties were introduced and cell decompositions of a Bott-Samelson variety were constructed using shuffles. When the sequences of simple reflections defining the double Bott-Samelson variety are reduced, the Deodhar-type decomposition on the double flag variety defined by Webster and Yakimov was recovered. A naturally defined Poisson structure on the double Bott-Samelson variety was also studied in the thesis, and each cell in the cell decomposition was shown to be coisotropic. For the cells that are Poisson, coordinates on the cells were also constructed and were shown to be log-canonical for the Poisson structure. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Chemistry / Master / Master of Philosophy

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This dissertation consists of three essays in labor economics. The first essay models how migrants crossing the border between the United States and Mexico respond to increases in border enforcement. We model a potential migrants' joint decision of whether to cross the border and, if so, where to cross the border using a random utility function. Our model allows us to calculate the migrants' substitution patterns: does more enforcement primarily on one part of the border primarily deter migrants from crossing the border altogether, or simply divert them to other parts of the border? We find that a substantial proportion of migrants are indeed diverted. These findings should serve as a caveat to policy makers who seek to address immigration reform issues primarily through tightening the border.The second chapter models the internal migration decisions of U.S. households during the period 935 to 1940. We measure the impact of spending on New Deal programs on migration patterns. Using a model of random utility similar to that in prior chapter, we find that more public works and relief spending in a region made it more attractive to potential migrants, while additional spending on the Agricultural Adjustment Administration (AAA) made the locale less attractive. The structural nature of our model allows us to compute counterfactual estimates to assess the overall impact of these programs. We find that regional disparities in spending on public works and relief programs we responsible for nearly 20% of long distance moves made between regions during this period.In the third chapter, we decompose the gap between mean sentences for males and females in the U.S. criminal justice system into the portion that can be explained by differences in the average severity of the crime committed by males and females and the portion explained by differences in how males and females who commit the same crime are treated. We find that differences in characteristics of the defendant can explain only half of the gap between mean male and females sentences, suggesting that women receive more lenient treatment in the U.S. criminal justice system.

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The wrist extensor muscles have been implicated in a work-related upper limb disorder referred to as non-specific arm pain (NSAP), which has an unknown pathophysiology. The primary objective of this thesis was to perform an electrophysiological evaluation of NSAP to gain a better understanding of the underlying pathophysiology. Secondary objectives were to determine the utility and reliability of the decomposition-based quantitative electromyography (DQEMG) system used to examine NSAP. The utility of the DQEMG system was first tested to determine whether physiological changes in muscles of healthy individuals performing low-level fatiguing contractions could be detected using this approach. Next, the reliability of the outcome variables produced through this system was tested on healthy individuals performing low-level non-fatiguing contractions. A case-control study was then performed using DQEMG to determine whether there were measurable changes in electrophysiological variables that suggest whether NSAP is myopathic or neuropathic in nature. Finally, the case control study was repeated using a less invasive approach of electrophysiological evaluation to determine if this method might be equally useful in determining the pathophysiology of NSAP. Results revealed DQEMG can be effectively and reliably used to detect changes in the physiological characteristics of motor units that accompany fatigue. Specifically, decreases in mean motor unit firing rates along with increases in amplitude, duration, and area parameters of needle- and surface-detected motor unit potentials (MUPs) suggest that recruitment is a main cause of increased electromyographic amplitude parameters with fatigue. Results of the reliability study suggested that DQEMG provides sufficiently consistent results to allow it to be effectively used for quantitative electromyographic (QEMG) analysis. In the first case control study, the QEMG parameters suggested that the underlying pathophysiology in NSAP may be myopathic in nature; specifically, QEMG findings for the NSAP group revealed smaller MUPs compared to the other groups. Lastly, the case control study using spike shape analysis across different levels of isometric wrist extension contractions was deemed to be useful in determining differences among the groups. This research suggests that NSAP may be myopathic in nature, since the NSAP group showed significantly lower mean spike amplitude and mean spike slope values compared to healthy subjects. / Thesis (Ph.D, Rehabilitation Science) -- Queen's University, 2008-08-27 14:53:55.892

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Some recently discussed stationary processes like fractionally integrated processes cannot be described by low order autoregressive or moving average (ARMA) models rendering the common algorithms for generation estimation and prediction partly very misleading. We offer an unified approach based on the Cholesky decomposition of the covariance matrix which makes these problems exactly solvable in an efficient way. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

A quota-based integrated commercial fishery owns fishing trawlers, processing plants, and fish quotas. Such a fishery must decide how to schedule trawlers for fishing and landing, how to schedule processing of products, how to schedule labour for processing, and how to plan inventory of raw materials and products. This problem is of great economic significance to New Zealand, whose economy depends to a large extent on the fishery industry. To assist the fishery manager, we develop a mixed integer linear program (MILP) for optimal scheduling of fishing trawlers, production planning (processing) and labour allocation for a quota-based integrated fishery of New Zealand. The model decides when and where each trawler should go for fishing, how much fish each trawler should land, and how much product to produce in each period. Since the fishery is a private farm, its main objective will be profit maximization (or cost minimization if its demand is on contract). The government manages the conservation of fish through the quota allocation. In this thesis the objective of the fishery model is to maximise the total profit. We demonstrate our model with examples based on data from a major New Zealand fishery. We investigate ways to manage the uncertainties involved in trawler scheduling and production planning of the fishery. To manage end-of-planning-horizon effects in the fishery, we develop a simple safety stock approach. We also analyse the workability of a rolling horizon approach to solve the longer planning horizon models and to deal with the end-of-planning horizon effects. We investigate the effect of initial and final position of the trawlers on the profit. We also investigated many different challenging data sets to observe the impact on the effectiveness of our IFPM. The second objective of this thesis is to develop an efficient solution procedure for the MILP, named integrated fishery planning model (IFPM). The IFPM consists of a fishing subproblem, a processing subproblem, and complicating side constraints. We have tried techniques including LP relaxation, Lagrangean relaxation (LR), Dantzig-Wolfe decomposition (DWD) and decomposition-based pricing (DBP). We develop a new DBP method to solve the IFPM. It gives excellent computation times. We also develop a decomposition-based O'Neill pricing (DBONP) method to improve the solution obtained from DBP procedure. It improves the DBP solutions but takes longer time to solve the IFPM. Finally, we develop a simple and efficient reduced cost-based pricing (RCBP) method. It takes less time to solve the IFPM and yields excellent results. The initial formulations for several planning horizons are solved using the AMPL modelling language and CPLEX with branch and bound. Relevant results and computational difficulties are reported.

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