In this paper, we used the Autoregressive Distributed Lag (ARDL) model and the bounds test approach to estimate the elasticity of demand for natural gas in Western and Central Canada. The best model specification selected by Schwarz Information Criterion (SIC) for each province suggests that there exist long-run relationships between the dependent variable and independent variables for all provinces, except Ontario. Consumption per capita in these provinces can be explained by natural gas prices, electricity prices, income, and heating degree days (a measurement for the weather factor) in levels for the selected specification. The results show that natural gas demand is very inelastic with respect to natural gas prices and also with respect to heating degree days.

In this research we develop theoretical foundations and efficient solution methods for two classes of cluster-detection problems from optimization point of view. In particular, the s-club model and the biclique model are considered due to various application areas. An analytical review of the optimization problems is followed by theoretical results and algorithmic solution methods developed in this research. The maximum s-club problem has applications in graph-based data mining and robust network design where high reachability is often considered a critical property. Massive size of real-life instances makes it necessary to devise a scalable solution method for practical purposes. Moreover, lack of heredity property in s-clubs imposes challenges in the design of optimization algorithms. Motivated by these properties, a sufficient condition for checking maximality, by inclusion, of a given s-club is proposed. The sufficient condition can be employed in the design of optimization algorithms to reduce the computational effort. A variable neighborhood search algorithm is proposed for the maximum s-club problem to facilitate the solution of large instances with reasonable computational effort. In addition, a hybrid exact algorithm has been developed for the problem. Inspired by wide usability of bipartite graphs in modeling and data mining, we consider three classes of the maximum biclique problem. Specifically, the maximum edge biclique, the maximum vertex biclique and the maximum balanced biclique problems are considered. Asymptotic lower and upper bounds on the size of these structures in uniform random graphs are developed. These bounds are insightful in understanding the evolution and growth rate of bicliques in large-scale graphs. To overcome the computational difficulty of solving large instances, a scale-reduction technique for the maximum vertex and maximum edge biclique problems, in general graphs, is proposed. The procedure shrinks the underlying network, by confirming and removing edges that cannot be in the optimal solution, thus enabling the exact solution methods to solve large-scale sparse instances to optimality. Also, a combinatorial branch-and-bound algorithm is developed that best suits to solve dense instances where scale-reduction method might be less effective. Proposed algorithms are flexible and, with small modifications, can solve the weighted versions of the problems.

The topic of exact, exponential-time algorithms for NP-hard problems has received a lot of attention, particularly with the focus of producing algorithms with stronger theoretical guarantees, e.g. upper bounds on the running time on the form O(c^n) for some c. Better methods of analysis may have an impact not only on these bounds, but on the nature of the algorithms as well. The most classic method of analysis of the running time of DPLL-style ("branching" or "backtracking") recursive algorithms consists of counting the number of variables that the algorithm removes at every step. Notable improvements include Kullmann's work on complexity measures, and Eppstein's work on solving multivariate recurrences through quasiconvex analysis. Still, one limitation that remains in Eppstein's framework is that it is difficult to introduce (non-trivial) restrictions on the applicability of a possible recursion. We introduce two new kinds of complexity measures, representing two ways to add such restrictions on applicability to the analysis. In the first measure, the execution of the algorithm is viewed as moving between a finite set of states (such as the presence or absence of certain structures or properties), where the current state decides which branchings are applicable, and each branch of a branching contains information about the resultant state. In the second measure, it is instead the relative sizes of the modelled attributes (such as the average degree or other concepts of density) that controls the applicability of branchings. We adapt both measures to Eppstein's framework, and use these tools to provide algorithms with stronger bounds for a number of problems. The problems we treat are satisfiability for sparse formulae, exact 3-satisfiability, 3-hitting set, and counting models for 2- and 3-satisfiability formulae, and in every case the bound we prove is stronger than previously known bounds.

<p>In this thesis, I develop two sets of methods to help understand two distinct but also</p><p>related issues in financial economics.</p><p>First, representative agent models have been successfully applied to explain asset</p><p>market phenomenons. They are often simple to work with and appeal to intuition by</p><p>permitting a direct link between the agent's optimization behavior and asset market</p><p>dynamics. However, their particular modeling choices sometimes yield undesirable</p><p>or even counterintuitive consequences. Several diagnostic tools have been developed by the asset pricing literature to detect these unwanted consequences. I contribute to this literature by developing a new continuum of nonparametric asset pricing bounds to diagnose representative agent models. Chapter 1 lays down the theoretical framework and discusses its relevance to existing approaches. Empirically, it uses bounds implied by index option returns to study a well-known class of representative agent models|the rare disaster models. Chapter 2 builds on the insights of Chapter 1 to study dynamic models. It uses model implied conditional variables to sharpen asset pricing bounds, allowing a more powerful diagnosis of dynamic models.</p><p>While the first two chapters focus on the diagnosis of a particular model, Chapter</p><p>3 and 4 study the joint inference of a group of models or risk factors. Drawing on</p><p>multiple hypothesis testing in the statistics literature, Chapter 3 shows that many of</p><p>the risk factors documented by the academic literature are likely to be false. It also</p><p>proposes a new statistical framework to study multiple hypothesis testing under test</p><p>correlation and hidden tests. Chapter 4 further studies the statistical properties of</p><p>this framework through simulations.</p> / Dissertation

Masters Research - Master of Philosophy / Introduction Forty-six elite adolescent male rugby league players (12-17 years) participated in a nine-week study to determine the effects of three exercise training programs on 0-30 metres sprint running time and bounds performance (10 bounds). Subjects were randomly assigned to a rugby league fitness group (F) n=12, a sprint group (S) n= 14 and a sprint-bounds group (SB) n= 20. Forty-two subjects completed the study. Methods Separate sessions for fitness, speed, and bounds were conducted once a week for nine weeks. To determine the effect of training a two-way analysis of variance was performed, followed by post-hoc paired t-tests to allow pairwise comparisons when significant interactions were found. Significance was set at p<0.05. Statistical analysis was performed using SPSS for Mac (version 13.1). Effect sizes were calculated to evaluate the meaningfulness of observed changes. Results Moderate improvements (p<0.05; 5%) were observed in both the F and SB groups over 10 m. Speed changes over 30 m differed more among the groups. The F group recorded moderate (p<0.01; 4%) improvements, small improvements (p<0.01; 3%) in the SB group and trivial difference (p<0.05) in the S group. The F and S groups improved by approximately 7% (p<0.01) in bounds performance over 10 bounds whereas the SB group improved by approximately 10% (p<0.01) in bounds performance over 10 bounds. Group S had faster sprint times (p<0.05) prior to training compared to groups F and SB. Discussion All three programs led to improvements in sprint speed and bounds distance, but the extent of the improvements varied with the specificity of the training program and pre-training performance level. Groups F and SB had 4-5% improvements in sprint speed over 30 m whereas group S showed relatively trivial changes. In all groups, the improvements were greater over 10 m and least over 30 m. Bounds distance improved more than sprint speed, and the greatest improvement was achieved in the SB group compared to the F and S groups. Conclusion Rugby league training (game specific drills and extended efforts) coupled with the various components of physical activity can improve speed and power as effectively as specific speed and power training in adolescent boys. Training for acceleration can selectively improve 0-10 m speed more than 0-30 m speed. Sprint and bounds training have been shown to be safe and effective methods to increase speed and power in this group of adolescents.

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. We derive upper and lower relative loss bounds for a class of universal learning algorithms involving a switching dynamics over the choice of the experts. On the basis of the performance bounds we provide the optimal a priori discretization of the switching-rate parameter that governs the switching dynamics. We demonstrate the algorithm in the context of wireless networks.

abstract: Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the $D_p$-divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the $D_p$-divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

Esta dissertação busca avaliar o comportamento da renda mediana e da desigualdade de rendimentos tratando o problema de seleção, através de uma abordagem ainda não utilizada em estudos semelhantes no Brasil. A metodologia empregada busca tratar o problema de seleção utilizando apenas hipóteses fracas e pautadas em argumentos econômicos, estimando os menores intervalos possíveis para a distribuição de renda da população. Os resultados obtidos mostram que as medianas dos rendimentos potenciais em 2002 e 2004 eram inferiores aos de 1996. Adicionalmente, a desigualdade de renda potencial recuou no Brasil entre 1996 e 2006. / This dissertation aims to evaluate the median income and income inequality behavior treating the selection problem with an approach not yet used in similar studies in Brazil. The present methodology tries to address the selection problem using only weak assumptions based on economic arguments, estimating the smallest possible intervals for the population income distribution. The results show that the mean potential income of 2002 and 2004 was smaller than the one of 1996. Additionally, the potential income inequality in Brazil fell from 1996 to 2006.

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G - v is less than the total domination number of G. These graphs we call γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We characterize the connected graphs with minimum degree one that are γ t-critical and we obtain sharp bounds on their maximum diameter. We calculate the maximum diameter of a k-γt-critical graph for k≤8 and provide an example which shows that the maximum diameter is in general at least 5k/3 - O(1).

After a detailed discussion of the variation theorem for upper bound calculation of eigenvalues, many standard procedures for determining lower bounds to eigenvalues are presented with chemical applications in mind. A new lower bound method, arbitrary choice without trunctation is presented and tested on the helium atom. This method is attractive because it does not require knowledge of the eigenvalues or eigenvectors of the base problem. In application, however, it is shown that the method is disappointing for two reasons: 1) the method does not guarantee improved bounds as calculational effort is increased; and 2) the method requires some a priori information which, in general, may not be available. A possible direction for future work is pointed out in the end. An extension of a lower bound method by Calogero and Marchioro has been developed and is presented in appendix G along with comments on the effective field method in appendix H for Virginia Tech access only. / Ph. D. / To avoid copyright infringements, access to these three appendices (G, H, and I) has been permanently limited to the Virginia Tech campus. In the case that Virginia Tech places these appendices freely on the internet, Virginia Tech is solely responsible for copyright violations.