This dissertation examines organic food marketing from three aspects: household demand for organic food, household choice of retail formats accounting for preference organic food preference, and farmers’ joint adoption of organic farming and direct marketing methods. In Chapter Two, given the fast growth of private label milk and organic milk in the U.S., we estimate a censored demand system to study the demand relations among types of milk differentiated by brand types and organic status, using recent Nielsen Homescan data. We find that sociodemographic factors still play important roles in a household choice of milk types, and fluid milk is an inferior good. Moreover, as income increases, households are more likely to shift from buying conventional milk to organic milk and from private label conventional milk to branded conventional milk, as indicated by the asymmetric cross price elasticities. In Chapter Three, we examine whether households’ preference for organic food can affect their retail format choices for their grocery shopping trips. We model households’ choices of five major retail format with a conditional logit model, also using the Nielsen Homescan data. Our main findings are that regular organic user households are more likely to patronage organic specialty stores and discount stores, but less likely to shop in warehouse clubs. Price, consumer loyalty, and household shopping behavior also affects household retail format choice. In Chapter Four, we examine the relation between farmers’ adoption of organic farming and direct marketing, given their similar objectives in satisfying consumer demand and increasing farm income. We model farmers’ adoption of the two practices with a bivariate simultaneous linear probability model using data from USDA Agricultural Resource Management Survey. Our main finding is that the farmers’ adoption of organic farming decreases their probability of adopting direct marketing, whereas the reverse effect is insignificant. Also, organic farming is found to improve gross farm income.

The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are discussed by using particular example. In the second chapter, we focus on solving the linear difference equations by using the undetermined coefficient method and the variation of constants formula. Moreover, we establish the matrix exponential function which is the solution of the initial value problems (IVP) by the Putzer algorithm.

The aims of this thesis are to reduce the complexity and increasethe accuracy of rotations carried out inthe fast Fourier transform (FFT) at algorithmic and arithmetic level.In FFT algorithms, rotations appear after every hardware stage, which are alsoreferred to as twiddle factor multiplications. At algorithmic level, the focus is on the development and analysisof FFT algorithms. With this goal, a new approach based on binary tree decompositionis proposed. It uses the Cooley Tukey algorithm to generate a large number ofFFT algorithms. These FFT algorithms have identical butterfly operations and data flow but differ inthe value of the rotations. Along with this, a technique for computing the indices of the twiddle factors based on the binary tree representation has been proposed. We have analyzed thealgorithms in terms of switching activity, coefficient memory size, number of non-trivial multiplicationsand round-off noise. These parameters have impact on the power consumption, area, and accuracy of the architecture.Furthermore, we have analyzed some specific cases in more detail for subsets of the generated algorithms. At arithmetic level, the focus is on the hardware implementation of the rotations.These can be implemented using a complex multiplier,the CORDIC algorithm, and constant multiplications. Architectures based on the CORDIC and constant multiplication use shift and add operations, whereas the complex multiplication generally uses four real multiplications and two adders.The sine and cosine coefficients of the rotation angles fora complex multiplier are normally stored in a memory.The implementation of the coefficient memory is analyzed and the best possible approaches are analyzed.Furthermore, a number of twiddle factor multiplication architectures based on constant multiplications is investigated and proposed. In the first approach, the number of twiddle factor coefficients is reduced by trigonometric identities. By considering the addition aware quantization method, the accuracy and adder count of the coefficients are improved. A second architecture based on scaling the rotations such that they no longer have unity gain is proposed. This results in twiddle factor multipliers with even lower complexity and/or higher accuracy compared to the first proposed architecture.

This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.

La compétitivité des entreprises manufacturières dépend fortement de la productivité des machines etdes moyens de production. Pour garantir un haut niveau de productivité il est indispensable de minimiser lestemps d'arrêt dus aux fautes ou dysfonctionnements. Cela nécessite des méthodes efficaces pour détecter et isolerles fautes apparues dans un système (FDI). Dans cette thèse, une méthode FDI à base de modèles est proposée.La méthode est conçue pour la classe des systèmes à événements discrets industriels composés d’une bouclefermée du contrôleur et du processus. En comparant les comportements observés et attendus par le modèle, il estpossible de détecter et d’isoler des fautes. A la différence de la plupart des approches FDI des systèmes àévénements discrets, une méthode basée sur des modèles du comportement normal au lieu de modèles descomportements fautifs est proposée. Inspiré par le concept des résidus bien connu pour le diagnostic dessystèmes continus, une nouvelle approche pour l’isolation des fautes dans les systèmes à événements discrets aété développée. La clé pour l’application des méthodes FDI basées sur des modèles est d’avoir un modèle justedu système considéré. Comme une modélisation manuelle peut être très laborieuse et coûteuse pour dessystèmes à l’échelle industrielle, une approche d’identification pour les systèmes à événements discrets enboucle fermée est développée. Basée sur un algorithme connu pour l’identification des modèles monolithiques,une adaptation distribuée est proposée. Elle permet de traiter de grands systèmes comportant un haut degré deparallélisme. La base de cette approche est une décomposition du système en sous systèmes. Cettedécomposition est automatisée en utilisant un algorithme d’optimisation analysant le comportement observé dusystème. Les méthodes conçues dans cette thèse ont été mises en oeuvre sur une étude de cas et sur uneapplication d’échelle industrielle. / The competitiveness of manufacturing companies strongly depends on the productivity of machinesand production processes. To guarantee a high level of productivity, downtimes occurring due to faults have tobe kept as short as possible. This necessitates efficient fault detection and isolation (FDI) methods. In this work,a model-based FDI method for the widely used class of industrial closed-loop Discrete Event Systems isproposed. The considered systems consist of the closed-loop of plant and controller. Based on the comparison ofobserved and modeled system behavior, it is possible to detect and to isolate faults. Unlike most known methodsfor FDI in Discrete Event Systems, this work proposes working with a model of the fault-free behavior ratherthan working fault models. Inspired by the concept of residuals known from FDI in continuous systems, a newapproach for fault isolation based on fault-free Discrete Event System models is developed. The key of anymodel-based diagnosis method is to have an accurate model of the considered system. Since manual modelbuildingcan be very difficult for large industrial systems, an identification approach for this class of systems isintroduced. Based on an already existing monolithic identification algorithm, a distributed adaptation isdeveloped which allows treating large, concurrent systems. The key of the proposed approach is an automaticdecomposition of a given closed-loop Discrete Event System using an optimization approach which analyzesobserved system behavior. The methods developed in this thesis are applied to a mid-sized laboratory system andto an industrial winder to show their scalability.

L’objet de ce travail est l’utilisation de certains formalismes non classiques (analyses non standard, analyses constructives) afin de proposer des bases théoriques nouvelles autour des problèmes de discrétisations d’objets continus. Ceci est fait en utilisant un modèle discret du système des nombres réels appelé droite d’Harthong-Reeb ainsi que la méthode arithmétisation associée qui est un processus de discrétisation des fonctions continues. Cette étude repose sur un cadre arithmétique non standard. Dans un premier temps, nous utilisons une version axiomatique de l’arithmétique non standard. Puis, dans le but d’améliorer le contenu constructif de notre méthode, nous utilisons une autre approche de l’arithmétique non standard découlant de la théorie des Ω-nombres de Laugwitz et Schmieden. Cette seconde approche amène à une représentation discrète et multi-résolution de fonctions continues.Finalement, nous étudions dans quelles mesures, la droite d’Harthong-Reeb satisfait les axiomes de Bridges décrivant le continu constructif. / The aim of this work is to introduce new theoretical basis for the discretization of continuous objects using non classical formalisms. This is done using a discrete model of the continuum called the Harthong-Reeb line together with the related arithmetization method which is a discretisation process of continuous functions. This study stands on a nonstandard arithmetical framework. Firstly, we use an axiomatic version of nonstandard arithmetic. In order to improve the constructive content of our method, the next step is to use another approach of nonstandard arithmetic deriving from the theory of Ω-numbers by Laugwitzand Schmieden. This second approach leads to a discrete multi-resolution representation of continuous functions. Afterwards, we investigate to what extent the Harthong-Reeb line fits Bridges axioms of the constructive continuum.

Hamming-distance graphs arise naturally in the study of error-correcting codes and have been utilized by several authors to provide new proofs for (and in some cases improve) known bounds on the size of block codes. We study various standard graph properties of the Hamming-distance graphs with special emphasis placed on the chromatic number. A notion of robustness is defined for colorings of these graphs based on the tolerance of swapping colors along an edge without destroying the properness of the coloring, and a complete characterization of the maximally robust colorings is given for certain parameters. Additionally, explorations are made into subgraph structures whose identification may be useful in determining the chromatic number.

The game of Subset Take-Away is an impartial combinatorial game posed by David Gale in 1974. The game can be played on various discrete structures, including but not limited to graphs, hypergraphs, polygonal complexes, and partially ordered sets. While a universal winning strategy has yet to be found, results have been found in certain cases. In 2003 R. Riehemann focused on Subset Take-Away on bipartite graphs and produced a complete game analysis by studying nim-values. In this work, we extend the notion of Take-Away on a bipartite graph to Take-Away on particular hypergraphs, namely oddly-uniform hypergraphs and evenly-uniform hypergraphs whose vertices satisfy a particular coloring condition. On both structures we provide a complete game analysis via nim-values. From here, we consider different discrete structures and slight variations of the rules for Take-Away to produce some interesting results. Under certain conditions, polygonal complexes exhibit a sequence of nim-values which are unbounded but have a well-behaved pattern. Under other conditions, the nim-value of a polygonal complex is bounded and predictable based on information about the complex itself. We introduce a Take-Away variant which we call “Take-As-Much-As-You-Want”, and we show that, again, nim-values can grow without bound, but fortunately they are very easily described for a given graph based on the total number of vertices and edges of the graph. Finally we consider Take-Away on a specific type of partially ordered set which we call a rank-complete poset. We have results, again via an analysis of nim-values, for Take-Away on a rank-complete poset for both ordinary play as well as misère play.

Knot nullification is an unknotting operation performed on knots and links that can be used to model DNA recombination moves of circular DNA molecules in the laboratory. Thus nullification is a biologically relevant operation that should be studied. Nullification moves can be naturally grouped into two classes: coherent nullification, which preserves the orientation of the knot, and incoherent nullification, which changes the orientation of the knot. We define the coherent (incoherent) nullification number of a knot or link as the minimal number of coherent (incoherent) nullification moves needed to unknot any knot or link. This thesis concentrates on the study of such nullification numbers. In more detail, coherent nullification moves have already been studied at quite some length. This is because the preservation of the previous orientation of the knot, or link, makes the coherent operation easier to study. In particular, a complete solution of coherent nullification numbers has been obtained for the torus knot family, (the solution of the torus link family is still an open question). In this thesis, we concentrate on incoherent nullification numbers, and place an emphasis on calculating the incoherent nullification number for the torus knot and link family. Unfortunately, we were unable to compute the exact incoherent nullification numbers for most torus knots. Instead, our main results are upper and lower bounds on the incoherent nullification number of torus knots and links. In addition we conjecture what the actual incoherent nullification number of a torus knot will be.

Emergency department (ED) overcrowding has been a common complaint in Emergency Medicine in Canada for many years. Its adverse effects of prolonged waiting times cause patient dissatisfaction and unsafety. Previous studies indicate that adding a physician in triage (PIT) can increase accuracy and efficiency in the initial process of patient evaluation. However, the scientific evidence of the PIT impact on ED is far away from sufficient before its widespread implementation. This research is to search solutions using PIT to identify areas of improvement for the ED patient flow, based upon a validated discrete-event simulation (DES) model. As an efficient decision-making tool, the DES model also helps to develop an understanding of the current ED performance and quantitatively test various design alternatives for ED operations. / February 2017