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Enabling learners to successfully use their second language (L2) in meaningful ways is a critical goal of instruction. Ultimately, most learners want to meet the L2 demands of the contexts in which they will use the language. To accomplish this, learners must develop linguistic knowledge and apply it in a manner that is contextually appropriate considering the requirements of the task at hand. In other words, learners must develop their L2 across both linguistic and communicative aspects to use it successfully. However, there is a paucity of L2 research in which linguistic and communicative performance have been simultaneously investigated.In this study, I investigated the development of English as a Foreign Language (EFL) learners’ L2 written production across the lexical and communicative dimensions of performance. The study involved 290 Japanese participants recruited from 20 intact EFL classes at four tertiary educational institutions in Japan, representing a wide range of L2 English proficiency levels and instructional contexts. The study used a non-intervention, repeated-measures design, allowing for the general development of participants’ L2 English writing to be examined. Participants’ L2 English written responses were collected using four argumentative writing tasks, which were administered at the beginning and end of the first and second semesters in a counterbalanced manner. Although a total of 952 responses were collected, responses shorter than 50 words were removed, leaving a total of 775 responses written by 250 participants. The 775 responses included in the primary analyses constituted a corpus of 89,122 words. Twenty-four single-word, multi-word, and lexical variation measures were calculated for the responses and subjected to an exploratory factor analysis. Seven latent lexical factors were identified in the data: High-Frequency Trigrams, Lexical Clarity, High-Frequency Bigrams, Lexical Variation, Lexical Breadth, Low-Frequency N-Grams, and Directional Association Strength of N-Grams. In addition, raters scored the responses for functional adequacy (i.e., Content, Comprehensibility, Organization, and Task Completion) and Lexical Appropriateness. The scores were analyzed using many-facet Rasch measurement, which converted the ordinal scores into equal-interval measures that had been adjusted for the influences of task and rater severity. The lexical factor scores and communicative Rasch measures were examined using linear mixed modeling, dominance analysis, and latent growth modeling to investigate (a) if and how lexical development had occurred, (b) if and how communicative development had occurred, (c) the relationships between the lexical and communicative components, and (d) the relationship between lexical and communicative growth. For the lexical factors, the results indicated that Directional Association Strength of N-Grams scores increased in a linear manner. Directional Association Strength of N-Grams comprised ΔP scores, which indicate the degree to which the first word(s) are predictive of the following word(s) in two- and three-word combinations. Thus, the results indicated that participants’ use of multi-word expressions improved. On the other hand, Lexical Clarity, which comprised imageability, concreteness, meaningfulness, and hypernymy scores, showed quadratic change, with scores improving and then regressing. Thus, the findings provide evidence of differing developmental trends for lexical aspects of L2 writing. For the communicative measures, the results indicated that Comprehensibility, Organization, and Lexical Appropriateness changed substantially over time. Improvement of Task Completion was dependent on the university context, and little change was observed for Content. Lexical Appropriateness showed the most improvement, with evidence of both linear and quadratic change. Bias interaction analyses also confirmed the presence of linear and quadratic trends for the communicative measures. Thus, the findings provide evidence of differing developmental trends for communicative aspects of L2 writing. For the relationships between the lexical and communicative components, the results indicated that two lexical factors were of key importance: Lexical Variation and Directional Association Strength of N-Grams. Lexical Variation was found to predict Content, Organization, and Task Completion; and Directional Association Strength of N-Grams was found to predict Comprehensibility and Lexical Appropriateness. The findings suggest that L2 performance assessments should not conflate measurement of lexical variation and use of multi-word expressions because they diverge in terms of the communicative outcomes they predict. The results also indicated a positive relationship between lexical and communicative development. A parallel process latent growth model was constructed that related lexical and communicative growth. The paths tested in the model suggest participants who had lower initial communicative scores were able to increase their lexical scores at faster rates, which in turn leveraged communicative growth. The findings highlight the potential for learners to improve their communicative ability through a targeted focus on multi-word expressions. / Applied Linguistics

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Graph Theory is a widely studied topic. A graph is defined by two important features: nodes and edges. Nodes can represent people, cities, variables, resources, products, while the edges represent a relationship between two nodes. Using graphs to solve problems has played a major role in a diverse set of industries for many years. Integer Programs (IPs) are mathematical models used to optimize a problem. Often this involves maximizing the utilization of resources or minimizing waste. IPs are most notably used when resources must be of integer value, or cannot be split. IPs have been utilized by many companies for resource distribution, scheduling, and conflict management. The node packing or independent set problem is a common combinatorial optimization problem. The objective is to select the maximum nodes in a graph such that no two nodes are adjacent. Node packing has been used in a wide variety of problems, which include routing of vehicles and scheduling machines. This thesis introduces several new graph structures, cliqued hole, odd bipartite hole, and odd k-partite hole, and their corresponding valid inequalities for the node packing polyhedron. These valid inequalities are shown to be new valid inequalities and conditions are provided for when they are facet defining, which are known to be the strongest class of valid inequalities. These new valid inequalities can be used by practitioners to help solve node packing instances and integer programs.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programs (IP) are used in companies and organizations across the world to reach financial and time-related goals most often through optimal resource allocation and scheduling. Unfortunately, integer programs are computationally difficult to solve and in some cases the optimal solutions are unknown even with today’s advanced computing machines. Lifting is a technique that is often used to decrease the time required to solve an IP to optimality. Lifting begins with a valid inequality and strengthens it by changing the coefficients of variables in the inequality. Often times, this technique can result in facet defining inequalities, which are the theoretically strongest inequalities. This thesis introduces a new type of lifting called synchronized simultaneous lifting (SSL). SSL allows for multiple sets of simultaneously lifted variables to be simultaneously lifted which generates a new class of inequalities that previously would have required an oracle to be found. Additionally, this thesis describes an algorithm to perform synchronized simultaneous lifting for a binary knapsack inequality called the Synchronized Simultaneous Lifting Algorithm (SSLA). SSLA is a quadratic time algorithm that will exactly simultaneously lift two sets of simultaneously lifted variables. Short computational studies show SSLA can sometimes solve IPs to optimality that CPLEX, an advanced integer programming solver, alone cannot solve. Specifically, the SSL cuts allowed a 76 percent improvement over CPLEX alone.

O foco central desta tese é o desenvolvimento de algoritmos para o problema de recoloração convexa de caminhos. Neste problema, é dado um caminho cujos vértices estão coloridos arbitrariamente, e o objetivo é recolorir o menor número possível de vértices de modo a obter uma coloração convexa. Dizemos que uma coloração de um grafo é convexa se, para cada cor, o subgrafo induzido pelos vértices dessa cor é conexo. Sabe-se que este problema é NP-difícil. Associamos a este problema um poliedro, e estudamos sua estrutura facial, com vistas ao desenvolvimento de um algoritmo. Mostramos várias inequações válidas para este poliedro, e provamos que várias delas definem facetas. Apresentamos um algoritmo de programação dinâmica que resolve em tempo polinomial o problema da separação para uma classe grande de inequações que definem facetas. Implementamos um algoritmo branch-and-cut baseado nesses resultados, e realizamos testes computacionais com instâncias geradas aleatoriamente. Apresentamos adicionalmente uma heurística baseada numa formulação linear que obtivemos. Estudamos também um caso especial deste problema, no qual as instâncias consistem em caminhos coloridos, onde cada cor ocorre no máximo duas vezes. Apresentamos um algoritmo de 3/2-aproximação para este caso, que é também NP-difícil. Para o caso geral, é conhecido na literatura um algoritmo de 2-aproximação. / The focus of this thesis is the design of algorithms for the convex recoloring problem on paths. In this problem, the instance consists of a path whose vertices are arbitrarily colored, and the objective is to recolor the least number of vertices so as to obtain a convex coloring.Acoloring of a graph is convex if, for each color, the subgraph induced by the vertices of this color is connected. This problem is known to be NP-hard. We associate a polyhedron to this problem and investigate its facial structure. We show various classes of valid inequalities for this polyhedron and prove that many of them define facets.We present a polynomial-time dynamic programming algorithm that solves, in polynomial time, the separation problem for a large class of facet-defining inequalities.We report on the computational experiments with a branch-and-cut algorithm that we propose for the problem. Additionally, we present a heuristic that is based on a linear formulation for the problem. We also study a special case of this problem, restricted to instances consisting of colored paths in which each color occurs at most twice. For this case, which is also NP-hard, we present a 3/2-approximation algorithm. For the general case, it is known a 2-approximation algorithm.

There are several reasons to research the effects of axial twist exposures and the resulting loading on the spine. The lack of consensus from the limited work that has previously examined the role of axial twist moments and motions in the development of spine injuries or generation of low back pain is the primary reason. From recently published works, axial twist moments appear to represent an increased risk for injury development when it acts in concert with loading about other physiological axes (i.e. flexion, extension, and compression). However, there is a large body of epidemiologic data identifying axial twist moments and/or motion as risk factors for low back disorders and pain, demonstrating the need for this series of investigations. It is likely that these combined exposures increase risk through altering the spine’s load distribution (passive resistance) by modifying the mechanics, but this deduction and related causal mechanism need to be researched. The global objective of this research was focused on determining whether there is evidence to support altered load distribution in the spine, specifically between the intervertebral disc and facets, in response to applied axial twist moments (when added in combination with one and two axes of additional loading). Also included was whether these modes of loading can modify spine mechanics and contribute and/or alter the development of damage and pain. This objective was addressed through one in-vivo (Drake and Callaghan, 2008a– Chapter #2) and three in-vitro (Drake et al., 2008– Chapter #4; Drake and Callaghan, 2008b– Chapter #5; Drake and Callaghan, 2008c– Chapter #6) studies that: (1) Quantified the amount of passive twist motion in the lumbar spine when coupled with various flexion-extension postures; (2) Documented the effects of flexion-extension postures and loading history on the distance between the facet articular surfaces; (3) Evaluated the result of axial twist rotation rates on acute failure of the spine in a neutral flexion posture; and (4) Explored whether repetitive combined loading has the ability to cause enough deformation to the spine to generate pain. Through the combination of findings previously reported in the literature and the outcomes of Drake and Callaghan (2008a– Chapter #2) and Drake et al. (2008– Chapter #4), a postural mediated mechanism was hypothesized to be responsible for governing the load distribution between the facet joints and other structures of the spine (i.e. disc, ligaments). Increased flexed postures were found to decrease the rotational stiffness by resulting in larger twist angles for the same applied twist moment in-vivo relative to a neutral flexion posture (Drake and Callaghan, 2008a– Chapter #2). This suggested there might be an increased load on the disc due to a change in facet coupling in these combined postures. Similarly, increased angles were observed in flexed and twisted postures for in-vitro specimens relative to a neutral flexion posture. These observed differences were found to correspond with altered facet joint mechanics. Specifically that flexed twisted postures increased the inter-facet spacing relative to the initial state of facet articulation (Drake et al., 2008– Chapter #4). These finding supported the postulated postural mechanism. Therefore, in a neutral posture the facet joints likely resisted the majority of any applied twist moment based on the limited range of motion and higher axial rotational stiffness responses observed. It was suspected that the changes in mechanics would likely cause a change in the load distribution however the magnitude of change in load distribution remains to be quantified. Further support for this postulated postural mechanism comes from the mode of failure for specimens that were exposed to 10,000 cycles of 5° axial twist rotation while in a static flexed posture (Drake and Callaghan, 2008c– Chapter #6), and neutrally flexed specimens exposed to 1.5° of rotation for 10,000 cycles reported in the literature. Without flexion, the failure patterns were reported to occur in the endplates, facets, laminae and capsular ligaments, but not the disc. However, with flexion the repetitive axial twist rotational displacements caused damage primarily to the disc. If the load distribution was unchanged, the higher axial rotation angle should have caused the specimen to fail in less cycles of loading, and the failure pattern should not have changed. Modulators of this hypothesized mechanism include the velocity of the applied twist moment and the effects these have on the failure parameters and injury outcomes. The three physiologic loading rates investigated in this work were not shown to affect the ultimate axial twist rotational failure angle or moment in a neutral flexion/extension posture, but were shown to modify flexion-extension stiffness (Drake and Callaghan, 2008b– Chapter #5). All of the flexion-extension stiffness values post failure, from a one-time axial twist exposure, was less than those from a repetitive combined loading exposure that has been established to damage the intervertebral disc but not the facets. Therefore, it is likely that the facet joint provides the primary resistance to acute axial twist moments when the spine is in a neutral flexion posture, but there appears to be a redistribution of the applied load from the facets to the disc in repetitive exposures. The aforementioned studies determined there are changes in load distribution and load response caused by altered mechanics resulting from twist loading, but whether the exposures could possibly produce pain needed to be addressed. Previous research has determined that the disc has relatively low innervation in comparison to the richly innervated facet capsule and vertebra, with only the outer regions being innervated. Likewise, it is assumed that pain could be directly generated as the nucleus pulposus disrupted the innervated outer annular fibres in the process of herniation. Also, direct compression of the spinal cord or nerve roots has been shown to occur from the extruded nucleus and result in the generation of pain responses. Additionally, the nucleus pulposus has been shown to be a noxious stimulus that damages the function and structure of nerves on contact. The other source of nerve root compression commonly recognized is a decrease in intervertebral foramina space, which was previously believed to only be caused through losses in disc height. However, decreased intervertebral foramina space due to repetitive motions appears to be a viable pain generating pathway that may not directly correspond to simply a loss of specimen or disc height (Drake and Callaghan, 2008c– Chapter #6). This is new evidence for combined loading to generate pain through spinal deformation. The objective of many traditional treatments for nerve root compression focus on restoring lost disc height to remove the nerve root compression. Unfortunately, nerve root compression caused by repetitive loading may not be alleviated through this approach. This collection of studies was focused on determining whether altered load distribution in the spine, specifically between the intervertebral disc and facets, in response to applied axial twist loading (when added in combination with one and two axes of additional loading) was occurring, and examining how these modes of loading can contribute and/or alter the development of injury and pain. Therefore, findings generated from this thesis may have important implications for clinicians, researchers, and ergonomists.

There are several reasons to research the effects of axial twist exposures and the resulting loading on the spine. The lack of consensus from the limited work that has previously examined the role of axial twist moments and motions in the development of spine injuries or generation of low back pain is the primary reason. From recently published works, axial twist moments appear to represent an increased risk for injury development when it acts in concert with loading about other physiological axes (i.e. flexion, extension, and compression). However, there is a large body of epidemiologic data identifying axial twist moments and/or motion as risk factors for low back disorders and pain, demonstrating the need for this series of investigations. It is likely that these combined exposures increase risk through altering the spine’s load distribution (passive resistance) by modifying the mechanics, but this deduction and related causal mechanism need to be researched. The global objective of this research was focused on determining whether there is evidence to support altered load distribution in the spine, specifically between the intervertebral disc and facets, in response to applied axial twist moments (when added in combination with one and two axes of additional loading). Also included was whether these modes of loading can modify spine mechanics and contribute and/or alter the development of damage and pain. This objective was addressed through one in-vivo (Drake and Callaghan, 2008a– Chapter #2) and three in-vitro (Drake et al., 2008– Chapter #4; Drake and Callaghan, 2008b– Chapter #5; Drake and Callaghan, 2008c– Chapter #6) studies that: (1) Quantified the amount of passive twist motion in the lumbar spine when coupled with various flexion-extension postures; (2) Documented the effects of flexion-extension postures and loading history on the distance between the facet articular surfaces; (3) Evaluated the result of axial twist rotation rates on acute failure of the spine in a neutral flexion posture; and (4) Explored whether repetitive combined loading has the ability to cause enough deformation to the spine to generate pain. Through the combination of findings previously reported in the literature and the outcomes of Drake and Callaghan (2008a– Chapter #2) and Drake et al. (2008– Chapter #4), a postural mediated mechanism was hypothesized to be responsible for governing the load distribution between the facet joints and other structures of the spine (i.e. disc, ligaments). Increased flexed postures were found to decrease the rotational stiffness by resulting in larger twist angles for the same applied twist moment in-vivo relative to a neutral flexion posture (Drake and Callaghan, 2008a– Chapter #2). This suggested there might be an increased load on the disc due to a change in facet coupling in these combined postures. Similarly, increased angles were observed in flexed and twisted postures for in-vitro specimens relative to a neutral flexion posture. These observed differences were found to correspond with altered facet joint mechanics. Specifically that flexed twisted postures increased the inter-facet spacing relative to the initial state of facet articulation (Drake et al., 2008– Chapter #4). These finding supported the postulated postural mechanism. Therefore, in a neutral posture the facet joints likely resisted the majority of any applied twist moment based on the limited range of motion and higher axial rotational stiffness responses observed. It was suspected that the changes in mechanics would likely cause a change in the load distribution however the magnitude of change in load distribution remains to be quantified. Further support for this postulated postural mechanism comes from the mode of failure for specimens that were exposed to 10,000 cycles of 5° axial twist rotation while in a static flexed posture (Drake and Callaghan, 2008c– Chapter #6), and neutrally flexed specimens exposed to 1.5° of rotation for 10,000 cycles reported in the literature. Without flexion, the failure patterns were reported to occur in the endplates, facets, laminae and capsular ligaments, but not the disc. However, with flexion the repetitive axial twist rotational displacements caused damage primarily to the disc. If the load distribution was unchanged, the higher axial rotation angle should have caused the specimen to fail in less cycles of loading, and the failure pattern should not have changed. Modulators of this hypothesized mechanism include the velocity of the applied twist moment and the effects these have on the failure parameters and injury outcomes. The three physiologic loading rates investigated in this work were not shown to affect the ultimate axial twist rotational failure angle or moment in a neutral flexion/extension posture, but were shown to modify flexion-extension stiffness (Drake and Callaghan, 2008b– Chapter #5). All of the flexion-extension stiffness values post failure, from a one-time axial twist exposure, was less than those from a repetitive combined loading exposure that has been established to damage the intervertebral disc but not the facets. Therefore, it is likely that the facet joint provides the primary resistance to acute axial twist moments when the spine is in a neutral flexion posture, but there appears to be a redistribution of the applied load from the facets to the disc in repetitive exposures. The aforementioned studies determined there are changes in load distribution and load response caused by altered mechanics resulting from twist loading, but whether the exposures could possibly produce pain needed to be addressed. Previous research has determined that the disc has relatively low innervation in comparison to the richly innervated facet capsule and vertebra, with only the outer regions being innervated. Likewise, it is assumed that pain could be directly generated as the nucleus pulposus disrupted the innervated outer annular fibres in the process of herniation. Also, direct compression of the spinal cord or nerve roots has been shown to occur from the extruded nucleus and result in the generation of pain responses. Additionally, the nucleus pulposus has been shown to be a noxious stimulus that damages the function and structure of nerves on contact. The other source of nerve root compression commonly recognized is a decrease in intervertebral foramina space, which was previously believed to only be caused through losses in disc height. However, decreased intervertebral foramina space due to repetitive motions appears to be a viable pain generating pathway that may not directly correspond to simply a loss of specimen or disc height (Drake and Callaghan, 2008c– Chapter #6). This is new evidence for combined loading to generate pain through spinal deformation. The objective of many traditional treatments for nerve root compression focus on restoring lost disc height to remove the nerve root compression. Unfortunately, nerve root compression caused by repetitive loading may not be alleviated through this approach. This collection of studies was focused on determining whether altered load distribution in the spine, specifically between the intervertebral disc and facets, in response to applied axial twist loading (when added in combination with one and two axes of additional loading) was occurring, and examining how these modes of loading can contribute and/or alter the development of injury and pain. Therefore, findings generated from this thesis may have important implications for clinicians, researchers, and ergonomists.