Title: Compact objects in categories of modules Author: Peter Kálnai Department: Department of Algebra Supervisor: Mgr. Jan Žemlička, Ph.D., Department of Algebra Abstract: In the thesis we state baic properties of compact objects in various appropriate categories like categories of modules, stable factor category over a perfect ring and Grothendieck categories. We find a ring R such that the class of dually slender R-modules is closed under direct products under some set-theoretic assumption. Finally, we characterize the conditions, when countably generat- ed projective modules are finitely generated, expressed by their Grothendieck monoid. Keywords: compact, dually slender module, stable module category, projective module, self-small

Apresentamos uma generalização para as classes das álgebras quase inclinadas e quase hereditárias, que chamamos de álgebras m-quase inclinadas e m-quase hereditárias. Para estas últimas, pode-se obter uma trissecção de suas categorias de módulos determinada pelas subcategorias L^m = {X indecomponível; dimensão projetiva de Y é menor ou igual a m, para cada antecessor Y de X} e R = {X indecomponível; dimensão injetiva de Y é menor ou igual a 1, para cada sucessor Y de X}, além de ser possível mostrar que se existe um módulo E_m de forma a obtermos a igualdade de conjuntos {X módulo; Hom(E_m, \\tau X) = 0} = {X módulo; dimensão projetiva de X é menor ou igual a m}, então E_m é soma de somandos de módulos em R e todo caminho de indecomponíveis com início em um somando E de E_m e final em um módulo projetivo pode ser refinado a um caminho de morfismos irredutíveis, que é ainda seccional. Como consequência desse resultado obtém-se que as álgebras m-quase hereditárias são caracterizadas pelo fato de que todos seus módulos projetivos pertencem a L^m. É possível verificar que toda álgebra m-quase inclinada de dimensão global m+1 é m-quase hereditária e, consequentemente, que toda álgebra hereditária por partes de tipo mod H, para alguma álgebra hereditária H, com dimensão global m+1 é m-quase hereditária. Apresentamos ainda um exemplo de uma álgebra 2-quase hereditária que não é 2-quase inclinada, não sendo válida, portanto, a recíproca do resultado acima. Buscamos, dessa forma, estabelecer condições que quando assumidas sobre uma álgebra 2-quase hereditária possam garantir que esta é 2-quase inclinada e, em particular, hereditária por partes. Recorremos, para isso, à aplicação obtida por meio de uma adaptação de resultados de Happel, Reiten e Smalo, que sob certas hipóteses permite concluir que uma álgebra é álgebra de endomorfismos de um objeto inclinante. Como resultado, mostra-se que uma álgebra 2-quase hereditária com certas outras propriedades e que satisfaz as condições (H1), (H2) e (H3) é 2-quase inclinada. / We present a generalization of the classes of quasitilted and almost hereditary algebras, which we call m-quasitilted and m-almost hereditary algebras. For the latter one, we can obtain a trisection of their module categories determined by the following subcategories L^m = {X indecomposable; projective dimension of Y is at most m for each predecessor Y of X} and R = {X indecomposable; injective dimension of Y is at most 1 for each successor Y of X}. Moreover, if there exists a module E_m such that {X; Hom(E_m, \\tau X) = 0} = {X; projective dimension of X is at most m} then E_m is a sum of direct summands of modules in R and any path of indecomposable modules starting in a module E which is a direct summand of E_m and ending in a projective module can be refined to a path of irreducible morphisms, which is also sectional. This result on paths allow us to obtain a characterization for m-almost hereditary algebras in terms of their projective modules. It is also possible to prove that any m-quasitilted algebra with global dimension m+1 is a m-almost hereditary algebra and as a consequence we can obtain that any piecewise hereditary algebra of type mod H, for some hereditary algebra H, and with global dimension m+1 is m-almost hereditary. We present an example of a 2-almost hereditary which is not 2-quasitilted, which entails that the converse of the above mentioned result does not hold true. Thus we seek for conditions which can ensure that a given 2-almost hereditary is 2-quasitilted and, in particular, a piecewise hereditary algebra. For this, we use the correspondence obtained as an adaptation of results of Happel, Reiten and Smalo, which under certain assumptions shows that an algebra is an endomorphism algebra of a tilting object. It is shown that a 2-almost hereditary algebra with some other properties and satisfying (H1), (H2) and (H3) is 2-quasitilted.

The Utah Department of Transportation (UDOT) has completed a Light Detection and Ranging (LiDAR) data inventory that includes access locations across the UDOT network. The new data are anticipated to be extremely useful in better defining safety and in completing a systemwide analysis of locations where safety could be improved, or where safety has been improved across the state. The Department of Civil and Environmental Engineering at Brigham Young University (BYU) has worked with the new data to perform a safety analysis of the state related to access management, particularly related to driveway spacing and raised medians. The primary objective of this research was to increase understanding of the safety impacts across the state related to access management. These objectives were accomplished by using the LiDAR database to evaluate driveway spacing and locations to aid in hot spot identification and to develop relationships between access design and location as a function of safety and access category (AC). Utah Administrative Rule R930-6 contains access management guidelines to balance the access found on a roadway with traffic and safety operations. These guidelines were used to find the maximum number of driveways recommended for a roadway. ArcMap 10.3 and Microsoft Excel were used to visualize the data and identify hot spot locations. An analysis conducted in this study compared current roadway characteristics to the R930-6 guidelines to find locations where differences occurred. This analysis does not indicate the current AC is incorrect; it simply means that the assigned AC does not meet current roadway characteristic based on the LiDAR data analysis. UDOT can decide what this roadway will become in the future and help shape each segment using the AC outlined in the R930-6. A hierarchal Bayesian statistical before-after model, created in previous BYU safety research, was used to analyze locations where raised medians have been installed. Twenty locations where raised medians were installed in Utah between 2002 to 2014 were used in this model. The model analyzed the raised medians by AC. Only three AC were represented in the data. Regression plots depicting a decrease in crashes before and after installation, posterior distribution plots showing the probability of a decrease in crashes after installation, and crash modification factor (CMF) plots presenting the CMF values estimated for different vehicle miles traveled (VMT) values were all created as output from the before-after model. Overall, installing a raised median gives an approximate reduction of 53 percent for all crashes. Individual AC analysis yielded results ranging from 32 to 44 percent for all severity groups except severity 4 and 5. When the model was only run for crash severity 4 and 5, a larger reduction of 57 to 58 percent was found.

This study examined the psychometric properties of the Trauma Inventory for Partners of Sex Addicts (TIPSA). Using the Nominal Response Model (NRM), I examined several aspects of item and option functioning including discrimination, empirical category ordering, and information. Category Boundary Discrimination (CBD) parameters were calculated to determine the extent to which respondents distinguished between adjacent categories. Indistinguishable categories were collapsed through recoding. Empirically disordered response categories were also collapsed through recoding. Findings revealed that recoding solved some technical functioning issues in some items, and also revealed items (and perhaps option anchors) that were probably poorly conceived initially. In addition, nuisance or error variance was reduced only marginally by recoding, and the relative standing of respondents on the trait continuum remained largely unchanged. Items in need of modification or removal were identified, and issues of content validity were discussed.

The left hemisphere (LH) is accepted as the dominant hemisphere for language processing. There is also evidence confirming the language processing abilities of the right hemisphere (RH), particularly its lexical-semantic processing potential (Chiarello, 1988; Joanette, Goulet, & Hannequin, 1990). The capacity of the RH for language processing is significant to the investigation of language processing following LH lesions. However, the precise neurocognitive mechanisms underlying language processing following lesion remain to be fully elucidated. Subsequently, the overall aim for this thesis is to investigate hemispheric contributions to semantic processing following unilateral lesions, and to explore the significance of the contribution made by the RH. In order to achieve this overall aim, the current thesis firstly explores the hemispheric contributions made to lexical-semantic processing for healthy adults, and then shifts focus to explore the changes in hemispheric processing for participants with unilateral lesions (LH and RH). Comparisons of hemispheric activation between these groups will clarify the underlying hemispheric mechanisms that facilitate language processing following unilateral lesion. This thesis includes four complementary investigations of hemispheric contributions to semantic processing. The first study combined divided visual field (DVF) priming with event-related potentials (ERPs), in order to investigate controlled hemispheric semantic priming for young healthy adults. Two experiments were employed for a between subjects comparison of time-course differences (stimulus onset asynchrony, or SOA, varied between experiments) in hemispheric activation of associated and nonassociated category members. Continuous electroencephalograms were recorded throughout the priming task for each participant, and later analysed with reference to relevant ERP components (N400 and Late Positive Complex). Bilateral N400 priming was revealed for associated category members at both the short and long SOA. There was no significant N400 priming for the nonassociated category member condition. The examination of hemispheric priming of associated and nonassociated category member stimuli over the same time-course was continued in the second study for participants with unilateral LH lesions and matched controls. The second investigation aimed to determine the impact of unilateral LH lesions on controlled hemispheric semantic priming, utilising the DVF priming paradigm with participants following unilateral lesions. This study also aimed to explore associations between hemispheric activation during the online priming task and offline comprehension abilities. Differences in priming were observed between the LH lesion group and the control group, with participants in the LH lesion group requiring the association relationship to elicit priming. Priming also varied for participants as a function of their offline comprehension abilities, with RH priming associated with higher offline scores. The third investigation continued the exploration of hemispheric semantic activation following LH lesion, examining the impact of a LH lesion on interhemispheric control mechanisms, and the modification of hemispheric processing capacities with and without dominant hemisphere control. This investigation again utilised DVF priming with associated and nonassociated category member stimuli, in conjunction with the dual task paradigm. The dual task paradigm is designed to overload one hemisphere’s processing resources in order to remove interhemispheric suppression. Findings indicate that following LH lesions, the RH’s contribution is enhanced under conditions that are designed to overload the LH. The final study shifts from the investigation of participants with LH lesions to the impact of a RH lesion. This exploration of controlled hemispheric semantic priming following RH lesion sought to increase our understanding of the underlying mechanisms for semantic processing following unilateral lesion. The RH’s role in lexical-semantic processing has been documented consistently over approximately the last twenty years, however, there remains limited direct investigation of a RH lesion’s impact on contributions to semantic processing. A single case investigation utilised the same experimental procedure as the second study described. Findings suggest a similar activation pattern between the individual with RH lesion and the control participants, with both exhibiting bilateral activation of the associated and nonassociated category member stimuli. However, a subtle difference was found between the activation of the individual with RH lesion and that of the control group, with the individual with a RH lesion showing increased strategic processing difficulties at the longer SOA. Overall, the current thesis demonstrates the importance of the RH for efficient strategic semantic processing for both healthy adults, and people with unilateral lesions. In addition, this thesis concludes that following a LH lesion, the RH contribution to controlled semantic processing may be associated with successful comprehension, and that RH contributions may be improved with the addition of a secondary task designed to overload LH processing. The present thesis provides evidence to support the use of the DVF priming paradigm in the investigation of hemispheric contributions to semantic processing following unilateral lesion. It is anticipated that these findings will improve the current understanding of the underlying hemispheric contributions to lexical-semantics following a unilateral lesion, and will encourage continuing investigation into the RH’s capacity to impact language recovery.

The overall aim of this thesis is to demonstrate the usefulness and the efficacy of the Rasch model to provide solutions to a variety of measurement problems in the specific context of pain assessment. As Rasch models rest on the requirement of unidimensionality and as verbal self-report has been described as the most valid measure of the experience of pain (Melzack and Katz, 2006), all chapters of the present work focus on the measurement of a single dimension of the pain experience, its intensity and on self-reported rating scales assessing this dimension. Chapter 1 presents the basics of the Rasch methodology and describes how one model of the Rasch family of models, the many-facet model, can be applied to the analysis of pain intensity responses following CO2 laser heat stimulation. Several intensities of stimulation were delivered on the hand of one hundred subjects who had to rate their pain perception on a three-level verbal rating scale. This methodological chapter stressed the ability of the Rasch models to transform the original ordinal scores into linear measures on an interval scale. Advantages and disadvantages of the Rasch methodology are discussed. Chapter 2 presents a second application of the Rasch methodology: the development and validation of a new measurement tool. In that chapter, an item questionnaire, the Situational Pain Scale (SPS), measuring the mental representation of pain in imaginary painful situations was developed and validated with healthy and chronic pain adults. Chronic pain patients also completed questionnaires assessing clinical and emotional attributes. Responses to the SPS were analyzed according to the rating scale Rasch model to select unidimensional and unbiased items. The final SPS consisted of 18 items with a widespread measurement range, a distribution well-targeted for the sample of healthy subjects and chronic pain patients and a high index of measurement precision. The measure of pain representation was significantly related to present pain intensity and anxiety about pain. Fibromyalgia patients showed significantly higher pain representation measures than all other groups. The psychometric properties of the SPS allows to further test its value to predict behaviors such as chronification of an acute pain condition or coping strategies developed by the chronic pain patient Chapter 3 detailed a third application of the Rasch models: the investigation and optimization of rating scale functioning. It more specifically examines the question of the optimal number of response levels required to assess the intensity of pain. A first section details the problematic, reviews studies previously conducted and presents the statistical indexes provided by the Rasch methodology for investigating the functioning of rating scales. Two empirical studies follow. They investigate the optimal number of response levels required to assess the intensity of pain by means of the Rasch analysis. The first study is devoted to the examination of three verbal rating scales (four, five and ten response categories) in healthy adults rating the 18 items of the SPS (developed in chapter 2). Results showed that the 10- and the 5-level verbal rating scales (VRSs) were not effective to assess pain intensity but that the 4-level one was. Recategorization procedures applied on the 10- and the 5-level VRSs revealed that the optimal number of response levels was also around four. In conclusion, this study shows that the human being can only distinguish four response levels when assessing the pain intensity of hypothetical events on a VRS. The second empirical study is devoted to the examination of faces scales (FSs) in healthy children aged from four to seven years. Results of this second study showed an improvement in the ability to distinguish the response categories with age. The 4-5 year-old children could only distinguish two response categories and the 6-7 year-old children were able to discern the three levels of a three-level faces scale. In conclusion, young children do not distinguish as many faces as proposed by the majority of available faces scales. / L'objectif de cette thèse est de montrer l'utilité et l'efficacité du modèle de Rasch dans l'apport de solutions à divers problèmes rencontrés lors de la mesure de la douleur. Etant donné que le modèle de Rasch repose sur l'exigence d'unidimensionnalité et que l'auto-évaluation par le sujet a été décrite comme étant la mesure la plus valide de l'expérience de la douleur (Melzack and Katz, 2006), tous les chapitres de la thèse se sont focalisés sur la mesure d'une seule dimension de la douleur, son intensité, et sur les échelles d'auto-évaluation mesurant cette dimension. Le chapitre 1 présente les fondements de la méthodologie Rasch et décrit comment un des modèles de Rasch, le modèle multi-facettes, peut être appliqué à l'analyse de scores d'intensité de douleur fournis en réponse à des stimulations de chaleur délivrées à l'aide d'un laser CO2. Plusieurs intensités de stimulation ont été délivrées sur la main de cent sujets sains qui devaient évaluer leur perception de douleur sur une échelle verbale simple à trois niveaux de réponse. Ce chapitre méthodologique met l'accent sur la capacité du modèle de Rasch à transformer les scores originaux ordinaux en mesures linéaires sur une échelle d'intervalles. Les avantages et inconvénients de la méthodologie Rasch y sont discutés. Le chapitre 2 présente une seconde application de la méthodologie Rasch: le développement et la validation d'un nouvel instrument de mesure. Dans ce chapitre, un questionnaire, le Situational Pain Scale (SPS), mesurant la représentation mentale de la douleur lors de situations de douleur imaginaires est développé et validé dans une population d'adultes sains et de patients douloureux chroniques. Les patients douloureux chroniques ont également rempli une batterie de questionnaires évaluant diverses variables cliniques et émotionnelles. Les réponses au SPS ont été analysées à l'aide du modèle rating scale afin de sélectionner les items satisfaisant au critère d'unidimensionnalité et d'invariance de l'échelle. L'échelle finale comprend 18 items présentant une large étendue de mesure, une distribution bien ciblée par rapport à l'échantillon de sujets sains et de patients douloureux chroniques et une précision de mesure élevée. La mesure de la représentation de la douleur est significativement corrélée avec l'intensité de la douleur au moment de l'évaluation ainsi qu'avec l'anxiété spécifiquement liée à la douleur. Les patients fibromyalgiques ont une représentation de la douleur plus élevée que tous les autres groupes. Les qualités psychométriques de l'échelle permettent, dans le futur, de tester sa capacité à prédire certains comportements comme par exemple le risque de chronification d'un état de douleur aiguë ou encore les stratégies développées par le patient pour faire face à son état de douleur chronique. Le chapitre 3 détaille une troisième application des modèles de Rasch : l'investigation et l'optimisation du fonctionnement des échelles de réponse. Ce chapitre examine plus spécifiquement la question du nombre optimal de niveaux de réponse nécessaire pour évaluer l'intensité de la douleur. Une première section introduit la problématique, présente une revue de la littérature sur la question et détaille les indices statistiques fournis par la méthodologie Rasch pour étudier le fonctionnement des échelles de réponse. Deux études empiriques suivent. Elles étudient le nombre optimal de niveaux de réponse nécessaire pour l'évaluation de la douleur. La première étude est consacrée à l'investigation de trois échelles verbales simples (quatre, cinq et dix catégories de réponse) chez des adultes sains évaluant les 18 items du SPS dont le développement a été présenté au chapitre 2. Les résultats montrent que les échelles verbales simples (EVSs) à dix et cinq niveaux ne sont pas efficaces pour évaluer l'intensité de la douleur alors que l'échelle à quatre niveaux l'est. Les procédures de recatégorisation appliquées sur les EVSs à dix et cinq niveaux révèlent que le nombre optimal de niveaux de réponse est de quatre. En conclusion, cette étude montre que l'être humain ne peut distinguer que quatre niveaux de réponse lorsqu'il évalue des situations imaginaires sur une EVS. La seconde étude empirique est consacrée à l'investigation des échelles visages chez des enfants sains âgés de quatre à sept ans. Les résultats de cette seconde étude montrent une amélioration dans la capacité à distinguer les catégories de réponse avec l'âge. Les enfants de quatre et cinq ans ne peuvent distinguer que deux catégories de réponse alors que les enfants de six et sept ans peuvent distinguer les trois niveaux d'une échelle à trois visages. En conclusion, les jeunes enfants ne peuvent pas distinguer autant de visages que proposés par la majorité des échelles visages publiées.

Uppsatsen syftar till att studera hur gymnasieskolor profilerar sig genom marknadsföring. Detta tillämpas genom en diskursanalytisk studie av sex gymnasieskolor, som alla tillgodoser det Samhällsvetenskapliga programmet, belägna i Uppsala kommun. Av den marknadsföring som funnits tillgänglig har urvalet begränsats till respektive skolas hemsida. Resultatet visar på ett samband mellan hur skolorna talar om utbildning och elev. Det centrala för detta samband är hur eleven, genom skolornas marknadsföring, konstrueras som en konsument av utbildning. I denna konstruktion av utbildningsalternativ framträder olika profileringskategorier som skolorna tyr sig till genom marknadsföring. Den gemensamma profileringskategorin är den marknadsorienterade som visar hur skolorna presenterar sitt utbildningsalternativ genom att negativt särskilja sig från konkurrerande skolor. I detta finns en förskjutning från information om utbildning till marknadsföring av utbildning. I sin tur innebär detta att den information eleven tar del av inför sitt gymnasieval, också innehåller inslag av erbjudanden och reklam. I och med att eleven konstrueras som konsument har det skapats en kunskaps- och maktrelation mellan elev och skola. Denna relation konstruerar sedermera en situation där skolorna är beroende av att marknadsorientera sig för att utmärka sig i konkurrenssituationen som uppstått av det fria skolvalet. / The essay aims to study how secondary schools are profiled by marketing. This is applied through a discourse analytic study of six secondary schools, all of which meet the Social Science program, located in Uppsala. Of the marketing that has been available, the selection is limited to each school's website. The results show a correlation between how schools are talking about education and students. The key to this correlation is that the student through the schools marketing is designed as a consumer of education. This construction of educational options shows different profiling categories that schools cling to through marketing. The common profiling category is the market orientated that shows how schools will present their educational options by negative differentiate itself from rival schools. This is a shift from information on education for the promotion of education. In turn, this means that the information students take part in before secondary school also contains elements of promotions and advertising. As the student is constructed as a consumer, a knowledge and power relationship between student and school has been created. This knowledge and power relations construct later a situation where schools are dependent on market orientation to excel in the competitive environment created by the free school choice.

ABSTRACT Where do we get our ideas about the concept of `race'? The conceptualization of `race' has long been a topic of interest in the social sciences and society in general. The word `race' has been used and defined in different ways and different purposes throughout U.S. history. The definition of `race' therefore is arbitrary, changing according to the situation, but the consequences of how the word `race' is used are concrete and effect peoples lives daily. This research, in accord with much of the literature on the topic, shows that public schools play a major role in the conceptualization of `race'. Furthermore, what children are learning about `race;' in schools is not in an academic fashion but rather through inferences by the media, textbooks, and interactions with friends, teachers and school staff. I have conducted both qualitative (semi-structured interviews) and quantitative (questionnaires) research in order to explore where young adults say that they began to conceptualize `Race'. The results show that public schools, the home and neighborhoods of the young adults are the places that have influenced their `racial' conceptualization the most. I posit that we should provide the most up to date, accurate and pedagogically appropriate information as possible in public schools to aid our children in their process the conceptualization of the concept of `race'.

A state sum is an expression approximating the partition function of a d-dimensional field theory on a closed d-manifold from a triangulation of that manifold. To consider state sums in completely local 2-dimensional topological field theories (TFT's), we introduce a mechanism for incorporating triangulations of surfaces into the cobordism ([infinity],2)-category. This serves to produce a state sum formula for any fully extended 2-dimensional TFT possibly with extra structure. We then follow the Cobordism Hypothesis in classifying fully extended 2-dimensional G-equivariant TFT's for a finite group G. These are oriented theories in which bordisms are equipped with principal G-bundles. Combining the mechanism mentioned above with our classification results, we derive Turaev's state sum formula for such theories. / text

The increased use of polytomous item formats has led assessment developers to pay greater attention to the detection of differential item functioning (DIF) in these items. DIF occurs when an item performs differently for two contrasting groups of respondents (e.g., males versus females) after controlling for differences in the abilities of the groups. Determining whether the difference in performance on an item between two demographic groups is due to between group differences in ability or some form of unfairness in the item is a more complex task for a polytomous item, because of its many score categories, than for a dichotomous item. Effective DIF detection methods must be able to locate DIF within each of these various score categories. The Mantel, Generalized Mantel Haenszel (GMH), and Logistic Regression (LR) are three of several DIF detection methods that are able to test for DIF in polytomous items. There have been relatively few studies on the effectiveness of polytomous procedures to detect DIF; and of those studies, only a very small percentage have examined the efficiency of the Mantel, GMH, and LR procedures when item discrimination magnitudes and category intersection parameters vary and when there are different patterns of DIF (e.g., balanced versus constant) within score categories. This Monte Carlo simulation study compared the Type I error and power of the Mantel, GMH, and OLR (LR method for ordinal data) procedures when variation occurred in 1) the item discrimination parameters, 2) category intersection parameters, 3) DIF patterns within score categories, and 4) the average latent traits between the reference and focal groups. Results of this investigation showed that high item discrimination levels were directly related to increased DIF detection rates. The location of the difficulty parameters was also found to have a direct effect on DIF detection rates. Additionally, depending on item difficulty, DIF magnitudes and patterns within score categories were found to impact DIF detection rates and finally, DIF detection power increased as DIF magnitudes became larger. The GMH outperformed the Mantel and OLR and is recommended for use with polytomous data when the item discrimination varies across items.