Model categories

The purpose of this thesis is to present some fundamental results about model categories, and to give some examples of categories that can be equipped with a model structure.

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

On the homotopy theory of spectral categories

"Vegeu el resum a l'inici del document del fitxer adjunt."

Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

Antenna theory in resonating systems derived from fundamental electromagnetism

Theoretische Elektrotechnik, Elektromagnetische Verträglichkeit, Antennentheorie, Elektrodynamik, Mathematische Methoden der Physik, Leitungstheorie, Mikrowellentechnik, Hohlraumresonatoren

A curious example of two model categories and some associated differential graded algebras

"Vegeu el resum a l'inici del document del fitxer adjunt."

Examining sport commitment and intentions to participate in intramural sports : application of the Sport Commitment Model and the Theory of Planned Behaviour in a campus recreational sport setting

Fifty-six percent of Canadians, 20 years of age and older, are inactive (Canadian Community Health Survey, 200012001). Research has indicated that one of the most dramatic declines in population physical activity occurs between adolescence and young adulthood (Melina, 2001; Stephens, Jacobs, & White, 1985), a time when individuals this age are entering or attending college or university. Colleges and universities have generally been seen as environments where physical activity and sport can be promoted and accommodated as a result of the available resources and facilities (Archer, Probert, & Gagne, 1987; Suminski, Petosa, Utter, & Zhang, 2002). Intramural sports, one of the most common campus recreational sports options available for post-secondary students, enable students to participate in activities that are suited for different levels of ability and interest (Lewis, Jones, Lamke, & Dunn, 1998). While intramural sports can positively affect the physical activity levels and sport participation rates of post-secondary students, their true value lies in their ability to encourage sport participation after school ends and during the post-school lives of graduates (Forrester, Ross, Geary, & Hall, 2007). This study used the Sport Commitment Model (Scanlan et aI., 1993a) and the Theory of Planned Behaviour (Ajzen, 1991) with post secondary intramural volleyball participants in an effort to examine students' commitment to intramural sport and 1 intentions to participate in intramural sports. More specifically, the research objectives of this study were to: (1.) test the Sport Commitment Model with a sample of postsecondary intramural sport participants(2.) determine the utility of the sixth construct, social support, in explaining the sport commitment of post-secondary intramural sport participants; (3.) determine if there are any significant differences in the six constructs of IV the SCM and sport commitment between: gender, level of competition (competitive A vs. B), and number of different intramural sports played; (4.) determine if there are any significant differences between sport commitment levels and constructs from the Theory of Planned Behaviour (attitudes, subjective norms, perceived behavioural control, and intentions); (5.) determine the relationship between sport commitment and intention to continue participation in intramural volleyball, continue participating in intramurals and continuing participating in sport and physical activity after graduation; and (6.) determine if the level of sport commitment changes the relationship between the constructs from the Theory of Planned Behaviour. Of the 318 surveys distributed, there were 302 partiCipants who completed a usable survey from the sample of post-secondary intramural sport participants. There was a fairly even split of males and females; the average age of the students was twenty-one; 90% were undergraduate students; for approximately 25% of the students, volleyball was the only intramural sport they participated in at Brock and most were part of the volleyball competitive B division. Based on the post-secondary students responses, there are indications of intent to continue participation in sport and physical activity. The participation of the students is predominantly influenced by subjective norms, high sport commitment, and high sport enjoyment. This implies students expect, intend and want to 1 participate in intramurals in the future, they are very dedicated to playing on an intramural team and would be willing to do a lot to keep playing and students want to participate when they perceive their pursuits as enjoyable and fun, and it makes them happy. These are key areas that should be targeted and pursued by sport practitioners.

Looking for a Matrix model for ABJM theory

Encouraged by the recent construction of fuzzy sphere solutions in the Aharony, Bergman, Jafferis, and Maldacena (ABJM) theory, we re-analyze the latter from the perspective of a Matrix-like model. In particular, we argue that a vortex solution exhibits properties of a supergraviton, while a kink represents a 2-brane. Other solutions are also consistent with the Matrix-type interpretation. We study vortex scattering and compare with graviton scattering in the massive ABJM background, however our results are inconclusive. We speculate on how to extend our results to construct a Matrix theory of ABJM.

Restaurant Health and Hygiene: A Model Program with Theory-Based Guidelines for Implementation

Poor hygienic practices and illness of restaurant employees are major contributors to the contamination of food and the occurrence of food-borne illness in the United States, costing the food industry and society billions of dollars each year. Risk factors associated with this problem include lack of proper handwashing; food handlers reporting to work sick; poor personal hygiene; and bare hand contact with ready-to-eat foods. However, traditional efforts to control these causes of food-borne illness by public health authorities have had limited impact, and have revealed the need for comprehensive and innovative programs that provide active managerial control over employee health and hygiene in restaurant establishments. Further, the introduction and eventual adoption by the food industry of such programs can be facilitated through the use of behavior-change theory. This Capstone Project develops a model program to assist restaurant owners and operators in exerting active control over health and hygiene in their establishments and provides theory-based recommendations for the introduction of the program to the food industry.

Health beliefs affect the correct replacement of daily disposable contact lenses:predicting compliance with the Health Belief Model and the Theory of Planned Behaviour

Purpose: To assess the compliance of Daily Disposable Contact Lenses (DDCLs) wearers with replacing lenses at a manufacturer-recommended replacement frequency. To evaluate the ability of two different Health Behavioural Theories (HBT), The Health Belief Model (HBM) and The Theory of Planned Behaviour (TPB), in predicting compliance. Method: A multi-centre survey was conducted using a questionnaire completed anonymously by contact lens wearers during the purchase of DDCLs. Results: Three hundred and fifty-four questionnaires were returned. The survey comprised 58.5% females and 41.5% males (mean age 34. ±. 12. years). Twenty-three percent of respondents were non-compliant with manufacturer-recommended replacement frequency (re-using DDCLs at least once). The main reason for re-using DDCLs was "to save money" (35%). Predictions of compliance behaviour (past behaviour or future intentions) on the basis of the two HBT was investigated through logistic regression analysis: both TPB factors (subjective norms and perceived behavioural control) were significant (p. <. 0.01); HBM was less predictive with only the severity (past behaviour and future intentions) and perceived benefit (only for past behaviour) as significant factors (p. <. 0.05). Conclusions: Non-compliance with DDCLs replacement is widespread, affecting 1 out of 4 Italian wearers. Results from the TPB model show that the involvement of persons socially close to the wearers (subjective norms) and the improvement of the procedure of behavioural control of daily replacement (behavioural control) are of paramount importance in improving compliance. With reference to the HBM, it is important to warn DDCLs wearers of the severity of a contact-lens-related eye infection, and to underline the possibility of its prevention.

Endothelial- and Platelet-Derived Microparticles Are Generated During Liver Resection in Humans.

BACKGROUND Cell-derived plasma microparticles (<1.5 μm) originating from various cell types have the potential to regulate thrombogenesis and inflammatory responses. The aim of this study was to test the hypothesis that microparticles generated during hepatic surgery co-regulate postoperative procoagulant and proinflammatory events. METHODS In 30 patients undergoing liver resection, plasma microparticles were isolated, quantitated, and characterized as endothelial (CD31+, CD41-), platelet (CD41+), or leukocyte (CD11b+) origin by flow cytometry and their procoagulant and proinflammatory activity was measured by immunoassays. RESULTS During liver resection, the total numbers of microparticles increased with significantly more Annexin V-positive, endothelial and platelet-derived microparticles following extended hepatectomy compared to standard and minor liver resections. After liver resection, microparticle tissue factor and procoagulant activity increased along with overall coagulation as assessed by thrombelastography. Levels of leukocyte-derived microparticles specifically increased in patients with systemic inflammation as assessed by C-reactive protein but are independent of the extent of liver resection. CONCLUSIONS Endothelial and platelet-derived microparticles are specifically elevated during liver resection, accompanied by increased procoagulant activity. Leukocyte-derived microparticles are a potential marker for systemic inflammation. Plasma microparticles may represent a specific response to surgical stress and may be an important mediator of postoperative coagulation and inflammation.

A Thomason model structure on the category of small n-fold categories

We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.