Monoidal categories for the physics of integrable models

Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Categorical quantum computation

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Analyse de la structure logique des inférences légales et modélisation du discours juridique

Thèse par articles.

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.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Disorderly categories in picture postcards from colonial Papua and New Guinea

At the turn of the century in Melbourne, a notice typed on the verso of a postcard stated that the South Yarra Baptist Young Men's class was meeting on the following Sunday at 2.45 p.m. The card, published in the United Kingdom, was numbered 51828 in the Valentine series of Papuan postcards.1 The image, a photograph of Hanuabada village taken in the early 1880s, and the text, written early in 1900, are contradictory and constitute separate realms of evidence that invite a renegotiation of meaning, analysis, and interpretation of the relationships between images, tourism, colonial rule, and ethnographic knowing. The visual evidence suggests the postcard may have played an ethnographic, educative role in the public understanding of Papua, which had just become an Australian Territory and was not yet well known. It is also suggestive of educative roles related to mission endeavours, subimperialist ambitions and the new tourist traffic through the ports of Port Moresby, Samarai, and Rabaul.

Definition of airworthiness categories for civil Unmanned Aircraft Systems (UAS)

This paper introduces a novel strategy for the specification of airworthiness certification categories for civil unmanned aircraft systems (UAS). The risk-based approach acknowledges the fundamental differences between the risk paradigms of manned and unmanned aviation. The proposed airworthiness certification matrix provides a systematic and objective structure for regulating the airworthiness of a diverse range of UAS types and operations. An approach for specifying UAS type categories is then discussed. An example of the approach, which includes the novel application of data-clustering algorithms, is presented to illustrate the discussion.

Assessing the relationship between global warming and mortality : lag effects of temperature fluctuations by age and mortality categories

Although interests in assessing the relationship between temperature and mortality have arisen due to climate change, relatively few data are available on lag structure of temperature-mortality relationship, particularly in the Southern Hemisphere. This study identified the lag effects of mean temperature on mortality among age groups and death categories using polynomial distributed lag models in Brisbane, Australia, a subtropical city, 1996-2004. For a 1 °C increase above the threshold, the highest percent increase in mortality on the current day occurred among people over 85 years (7.2% (95% CI: 4.3%, 10.2%)). The effect estimates among cardiovascular deaths were higher than those among all-cause mortality. For a 1 °C decrease below the threshold, the percent increases in mortality at 21 lag days were 3.9% (95% CI: 1.9%, 6.0%) and 3.4% (95% CI: 0.9%, 6.0%) for people aged over 85 years and with cardiovascular diseases, respectively. These findings may have implications for developing intervention strategies to reduce and prevent temperature-related mortality.

The effect of various temperature indicators on different mortality categories in a subtropical city of Brisbane, Australia.

BACKGROUND: The relationship between temperature and mortality has been explored for decades and many temperature indicators have been applied separately. However, few data are available to show how the effects of different temperature indicators on different mortality categories, particularly in a typical subtropical climate. OBJECTIVE: To assess the associations between various temperature indicators and different mortality categories in Brisbane, Australia during 1996-2004. METHODS: We applied two methods to assess the threshold and temperature indicator for each age and death groups: mean temperature and the threshold assessed from all cause mortality was used for all mortality categories; the specific temperature indicator and the threshold for each mortality category were identified separately according to the minimisation of AIC. We conducted polynomial distributed lag non-linear model to identify effect estimates in mortality with one degree of temperature increase (or decrease) above (or below) the threshold on current days and lagged effects using both methods. RESULTS: Akaike's Information Criterion was minimized when mean temperature was used for all non-external deaths and deaths from 75 to 84 years; when minimum temperature was used for deaths from 0 to 64 years, 65-74 years, ≥ 85 years, and from the respiratory diseases; when maximum temperature was used for deaths from cardiovascular diseases. The effect estimates using certain temperature indicators were similar as mean temperature both for current day and lag effects. CONCLUSION: Different age groups and death categories were sensitive to different temperature indicators. However, the effect estimates from certain temperature indicators did not significantly differ from those of mean temperature.

The perceived importance of mall retail categories and its effect on likelihood of purchase during a recession

Recessions impact the retail sector and as such research into consumer decision making during such times is imperative. In response to this, our study takes an innovative approach to examining how the perceived importance of retail store categories in a shopping mall influences the relationship between consumers' shopping attitudes and likelihood of purchasing in those categories during a recession. The overall findings show the importance of a product category to a consumer, which is often overlooked, has a strong explanatory influence on consumer purchase intentions for that specific retail store categories in a shopping mall under recession conditions. Findings also show that for consumers’ who have altered their shopping behaviour the perceived importance of a retail store category fully mediates the relationship for: Majors, Leisure, Food Catered and Mini Majors categories, and partial mediation for Apparel. Importance has no mediating effect for: Food Retail, General Retail, Mobile Phone Services, Home wares, and Retail Services. Our study makes a key contribution to the retail management literature with the findings suggesting that redefining and articulating the importance of the value offering for specific retail store categories can help reduce the impact of changes in consumers' recessionary shopping intentions across the mall tenant mix. Such actions can then help preserve the image of the shopping mall in the minds of the consumers when the economic recovery begins.

Cyclone intensity categories

The weather forecast centers in Australia and many other countries use a scale of cyclone intensity categories (categories 1-5) in their cyclone advisories, which are considered to be indicative of the cyclone damage potential. However, this scale is mainly based on maximum gust wind speeds. In a recent research project involving computer modeling of cyclonic wind forces on roof claddings and fatigue damage to claddings, it was found that cyclone damage not only depends on the maximum gust wind speed, but also on two other cyclone parameters, namely, the forward speed and radius to maximum winds. This paper describes the computer model used in predicting the cyclone damage to claddings and investigates the damage potential of a cyclone as a function of all the relevant cyclone parameters, based on which it attempts to refine the current scale of cyclone intensity categories.