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Human papillomavirus (HPV), a major sexually-transmitted disease, causes cervical cancer, in addition to numerous other cancers in females and males. This thesis uses mathematical modeling, theory and simulations to study the transmission dynamics of HPV, and associated dysplasia, in a community. A new deterministic model is designed and used to assess the population-level impact of Pap cytology screening on the transmission dynamics of the disease in a community. The model is rigorously analyzed for its dynamical features, vis-a-vis determining the conditions for the effective control (or elimination) and persistence of the disease. Furthermore, the effect of uncertainties in the estimates of the parameter values used in the numerical simulations of the model is accounted for via uncertainty and sensitivity analysis. Simulations of the model show that Pap screening dramatically reduces the incidence of cervical cancer in the community.

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Today, as computer systems are ubiquitous in our everyday life, there is no need to argue that their correctness is of capital importance. In order to prove (in a mathematical sense) that a given system satisfies a given property, formal methods have been introduced. They include concepts such as model checking and synthesis. Roughly speaking, when considering synthesis, we aim at building a model of the system which is correct by construction. In order to do so, models are mainly borrowed from game theory. During the last decades, there has been a shift from two-player qualitative zero-sum games (used to model antagonistic interactions between a system and its environment) to multiplayer quantitative games (used to model complex systems composed of several agents whose objectives are not necessarily antagonistic). In the latter setting, the solution concepts of interest include numerous equilibria, such as Nash equilibrium (NE) and subgame perfect equilibrium (SPE). While the existence of equilibria is widely studied, it is also well known that several equilibria may coexist in the same game. Nevertheless, some equilibria are more relevant than others. For example, if we consider a game in which each player aims at satisfying a given qualitative objective, it is possible to have both an equilibrium in which no player satisfies his objective and another one in which each player satisfies it. In this case one prefers the latter equilibrium which is more relevant.In this thesis, we focus on multiplayer turn-based games played on graphs either with qualitative or quantitative objectives. Our contributions are twofold: (i) we provide equilibria characterizations and (ii) we use these characterizations to solve decision problems related to the existence of relevant equilibria; and characterize their complexities. Firstly, we provide a characterization of a weaker notion of SPE (weak SPE) in multiplayer games with omega-regular objectives based on the payoff profiles which are realizable by a weak SPE. We then adopt another point of view by characterizing the outcomes of equilibria instead of their payoff profiles. In particular we focus on weak SPE outcome characterization. As for some kinds of games (e.g. multiplayer quantitative Reachability games), weak SPEs and SPEs are equivalent, this characterization is useful in order to study SPEs in these games.Secondly, we use those different equilibrium characterizations to provide the exact complexity classes of different decision problems related to the existence of relevant equilibria. We mainly focus on the constrained existence problem: if each player aims at maximizing his gain, this problem asks whether there exists an equilibrium such that each resulting player’s gain is greater than a threshold (one per player). We also consider variants of relevant equilibria based on the social welfare and the Pareto optimality of the players’ payoff. In this way, we prove the exact complexity classes for (i) the weak SPE constrained existence problem in multiplayer games with classical qualitative objectives such as Büchi, co-Büchi and Safety and (ii) the NE and SPE constrained existence problems (and variants) for qualitative and quantitative reachability games. In the latter case, the upper bounds on the required memory for such relevant equilibria are studied and proved to be finite. Studying memory requirements of strategies is important since with the synthesis process those strategies have to be implemented.Finally, we consider multiplayer, non zero-sum, turn-based timed games with qualitative Reachability objectives together with the concept of SPE. We prove that the SPE constrained existence problem is EXPTIME-complete for qualitative Reachability timed games. In order to obtain an EXPTIME algorithm, we proceed in different steps. In the first step, we prove that the game variant of the classical region graph is a good abstraction for the SPE constrained existence problem. In fact, we identify conditions on bisimulations under which the study of SPE in a given game can be reduced to the study of its quotient. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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This thesis consists of three essays on optimal monetary policy. In the first essay I study time-consistent monetary policy in an small open economy model with incomplete financial markets. I demonstrate the existence of two discretionary equilibria. The model is capable of explaining periods of different exchange rate volatilities as well as the transition between those regimes. Following a shock the economy can be stabilised either `quickly' or `slow', where both dynamic paths satisfy the conditions of optimality and time-consistency. I also show that a policy of partially targeting the exchange rate results in far worse welfare outcomes relative to a strict inflation targeting policy. In the second essay, I analyse how a policy maker can avoid expectation traps and coordination failures. Using a framework developed by Schaumburg and Tambalotti (2007) and Debortoli and Nunes (2010) in which a policy maker may or may not default on past promises I show that already mild degrees of precommitment are sufficient to generate uniqueness of the Pareto-preferred equilibrium. In the last chapter, I examine optimal monetary policy from an empirical perspective. I estimate a simple small open economy model separately for a policy maker acting under commitment and discretion and find that the data favours the commitment approach. Furthermore, the data suggest that the Bank of Canada did not target the nominal exchange rate in the inspected time period.

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Very high temperature (>900 °C) contact metamorphism and metasomatism of aluminous schist xenoliths in the mafic to ultramafic Cortlandt Complex, New York, resulted in formation of bodies of unusual Fe- and Al-oxide-rich rock called emery. During contact heating, disequilibrium thermal decomposition of the protolith schists in one closely examined xenolith produced two end-member materials: a quartzo-feldspathic water-undersaturated melt which partitioned much of the silica and calcium and all of the alkalis of the original schist; and a highly aluminous fine-grained emery residuum which contained spinel, magnetite, ilmenohematite, sillimanite, and sporadically corundum. During cooling, melt within the xenoliths was injected as cm-scale veinlets into the silica-poor solid residuum. Local increase in silica activity resulted in progressive silication reactions of spinel-rich residuum to several silicates. A simple model of progressive silication would require that reactions should occur from lower to higher silica content of product silicates in stages, e.g., spinel – sapphirine (Si/O=0.10), sapphirine – garnet (0.25), garnet – orthopyroxene (0.28), rather than directly from spinel to higher-silica minerals which would overstep intermediate reaction steps. However, observed reaction textures indicate the latter more complex behavior in which spinel may have reaction rims of, or occur as inclusions within, any of the three silicate minerals. Statistical analysis of several samples has shown the mode to be the spinel-orthopyroxene reaction rim boundary although orthopyroxene is the highest-silica product mineral, based on Si/O ratio. Chi-square test results are significant and show that the textural relations observed among spinel, sapphirine, garnet, and orthopyroxene are dependent. Increased silica activity therefore cannot be the only factor controlling the reaction sequence. Microprobe data has been collected in an attempt to correlate mineral compositions with the different textural occurrences. The effects of local equilibria appear to be the dominant factors in the overstepping of sequential reactions. Qualitative activity-activity diagrams proved useful for examining the effects of bulk composition on the relative stabilities of spinel and the three silicates, including variations in Fe/(Fe+Mg), bulk Mn and Zn contents, and minor local variation in oxygen fugacity. Matrix spinel compositions (i.e., those not modified by reaction to silicates) fall into two groups: a more magnesian one containing spinels with average Fe/(Fe+Mg) (Fe#) of 0.49 and a less magnesian one, average Fe# of 0.67. With regard to this bulk compositional effect, the more magnesian composition should reduce garnet stability due to the strong fractionation of Fe into garnet, thus favoring the reaction of spinel to orthopyroxene within silica-rich areas. In more aluminous areas, spinel will react to form sapphirine, then garnet, then possibly orthopyroxene. A less magnesian composition would expand the stability of garnet at the expense of sapphirine and, to a lesser extent, orthopyroxene. Zinc has a subtle effect on mineral stabilities. Because Zn is strongly partitioned into spinel, higher zinc contents (concentrations in some spinels are as high as 14.9 mol% gahnite) may expand the stability of that mineral considerably. Consequently, spinel stability may increase relative to the three silicates, but this may be quite variable due to variable reaction stoichiometry and different reaction-boundary slopes in the activity-activity diagram. In general, spinels with the highest Zn content occur next to orthopyroxene (ave. 4.9 mol% gahnite in spinels) for which the stability appears to be only slightly affected by this increase in Zn. The greatest decrease in silicate stability is observed in sapphirine. Spinels adjacent to sapphirine contain no more than 1.3 mol% gahnite. The effects of manganese and oxygen fugacity were also examined. Mn increases the stability of garnet due to strong partitioning of Mn into this mineral. It can be inferred using statistical and chemical data that this has some bearing on textural relations in garnet-bearing samples, but the lack of obvious Mn fractionation by other minerals examined makes it impossible to interpret the effects of Mn in the garnet-free samples. Calculated ferric-ferrous ratios in analyzed minerals were examined in an attempt to study the effect of oxygen fugacity on the stabilities of minerals. In the more magnesian compositions, which may correlate with slightly higher fO2 during reactions, spinels should react to form sapphirine, then possibly garnet or orthopyroxene with further silica activity increase. In lower-fO2 environments (perhaps those with higher bulk Fe#), spinel should react directly to form orthopyroxene. The coexistence of magnetite and ilmenohematite dictates T-fO2 conditions very nearly at those of the Hematite-Magnetite buffer. Minor fO2 variations that might have had an effect on silicate-forming reactions would only be recorded by small variations in magnetite and ilmenohematite solid solutions (ulvospinel and ilmenite contents, respectively). These data were not acquired in this study, however, so no definite conclusions could be made. / Master of Science