This thesis consists of five chapters on how to construct prediction sets for different types of data and models in a parametric or nonparametric Bayesian paradigm. The motivation of the models... Show moreThis thesis consists of five chapters on how to construct prediction sets for different types of data and models in a parametric or nonparametric Bayesian paradigm. The motivation of the models comes from applications in pharmaceutical manufacturing and quality control. Show less
This research aims to study the dynamic interaction between education and poetic identity, with a reference to the Obscure poets that came to the fore in the late 1970s and the early 1980s in... Show moreThis research aims to study the dynamic interaction between education and poetic identity, with a reference to the Obscure poets that came to the fore in the late 1970s and the early 1980s in Mainland China. It has been a prevailing idea that “successful” schooling in China has killed creativity and produced many unimaginative minds.Michelle Yeh’s and Maghiel van Crevel’s localized redefinition of poetic identity and Ivan Illich’s idea of deschooling, enable us to take a different perspective. I adopt mixed methods and use various resources such as oeuvre and textbooks. It shows that school education, family education, peer education, and mentor education have impacted on the forming of Obscure Poetry, and there is a fascinating “complicity” in the relationship between Obscure Poetry and Political Lyricism. There is definitely a relation between educational background and poetic identity, and it is not just, or even primarily, a negative relation. Literary traditions pass from one generation to another through various kinds of education. The complexity of the relationship between education and creative writing has often been reduced, overlooked and misconstrued, but the role of education remains a core perspective for our understanding of literature and of cultural traditions at large. Show less
This thesis consists of three chapters, the first two of which concern division points of elements of the multiplicative group of a number field. The third chapter involves division points of... Show moreThis thesis consists of three chapters, the first two of which concern division points of elements of the multiplicative group of a number field. The third chapter involves division points of points on an elliptic curve with complex multiplication over a number field. Show less
This thesis contains results on the arithmetic and geometry of del Pezzo surfaces of degree 1.In Chapter 1 we give the necessary background, assuming the reader is familiar with algebraic geometry.... Show moreThis thesis contains results on the arithmetic and geometry of del Pezzo surfaces of degree 1.In Chapter 1 we give the necessary background, assuming the reader is familiar with algebraic geometry. In Chapter 2, which is joint work with Julie Desjardins, we give necessary and sufficient conditions for the set of rational points on a del Pezzo surface of degree 1 from a certain family to be dense with respect to the Zariski topology. In Chapter 3 we study the action of the Weyl group on the E8 root system. The 240 roots in E8 are in one-to-one correspondence with the 240 exceptional curves on a del Pezzo surface of degree 1. We define the complete weighted graph where each vertex represents a root, and two vertices are connected by an edge with a weight defined by the dot product. We prove that for a large class of subgraphs of this graph, any two subgraphs from this class are isomorphic if and only if there is a symmetry of the graph that maps one to the other. We also give invariants that determine the isomorphism type of a subgraph. These results reduce computations on the graph significantly.In Chapter 4 we study the configurations of the 240 exceptional curves on a del Pezzo surface of degree 1, using results from Chapter 3. We prove that a point on a del Pezzo surface of degree 1 is contained in at most 16 exceptional curves in characteristic 2, at most 12 exceptional curves in characteristic 3, and at most 10 exceptional curves in all other characteristics. We give examples that show that the upper bounds are sharp in all characteristics, except possibly in characteristic 5.Finally, in Chapter 5 we show that if at least 9 exceptional curves intersect in a point on a del Pezzo surface S of degree 1, the corresponding point on an elliptic surface constructed from S is torsion on its fiber. This is less trivial than some experts thought. We use a list of all possible configurations of at least 9 pairwise intersecting exceptional curves computed in Chapter 3, and with an example from Chapter 4 we show that the analogue statement is false for 6 or fewer exceptional curves. Show less
