Proefschrift--Groningen.

Thesis (Ph.D.)--Catholic University of America. / Biographical sketch.

Thèse--Univ. de Lille.

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In this dissertation we survey a variety of methods for constructing zero-coupon yield curves. We show that, when accuracy is of the utmost importance, the bootstrap described by Hagan and West (2006), Smit (2000), and Daeves and Parlar (2000) provides the ideal framework. This bootstrap requires the use of an interpolation algorithm, and a large portion of this dissertation will thus be devoted to the task of establishing an ideal method for interpolating yield curve data. Only two of the interpolation methods considered in this dissertation are seen to perform promisingly: the monotone convex method developed by Hagan and West (2006), and the monotone preserving r(t)t method developed in this dissertation. We show that the monotone preserving r(t)t method performs slightly better than the monotone convex method, in terms of the continuity of the forward curve, and in terms of the stability of the interpolation function. When economic appeal is of the utmost importance, we find parametric models to be more suitable than bootstrapping. However, we show that bootstrapping can be used to obtain a hypothetical set of zero-coupon bond prices, which can be used to calibrate parametric models. We compare the performance of the Nelson and Siegel (1987) and Svensson (1992) models, when applied to a historic set of South African swap curves, and show that the Svensson (1992) model performs better than the Nelson and Siegel (1987) model on a consistent basis. Copyright / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

archives@tulane.edu / In this dissertation, we consider several topics in computational geometry motivated by applications in maps and networks in geographic scenes. We first propose several algorithms that compute the Fr\'echet distance between curves, whose edges are relatively long. One of the popular metrics to capture the similarity between curves is the Fr\'echet distance. In particular, we give a linear-time greedy algorithm for deciding and approximating the Fr\'echet distance and a near linear-time algorithm for computing the exact Fr\'echet distance between two curves in any constant dimension. Next, we propose efficient data structures for proximity and similarity search among curves under the Fr\'echet distance: Given a curve with $n$ vertices, for any query curve of size $m$, decide whether the Fr\'echet distance between the two curves is small or not. We give a data structure with $O(m\log^2 n)$ query time using $O(n \log n)$ space and preprocessing time. In the next stage, we explore the \emph{Approximate Near-Neighbors Queries} problem among curves: Given a set of curves, for any query curve, the aim is to report those input curves that are `approximately' close to the query. We obtain the first result on this problem under the continuous Fr\'echet distance. We exploit the metric studied above for simplification purposes. We specifically consider the problem of computing an alternative polygonal curve with the minimum number of links whose distance to the input curve is at most some given real value. We also propose several exact and approximation algorithms when the vertices of the output curve are selected from the input curve's vertices, its edges, any points in the ambient space. Finally, we turn our attention to a more general type of simplification applied to trees and graphs: We are given a geometric graph and a threshold, the goal is to compute an alternative geometric graph with a minimum total number of edges and vertices such that the distance between them is at most the threshold. We detail several NP-hardness and algorithmic results depending on the type of input/output graphs, the vertex placement of the output graph, and the distance measures between them. / 1 / Majid Mirzanezhad

The aim of this thesis is to provide an introduction to the study of elliptic curves and modular forms over general commutative rings or schemes. We will recall a few aspects of the classical theory of these objects (over the complex numbers) while placing emphasis on the geometric picture. Moreover, we will formulate the theory of elliptic curves in the modern language of algebraic geometry following the work of Katz and Mazur. In addition, we provide an application of p−adic modular forms to the theory of p−adic heights on elliptic curves.

The interpretation of data from psychological experiments often involves the analysis and comparison of curves, like the electrocardiogram, spectral sensitivity, or dose-response curves. Existing statistical techniques are often inadequate for making this type of analysis. This thesis presents alternative methods for handling the data comprising curves and discusses the advantages of these techniques against those of existing methods.

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No description available.