Customer Lifetime Value (CLV) ---which is a measure of the profit generating potential, or value, of a customer---is increasingly being considered a touchstone for customer relationship management. As the guide and benchmark for Customer Relationship Management (CRM) applications, CLV analysis has received increasing attention from both the marketing practitioners and researchers from different domains. Furthermore, the central challenge in predicting CLV is the precise calculation of customer’s length of service (LOS). There are several statistical approaches for this problem and several researchers have used these approaches to perform survival analysis in different domains. However, classical survival analysis techniques like Kaplan-Meier approach which offers a fully non-parametric estimate ignores the covariates completely and assumes stationary of churn behavior along time, which makes it less practical. Further, segments of customers, whose lifetimes and covariate effects can vary widely, are not necessarily easy to detect. Like many other applications, data mining is emerging as a compelling analysis tool for the CLV application recently. Comparatively, data mining methods offer an interesting alternative with the fact that they are less limited than the conventional statistical approaches. Customer databases contain histories of vital events such as the acquisition and cancellation of products and services. The historical data is used to build predictive models for customer retention, cross-selling, and other database marketing endeavors. In this research project we discuss and investigate the possibility of combining these statistical approaches with data mining methods to improve the performance for the CLV problem in a real business context. Part of the research effort is placed on the precise prediction of LOS of the customers in concentration of a real world business. Using the conventional statistical approaches and data mining methods in tandem, we demonstrate how data mining tools can be apt complements of the classical statistical models ---resulting in a CLV prediction model that is both accurate and understandable. We also evaluate the proposed integrated method to extract interesting business domain knowledge within the scope of CLV problem. In particular, several data mining methods are discussed and evaluated according to their accuracy of prediction and interpretability of results. The research findings will lead us to a data mining method combined with survival analysis approaches as a robust tool for modeling CLV and for assisting management decision-making. A calling plan strategy is designed based on the predicted survival time and calculated CLV for the telecommunication industry. The calling plan strategy further investigates potential business knowledge assisted by the CLV calculated.

There are several solutions for analysis of clustered binary data. However, the two most common tools in use today, generalized estimating equations and random effects or mixed models, rely heavily on asymptotic theory. However, in many situations, such as small or sparse samples, asymptotic assumptions may not be met. For this reason we explore the utility of the quadratic exponential model and conditional analysis to estimate the effect size of a trend parameter in small sample and sparse data settings. Further we explore the computational efficiency of two methods for conducting conditional analysis, the network algorithm and Markov chain Monte Carlo. Our findings indicate that conditional estimates do indeed outperform their unconditional maximum likelihood counterparts. The network algorithm remains the fastest tool for generating the required conditional distribution. However, for large samples, the Markov chain Monte Carlo approach accurately estimates the conditional distribution and is more efficient than the network algorithm.

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A probability programming language is developed and presented; applications illustrate its use. Algorithms and generalized theorems used in probability are encapsulated into a programming environment with the computer algebra system Maple to provide the applied community with automated probability capabilities. Algorithms of procedures are presented and explained, including detailed presentations on three of the most significant procedures. Applications that encompass a wide range of applied topics including goodness-of-fit testing, probabilistic modeling, central limit theorem augmentation, generation of mathematical resources, and estimation are presented.

Carbonate strata preserve indicators of local marine environments through time. Such indicators often include microfossils that have relatively unique conditions under which they can survive, including light, nutrients, salinity, and especially water temperature. As such, microfossils are environmental proxies. When these microfossils are preserved in the rock record, they constitute key components of depositional facies. Spence et al. (2004, 2007) has proposed several approaches for determining the facies of a given stratigraphic succession based upon these proxies. Cluster analysis can be used to determine microfossil groups that represent specific environmental conditions. Identifying which microfossil groups exist through time can indicate local environmental change. When new observations (microfossils) are found, classification analysis can be used to predict group membership. Kristen Briggs (2005) identified the microfossils present in sedimentary strata within a specific time interval (Morrowan) of Pennsylvanian-age rocks. In this study we expand analysis to overlying Atokan and Desmoinesian strata. The Bird Spring Formation in Arrow Canyon, Nevada records cycles of environmental change as evidenced by changes in microfossils. Our research investigates cluster and classification analyses as tools for determining the marine facies succession. Light, nutrients, salinity, and water temperature are very dependent on water depth; therefore, our analyses essentially indicate the relative rise and fall of sea-level during Early to Middle Pennsylvanian time.

In [JM02, section 14], Ji and MacPherson give new constructions of the Borel--Serre and reductive Borel--Serre compactifications [BS73, Zuc82] of a locally symmetric space. They use equivalence classes of eventually distance minimizing (EDM) rays to describe the boundaries of these compactications. The primary goal of this thesis is to construct the Satake compactifications of a locally symmetric space [Sat60a] using finer equivalence relations on EDM rays. To do this, we first construct the Satake compactifications of the global symmetric space [Sat60b] with equivalence classes of geodesics in the symmetric space. We then define equivalence relations on EDM rays using geometric properties of their lifts in the symmetric space. We show these equivalence classes are in one-to-one correspondence with the points of the Satake boundary. As a secondary goal, we outline the construction of the toroidal compactifications of Hilbert modular varieties [Hir71, Ehl75] using a larger class of "toric curves" and equivalence relations that depend on the compactications' defining combinatorial data.

In this thesis, we give a topological interpretation of knot contact homology, by considering intersections of a particular class of chains of open strings with the knot itself. In doing so, we provide evidence toward a differential graded algebra structure on the algebra generated by chains of open strings.

Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A picks up a nontrivial p-torsion point over K for only finitely many p. The proof of our main theorem primarily rests on three lemmas. The first lemma uses the reduction-exact sequence of an abelian survace defined over an unramified extension K of Qp to give a mod p2 condition for detecting when A has a nontrival p-torsion point defined over K. The second lemma employs crystalline Dieudonne theory to count the number of isomorphism classes of lifts of abelian surfaces over Fp to Z/pp that satisfy the conditions from our first lemma. Finally, the third lemma addresses the issue of the assumption in the first lemma that K is an unramified extension of Qp. Specifically, it shows that if A has a nontrival p-torsion point over a ramified extension K of Qp and p - 1 > d then this p-torsion point is actually defined over the maximal unramified subextension of K. We then combine these algebraic results to reduce the main analytic calculation toa series of straightforward estimates.

<p>p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} span.s1 {font: 11.5px Helvetica}</p> <p>This paper consists of mainly two parts. First it is a survey of some results on automorphisms of Riemann surfaces and Fuchsian groups. A theorem of Hurwitz states that the maximal automorphism group of a compact Riemann surface of genus g has order at most 84(g-1). It is well-known that the Klein quartic is the unique genus 3 curve that attains the Hurwitz bound. We will show in the second part of the paper that, in fact, the Klein curve is the unique non-singular curve in ℂP² that attains the Hurwitz bound. The last section concerns automorphisms of surfaces with cusps or punctured surfaces.</p> / Master of Science (MS)

<p>Students entering university for the first time face many new challenges and obstacles, which often include first year calculus. Many students come to university liking mathematics and hoping to study in a math intensive field, but encounter a roadblock when they stalt taking university-level calculus. Why do these first year mathematics courses cause problems? What challenges do the students face, and what can be done to help them overcome these obstacles and achieve their goals? In this study we set out to try to answer these questions by interviewing 16 students about their experiences taking first year calculus at McMaster University. Here we discuss our findings regarding the students' study habits, problem solving techniques and views of mathematics, as well as a number of other factors which could have caused them problems. We will also discuss how the views of the students are not always in alignment with those of the faculty and staff, as well as possible ways in which the teaching of calculus could be improved at McMaster University.</p> / Master of Science (MS)