Mathematical Sciences 2007 Completed MQPs
Failure, Clamp Load, and Heat in Screw Insertion
Student:
Adler, Jonathan D
Advisor:
WEEKES, S. L. (MA)
Sponsor:
Bose, Inc.
A self-tapping screw is a high-strength one-piece fastener that is driven into preformed holes. The goal of the MQP completed by Leo et al. and the 2006 Research Experience for Undergraduates in Industrial Mathematics and Statistics completed by Miller et al. was to create a mathematical model that allows users to input data about their self-tapping screw and the material it is entering and would output a torque curve which models the fastening process. We improve the algorithm to include the modeling of the failure of the joint as well as a model for the clamp load of the joint. We also investigate a model of heat generation in the screw that includes the speed of screw insertion.
Modeling Collaboration in Civil Engineering
Student:
Meko, Mark Joseph
Advisor:
HEINRICHER, A. C. (MA)
Collaboration in a complex civil engineering project is modeled by two linear programs using leaks and node collapse. These linear programs are based on an event-oriented network and a task-oriented network. The critical path method is used to identify possible areas for collaboration. Node collapse is used to model collaboration in the task-oriented network. Leaks between nodes are used in the event-oriented network to model collaboration and assign a value to the collaboration.
Functional Identities
Student:
Patkowski, Alexander Eric
Advisor:
SERVATIUS, B. (MA)
In this paper we establish some analysis of generating functions for values of summartory arithmetic functions. Our goal is to obtain some new summation formulae that arise in consideration of known results concerning integral representations of the summatory arithmetic functions. The formulas we use are the Poisson summation formula, Mellin inversion formula and standard properties of the Gamma function.
Analysis of Methods for Loss Reserving
Students:
Connor, Timothy P.
Liu, Xinjia
Lynskey, Gregory E
Rapaj, Ida
Advisor:
ABRAHAM, J. P. (MA)
Sponsor:
Hanover Insurance Co.
Hanover Insurance uses numerous methods to project total paid claims for all its lines of business. A system was developed to assess the accuracy of the projections, based on data for six accident years and four lines of business. A strictly mathematical forecasting method was sought; however, no model was found to replace the years of experience and knowledge of Hanover's actuaries.
Long Term Care Underwriting Risk Scoring Model
Students:
Kluza, Joanna B.
Kraynak, Joseph F.
Treese, William J.
Wicklund, Jaris B.
Advisor:
HEINRICHER, A. C. (MA)
Sponsor:
John Hancock Life Insurance Company
The project goal was to test a previously designed adaptive risk scoring model for long term care insurance underwriting using actual applicant data from John Hancock. A data filtering method for removing applicants who should not be used to train the model was developed. The model provides accurate risk class assignment, based solely on the medical conditions, when trained on the filtered data. In addition, the model identifies errors in the risk points assigned to individual medical conditions.
Alumni Scoring System
Students:
Murphy, Kirsten B.
Sotak, Onalie Louise
Advisor:
HEINRICHER, A. C. (MA)
Sponsor:
WPI Alumni Association
The primary goal of this project was to construct and evaluate a scoring method for ranking individuals in a database where those more likely to donate receive higher scores. The created spreadsheet takes donor information and generates an assigned score from 1-20. A manual for the spreadsheet was also created, enabling the WPI Office of Development and Alumni Relations to rank selected alumni in order of their likelihood to donate in the future.
Portfolio Optimization With Transaction Costs
Student:
Clark, Jessica M.
Mulready, Sean E.
Advisor:
HEINRICHER, A. C. (MA)
Investors often update their portfolios at regular time intervals by trading stocks, but there are costs associated with these trades. This project seeks to limit these transaction costs by controlling the portfolio turnover (absolute change as a fraction of book size) between time periods. The result is a multiperiod optimization problem with quadratic objective function and non-smooth constraints. The resulting portfolios outperformed benchmark portfolios in both expected utility and actual portfolio value.
Viscoelastic Cell Motility MOD
Student:
Port, Andrew A.
Ristau, Jeremy.
Advisor:
LUI, R. Y. (MA)
This project attempts to model the length, velocity, and internal stress experienced by a crawling cell as it moves on a substrate. We assume the cell's viscoelastic properties can be described by a Maxwell element. Through balance equations, we develop a Moving Boundary Problem. We solve this MBP numerically, as well as analyze its traveling wave solution. We then change our model to assume that the cell's actin concentration satisfies a second MBP and discuss our future plans for solving this new, more complicated model.
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Last modified: October 25, 2007 13:56:01