Mathematical Sciences 2006 Completed MQPs
Mathematics of Sudoku
Student:
Thompson, Ethan Douglas
Advisor:
SERVATIUS, B. (MA)
A 16?16 Magic X Sudoku is a Sudoku with the additional constrains that each block is a Magic Square and each number appears once on the two long diagonals. Nine binary orthogonal symmetries were discovered, for a reduction of the solution space by a factor of 512, and 1 non-orthogonal binary symmetry, which further reduces the problem by a factor between 1 and 2. Enumerating the 16?16 Magic X Sudoku requires significantly more computational resources than available even after optimization.
Robustifying Logistic Regression for Nonresponse
Student:
Marjerison, William M.
Advisor:
NANDRAM, B. (MA)
We predict finite population mean BMI nationally for children and adolescents using NHANES III survey data. There are many nonrespondents and no distributional assumption is made on BMI. As link functions for response indicators, we compare the logistic distribution assumption is made on BMI. As link functions for response indicators, we compare the logistic distribution and student's mixtures. Nonrespondents are assigned cells based on propensity scores to impute BMI, and uncertainty about this process is included. Predictive inference is done using least-squares, and we compare results with a recent method.
Impact of DG on the Local Electric Grid
Students:
Gallerani, Andrew
Liu, David I-Teh
Advisor:
SAEED, K. (SS)
In this project we constructed a System Dynamics model which simulates the interactions in the electrical distribution grid. We analyzed this model to understand if installing distributed generation units would be a feasible plan for extending the useful lifespan of the substation transformers. We concluded that the installation of the generators is an effective policy for extending the lifespan; however, the additional costs incurred through the generator installation transform the policy in most cases into purely poor economic planning.
Star Coloring of Graphs
Student:
Climis, Timothy M.
Advisor:
CHRISTOPHER, P. R. (MA)
The project explores graph theory's star coloring parameter, chi_s. This is a proper coloring where all paths of four vertices use at least three colors. We find a planar graph with chi_s=10 on the smallest known number of vertices. We also find bounds an the sum of chi_s of a graph and its complement. Additionally, we explore the parameter on permutation graphs, Mycielski graphs, and maximal planar graphs and their duals.
Long Term Care Underwriting
Students:
Arsenault, Elizabeth A.
Rackliff, Nicholas E.
Advisor:
ABRAHAM, J. P. (MA)The project presents a mathematical model created to determine a risk score for applicants for Long Term Care insurance. We developed software to assist in the imple- mentation and testing of the model. We analyze the suitabil- ity of our model, including the sensitivity of scores to the model's parameters. We formulate methods which could help train the model, including numerical regression to solve for model parameters and pair-wise comparisons between appli- cants to verify consistency of parameters and risk factors.
Mathematical Analysis of a System Dynamics Model
Student:
Papia, Vincent J.
Advisor:
PAVLOV, O. V. (SS)
This project provides a mathematical analysis of a seven-component ODE model of a peer-to-peer file sharing network. A steady state analysis was performed on the system. Under certain conditions, the steady state was shown to be unique; in addition, numerical simulations were performed using Simulink, a MATLAB package. Steady solutions and periodic solutions were found.
Modeling of Torque for Screw Insertion Process
Students:
Leo, Angela A.
Manivannan, Sanjayan
Potter, John R.
Advisor:
WEEKES, S. L. (MA)Sponsor:
BOSE CORPORATIONA self-tapping screw is a high-strength one-piece fastner that is driven into preformed holes. We analyze and improve a mathematical model of the self-tapping screw insertion process so that it can be used in manufacturing processes at the BOSE Corporation. We build a Graphical User Interface in MATHLAB which allows users to enter fundamental data and produces the corresponding torque curve. The accuracy and robustness of the model is tested by comparing predictions to empirical data collected at BOSE.
Analyzing Interest Allocation Methods
Students:
Beaudoin, Aaron Michael
Desrosiers, Mary E.
Quinn, Daniel F.
Advisor:
ABRAHAM, J. P. (MA)
The objective of this project was to analyze current retire- ment benefit trends and construct mathematical models for interest allocation. We demonstrated the equivalence of the Fixed-Index and Declining Investment Year Methods.
Second Electrolyte Wedge Problem
Student:
Ware, Kimberly M.
Advisor:
FEHRIBACH, J. D. (MA)
The Second Electrolyte Wedge problem studies diffusion-reaction-conduction processes associated with current production in a porous electrode. Two rate-determining reaction steps occur in this formulation - one in the electrolyte-solid interface. Existence and uniqueness of solutions to this problem are proven, and thus current density is proven to be finite. Numerical and asymptotic analysis are completed and expressions for the current density and total current produced by the electrolyte are given.
Statistical Analysis:MLB Defensive Production
Students:
Haskins, Allison M.
Lopes, Alyssa M.
Teixeira, Christopher M.
Advisor:
WILBUR, J. D. (MA)
While many statistical measures have been devised to measure team and player performance in professional baseball, relatively little work has been done to study and improve measures of defensive performance. This project's goals were to model defensive contribution to team performance and develop related measures of individual player defensive production. Factor analysis was employed to extract positional factors and combine them with pitching and offensive measures into a final logistic regression model to determine effects of defense on team performance.
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