# Recent Major Qualifying Projects

## Algebraic and Discrete Mathematics

### Combinatorial Structures in Cryptography

**Student:** Hardy, Seth Michael

**Advisor: **MARTIN, W. J. (MA)

Error correcting codes, such as Reed-Solomon codes, can be used to create authentication codes based on orthogonal arrays. These codes are provably secure up to a certain number of uses; however, as the number of desired uses goes up, so does the keylength. This project researches the security of a code whose messages (which function as private keys) have specific form that allows them to be represented in a more compact fashion. Specifically, messages with low Hamming weight are considered.

### Distance Sequences in Graph Theory

**Student: **Donovan, Elizabeth Ann

**Advisor: **CHRISTOPHER, P. R. (MA)

This project investigates problems involving the concept of distance in graph theory. Applications of these problems exist in such areas as optimizing facility locations. Defining the status of a vertex as the sum of the distances to all other vertices in a graph, we explore certain variations of this parameter, such as total status, minimum average distance and minimum and maximum chromatic status. We compute these parameters for various families of graphs, and obtain bounds for more general results.

## Computational and Applied Analysis

### Numerical Methods for Neutral Coated Inclusions Conductivity

**Student: **Murphy, Ethan K.

**Advisor: **SARKIS-MARTINS, M. (MA)

This project used finite element method to obtain neutral coated inclusions shapes for a thermal conductivity problem. Such an inclusion when inserted in a homogeneous matrix has the property that it does not disturb the uniform heat flow outside the inclusion. A free-boundary problem was formed and Newton's Method was used to handle the nonlinearity of the system. Dynamic mesh refinements were implemented to increase accuracy in certain areas. Iterations of the method yielded the desired neutrally coated shapes.

### Mathematical Modeling of Metal Bioremediation

**Student: **Vega, Nicole Marie

**Advisor: **WEEKES, S. L. (MA)

A model for metal bioremediation in groundwater is constructed. The mathematical model accounts for (i) the chemical processes that eventually render biomass inactive (ii) the toxicity of metal to biomass, and (iii) transport by groundwater. Numerical simulations of the reaction-convection-diffusion equations are carried out via an operator splitting method. The results of the model are compared to a structurally similar model for organic bioremediation. We find that metal cleanup differs significantly from organic cleanup due to the unique mechanisms involved.

## Operations Research and Control

### Stochastic Modeling of Real Time Queues

**Student: **Morgan, Brittany Rose

**Advisor: **DOYTCHINOV, B. (MA)

This project looked at a simple queuing system with three different due date distributions. For each task generated, a deadline was assigned. The server then served the most urgent task first, for a time-step, then reassessed the most urgent, and continued until all tasks were served. We have numerically simulated the due dates with the exponential, random, and triangular distributions, generated lead time profiles, and have compared the data with theoretical predictions to determine the accuracy of our method.

### Mathematical Models of Damage Spread in Networks

**Student: **St. Hilaire, Melissa April

**Advisor: **HEINRICHER, A. C. (MA)

This project describes mathematical models for how damage, measured in lost capacity, can spread through an organization. The model allows a company to simulate damage spread and compare different strategies for allocating repair resources after the initial damage has occurred. This project was completed in collaboration with Lehman Brothers investment firm in the aftermath of the terrorist attacks on September 11, 2001.

## Applied Statistics

### Hearing Data

**Students: **Barber, Gary Paul Kulasekaran, Nedunceliyan

**Advisor: **PETRUCCELLI, J. D. (MA)

Sonification, the representation of data in an auditory format, has already found use in Electrocardiograms and Geiger Counters, which suggests potential applications in realms dominated by visually-based analysis methods. This project developed and studied three approaches to the sonification of time series data, using the Additive Classical Decomposition of time series as the starting point, with its own statistical analysis-and- mapping and sonification programs. Results of investigations by controlled experiment using human subjects suggest the sonification methods are effective.

### Statistical Analysis of the MCAS

**Students: **Darling, Gwenevere Lorraine Mwaura, Frida Wambui

**Advisor: **PETRUCCELLI, J. D. (MA)

This MQP modeled the MCAS (Massachusetts Comprehensive Assessment System scores in relation to certain socio- economic and demographic variables (our predictors) identified through our research. We employed multivariate statistical methods to build a multivariate regression model to identify the form of the association between scores and predictors. We specified a set of regressors that are functions of the predictors. Our analysis identified the statistically significant variables as well as investigated the evolution of MCAS scores over time.

## Actuarial Mathematics

### Estimating Disability Incidence Rates for Long Term Care Insurance

**Students: **D'Onofrio, Michael; Lesco, James; Simone, Jeffrey and Twarog, Marek

**Advisors: **ABRAHAM, J. (MA) and HEINRICHER, A. C. (MA)

**Sponsor: **John Hancock

This paper uses data from the 1999 NLTCS and NHIS surveys to compute Long Term Care (LTC) prevalence rates. We develop several triggers, evaluate a test of cognitive ability, and compute prevalence rates for each trigger. We develop a model to compute LTC incidence rates based on the prevalence data. We find that incidence is a strictly increasing function of age and that there is a sharp increase in incidence rates starting at age ninety.

### Stochastic Modeling for Waiver of Premium

**Student: **Cistecky, Ondrej

**Advisor: **HEINRICHER, A. C. (MA)

A stochastic model is developed in APL and used to simulate the full distribution of present value of future costs of Sun Life Financial's extended death benefit claims. The program is proposed as a valuation tool which enables the development of realistic reserve levels. Using actual claim data and Sun Life assumptions simulation is used to verify that current reserve levels on extended death benefit claims are overly conservative.

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