# Consulting Projects and Activities – Fall 2003

#### An Algorithm for Locating Amino Acid Residues in Proteins

*October 16, 2003 to December 09, 2003*

*Client:* Dr. Mauricio M. Bustos, Department of Biological Sciences, UMBC

*Consultant:* Samuel G. Webster, Mathematics

*Description:* Proteins are molecules composed of linear sequences of amino acids. Each protein possesses its own unique, intricate, three-dimensional structure that determines its functionality. Very often, amino acids that are far apart in the linear sequence are found next to each other in the protein. The goal of molecular biologists is to correctly identify these amino acids and then alter the structure of the protein. I have designed an algorithm that extracts a 3-D volume element from a protein and returns all amino acids that lie within the element. Additionally, the linear sequence with the highlighted amino acids is returned.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Matthias K. Gobbert.*

#### Analysis of Nursing Behavior in Mother/Calf Dolphin Pairs

*October 16, 2003 to December 09, 2003*

*Client:* T. David Schofield, Manager, Ocean Health Programs/MARP, National Aquarium in Baltimore

*Consultant:* Karen L. Osborne, Statistics

*Description:* It is suspected that there is a difference in nursing and other care-giving behaviors between experienced dolphin mothers and inexperienced, i.e. first-time, dolphin mothers. Quantifiable differences in the occurrence of certain behaviors can be identified as playing an important role in the survivability of the calves. Behavioral data was provided on three dolphins and their calves for a 10-week time period. The assumption is that the frequency data follows a Poisson distribution and that these counts are potentially influenced by dolphin and time. A Poisson regression model was fit to the count data using these variables and appropriate tests were developed to determine if the differences were significant.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Nagaraj K. Neerchal.*

*Additional outcomes:* Karen L. Osborne continues to work with the client on additional data collection and analysis.

#### Statistical Analysis of Proteomics Data

*October 16, 2003 to December 09, 2003*

*Client:* Dr. Brian P. Bradley, Department of Biological Sciences, UMBC

*Consultants:* Ravi Siddani and Alex Sverdlov, Statistics

*Description:* An important application of proteomics is comparison of 2D gel images of protein mixtures taken from several treatment groups. These images can be coded as binary 30-by-30 matrices, with 1 indicating the presence, and 0 the absence, respectively, of a protein in a gel. Two statistical methods, a permutation test and a cluster analysis, have been implemented to see whether gels taken from 6 treatment groups have different structures. Distributions of permutation test statistics and the corresponding p-values were obtained for each pair of treatments under consideration. Clusters of gels showing the differences between treatment groups were obtained. The results were consistent for the two considered methods.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Nagaraj K. Neerchal.*

#### Lameness Index in Dairy Cattle

*October 16, 2003 to December 09, 2003*

*Client:* Dr. Uri Tasch, Department of Mechanical Engineering, UMBC

*Consultants:* Minglei Liu and Yanping Wu, Statistics

*Description:* A team led by Dr. Tasch developed a Reaction Force Detection (RFD) system to predict the lameness of cows, which is a very important issue for the dairy industry. The objective of this project was to evaluate the effectiveness of the RFD. In the project, a cutoff point was chosen for the predicted lameness index which minimizes misclassifications, and the various associations among the lameness and related variables were demonstrated by a variety of plots and tables.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Nagaraj K. Neerchal.*

#### Using a Fourier Method to Solve a Convection-Diffusion Equation

*October 16, 2003 to December 09, 2003*

*Client:* Dr. Andrew Tangborn, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, MD

*Consultant:* Zhibin Sun, Mathematics

*Description:* For a particular kind of partial differential equation, the convection-diffusion equation with periodic conditions, we can use a Fourier method, which is implemented by FFT, to transform it into a system of ordinary differential equations. These are solved using the Crank-Nicolson scheme for time-stepping. We saw that this Fourier method works well for certain problems whose frequency is in the range of the Fourier expansion. The results of experiments showed that the method was effective.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Matthias K. Gobbert.*

*Additional outcomes:* Following this project, Zhibin Sun was hired as Research Assistant by Dr. Tangborn.

#### A Finite Difference Solution of a One-Dimensional Non-Linear Reaction-Diffusion System with a Fast Reaction

*October 16, 2003 to December 09, 2003*

*Client:* Dr. Thomas I. Seidman, Department of Mathematics and Statistics, UMBC

*Consultant:* Ana Maria Soane, Mathematics

*Description:* A chemical process involving three reactive species is modeled by a non-linear system of three reaction-diffusion equations in one spatial dimension. The problem is challenging numerically, because one reaction is much faster than the other one. Mathematical analysis and numerical results exist for the steady-state system. The goal of this project was to solve the time-dependent system numerically to confirm the intuition on the system’s behavior. After discretizing in space using finite differences, implicit time stepping was used. Results for both the steady-state problem and for the transient problem were shown.

*This project was conducted as part of the consulting class Math/Stat 750 in Fall 2003 under the supervision of facilitator Dr. Matthias K. Gobbert.*

*Additional outcomes:* This project led to two publications:

- Ana Maria Soane, Matthias K. Gobbert, and Thomas I. Seidman. Numerical Exploration of a System of Reaction-Diffusion Equations with Internal and Transient Layers. Nonlinear Analysis: Real World Applications, in press.
- Ana Maria Soane, Matthias K. Gobbert, and Thomas I. Seidman. Design of an effective numerical method for a reaction-diffusion system with internal and transient layers. Technical Report number 2006, Institute for Mathematics and its Applications, University of Minnesota, 2004.