Consulting Projects in Past Semesters - Detailed
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Descriptions of the Consulting Projects
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 the 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, e.g., 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 provided follow 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 the facilitator
Dr. Nagaraj K. Neerchal
Additional outcomes: Karen Osborne continues to work with 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 are 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 the 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 is to
evaluate the effectiveness of the RFD. In the project, a cutoff point is
chosen for the predicted lameness index which minimizes
misclassifications, and the various associations among the lameness and
ralted variables are demonstrated by 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 the 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
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 will see that this Fourier
method works well for certain problems, whose frequency is in the range of
the Fourier expansion. The results of experiments show that the method is
effective.
This project was conducted as part of the consulting class Math/Stat 750
in Fall 2003 under the supervision of the 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 is 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 is used. Results both
for the steady-state problem and for the transient problem will be shown.
This project was conducted as part of the consulting class Math/Stat 750
in Fall 2003 under the supervision of the facilitator
Dr. Matthias K. Gobbert.
Additional outcomes: This project led to two publications:
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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.
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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.
The Standard Genetic Code Enhances Adaptive Evolution
of Proteins
March 11-21, 2004
Clients: Wen Zhu and Dr. Stephen Freeland,
Department of Biological Sciences,
UMBC
Consultant: Matthias K. Gobbert, Mathematics
Description:
The standard genetic code, by which most organisms translate genetic
material into protein metabolism, is non-randomly organized. The Error
Minimization hypothesis posits that natural selection produced a code
that buffers genomes against the impact of mutations. However, previous
studies supporting this hypothesis treat the code as an isolated trait,
ignoring its influence on the evolution of the protein coding genome
that it serves. A population genetic model of molecular evolution was
developed to test the rate of adaptive gene evolution under different
genetic codes. It is shown that the pattern of codon assignments has a
profound effect on the speed of adaptive evolution, and a
fundamental re-interpretation of the adaptive genetic code is offered,
from one that minimizes errors to one that enhances the efficacy of natural
selection. CIRC helped this work by performing the extensive numerical
simulations required.
Publications:
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Wen Zhu and Stephen Freeland.
The Standard Genetic Code Enhances Adaptive Evolution of Proteins.
Submitted.
Numerical Simulations of a
Current Neural Network Model
March 18, 2004 to May 10, 2004
Client: Dr. Jonathan Bell,
Department of Mathematics and Statistics,
UMBC
Consultant: Zorayr Manukyan, Mathematics
Description:
A certain integro-differential equation provides a model
describing electrical activity of neural net. A numerical
method for solving it was developed. The relationship between
parameters in the model results in different type of wave phenomena.
This project was conducted as part of the consulting class Math/Stat 750
in Spring 2004 under the supervision of the facilitator
Dr. Matthias K. Gobbert.
Cluster Analysis for Compositional Data
March 18, 2004 to May 10, 2004
Client: Dr. Erle Ellis,
Department of Geography and Environmental Systems,
UMBC
Consultant: Ronny O. Vallejos, Statistics
Description:
Cluster analysis is a statistical technique of interest
in many different fields for grouping data. This work presents a clustering
technique to deal with compositional data. That is, data
consisting of vectors in which the components are proportions
adding up to one. Various strategies for replacing zeros in the
data are discussed. To illustrate the method we present the
analysis of a data set from the Yangtze Plain region in China.
This project was conducted as part of the consulting class Math/Stat 750
in Spring 2004 under the supervision of the facilitator
Dr. Nagaraj K. Neerchal
Data Analysis for Concentration of Atrazine in
Ground Water and Area of Influence
March 18, 2004 to May 10, 2004
Client: Mr. Earl Greene,
U.S. Geological Survey,
Baltimore, MD
Consultant: Justin Newcomer and Rupa Bhensdadia, Statistics
Description:
Atrazine (a pesticide) is used to control broadleaf and grassy weeds.
The U.S. Environmental Protection Agency has set some standards for
maximum contaminant level of Atrazine in drinking water.
It is assumed that the Response variable, concentration of Atrazine can
be predicted with logistic regression. The model was fit using various
explanatory variables, collected for sample units. Also, an analysis
was done to find the area of influence for the above stated study.
This project was conducted as part of the consulting class Math/Stat 750
in Spring 2004 under the supervision of the facilitator
Dr. Nagaraj K. Neerchal
Sensitivity Analysis for a Plague Model
March 18, 2004 to May 10, 2004
Client: Dr. Holly Gaff,
Dynamics Technology, Inc.,
Arlington, VA
Consultant: Stephen Clark and Jonathan Desi, Mathematics
Description:
Plague is considered a prominent disease threat. In the past,
outbreaks have affec ted large amounts of the population. Today,
the threat of plague being used as a biological warfare and
terrorism agent is a realistic possibility. Researchers have
studied this topic and developed a mathematical model of
differential equations to understand how plague behaves.
Sensitivity analysis on certain parameters in the model was performed
to see how the behavior is affected.
This analysis will hopefully help researchers in this area better
understand the behavior of plague.
This project was conducted as part of the consulting class Math/Stat 750
in Spring 2004 under the supervision of the facilitator
Dr. Matthias K. Gobbert.
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