Mathematics Awareness Month, April 2002

Abstracts

April 12, 2002

Mathematics Symposium: "Mathematics Awareness Month at UNO"

Shelly Sutherland,
"Actuarial Modeling of the Cost Implications of Genome Research"
With the mapping of the human genome, individuals may soon have access to specific information regarding their susceptibility to genetically influenced disorders. Insurance companies without access to this information risk insuring a disproportionate number of affected policyholders, leading to significant financial losses and a possible destabilization of the insurance industry. In cases where a single gene promotes susceptibility to a disorder, actuarial modeling can estimate these losses using Markovian modeling techniques.

Richard Schultz,
"The Most Conservative Art in Modern America: Political Campaign Logos. A Statistical Analysis."
In this talk we will explore trends and characteristics of advertising logos for political campaigns current in April, 2002. Examples were randomly found on the Internet using common search engines. A sample of 100+ political graphics was selected and analyzed for various graphic and design elements, as well as content and color selection. A statistical analysis of this sample was performed. We will present the results and conclusions of this analysis.

R. Bennett, A.S. Buchan, M. Church, C. Haugen, C. Scheuermann,
"Fractals and the Cantor Set"
Everyone has seen a fractal. Many people have heard the term, but few know what a fractal is. Although a strict definition is hard to come by, fractals are not hard to describe. Anything that contains "self-similar" images is a fractal. For example, the human circulatory system is a fractal. If you look at the blood vessels in your hand, they resemble the overall shape that the complete system takes on. And since most occur naturally, we find we are surrounded by fractals. This talk will give a brief description of fractals, define the Cantor Set, prove that it is a fractal with zero length, and that it is closed, bounded, totally disconnected, and perfect. We will also discuss its fractal dimension.

Dr. Qiuming Zhu,
"Biomedical Data Processing: Gene Expression Profile Clustering"
A study of mathematical approaches for biomedical data processing is presented. The presentation is focused on the clustering methods for the analysis of gene expression profiling data obtained from the micro-array technology, and on showing the importance of mathematical foundations in the clustering techniques.

Gary Beck, F. McCurdy,
"Results of Intern/Program Director Survey on Clerkship Preparation for Residency"
Objective: Third year medical students are required to complete an 8-week course in Pediatrics (clerkship). Measured outcomes are used to assign grades and have been the subject of much research. Few studies have, however, been done to determine the impact of third-year clerkships on postgraduate preparedness. Therefore, we designed a survey that was to be completed by interns and their respective program directors (PD). The survey was intended to assess the degree to which interns felt they were prepared to take on the tasks of being an intern as well as the perceptions of the PD about the preparedness of the same interns for either Pediatrics or Medicine/Pediatrics training. Our hypothesis was interns would evaluate themselves more stringently than the program directors. Main Outcome Measures: A 32-question survey was developed and sent to graduates who selected training in either Pediatrics or Medicine/Pediatrics. The same survey was sent to their program directors. The questions pertain to clinical skills assessment as well as professional/ethical assessments. Participants were asked to rate each using a scale of 1=Not Satisfactory to 5=Outstanding. Participants: Interns who had selected postgraduate training in either Pediatrics or Medicine/Pediatrics and their respective program directors were sent a survey approximately 6-months into their first postgraduate year of training. Methods: Over the course of three years from 1999 to 2001, interns returned respectively 10 of 13, 12 of 15 and 8 of 12 for a total of 30 and program directors returned 13 of 13, 14 of 15, and 12 of 12 for a total of 39. Results of the surveys were entered into SPSS and basic descriptive statistics were used to make quick comparisons of the differences between PD and student responses. A statistical analysis of the data has been performed. Results: Students rated themselves as average to slightly above average in most categories over all the year groups. For 2 of 19 of the procedural skills questions, interns rated themselves average to slightly below average (average range 2.03 to 3.10). PD rated the interns slightly higher than the interns in most areas, with the exception of the procedural skills questions where their ratings correlated with the interns' ratings. The greatest differences in sample means were noted for six questions. All of these questions pertained to issues of professional conduct (i.e. ethical behavior, accountability, etc). PD rated the interns higher than the interns for all of these questions except for "Reports all errors of judgment immediately." On this question, the PD mean was 2.92 while the intern mean 3.33. Conclusions: Our results are suggestive that interns are better prepared to assume the professional roles needed by physicians, but they may not be as self-aware of those behaviors. Conversely, PD may not be as knowledgeable as they should be about intern's technical skills. Further study is needed to ascertain the details of our initial observations.

Dr. Zhenyuan Wang,
"Classification by Nonlinear Integral Projection Pursuit"
A new method based on nonlinear integral projections for classification is presented. The contribution rate of each combination of the feature attributes, including each singleton, toward the classification is represented by a fuzzy measure. The nonadditivity of the fuzzy measure reflects the interactions among the feature attributes. The weighted Choquet integral with respect to the fuzzy measure serves as an aggregation tool to project the feature space onto a real axis optimally according to some error criterion, and the classifying attribute is properly numericalized on the axis simultaneously that makes the classification simple. To implement the classification, we need to determine the unknown parameters, that is, the values of fuzzy measure and the weight function. This can be done by running a special adaptive genetic algorithm on the given training data. The new classifier is tested by an artificial training data set as well as several biological and medical data sets. It compares favorably with other existing classifiers on some well-known real-world benchmarks.

M. Culek, J. Davis, D. Deden, C. Farrow,
"Fourier Decomposition in Hilbert Spaces and Wavelet Sets"
This talk will report briefly on the classical Fourier Theory in arbitrary Hilbert spaces, introduce the notion of (orthogonal dyadic) wavelet, then discuss and illustrate the so-called Wavelet Sets i.e. subsets of the real line whose normalized characteristic functions are Fourier Transforms of wavelets.

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