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Written by: cburk
6/2/2009 2:18 PM

I am Dr. John Mordeson, Director of the Center for Mathematics of Uncertainty.

In order to support Creighton’s goal to provide research opportunities for undergraduate students, I offer a wide variety of research projects. The research projects are designed to provide students the opportunity to model problems of current and global interest. No prerequisite is needed to begin a research project The mathematics involved in the modeling process is very accessible to the student. Although the problems we will tackle can be quite complicated, the mathematics involved in the initial modeling process is fairly simple.

Although the topics available are diverse, many share a common theme. There is an overarching goal. Each such goal is made up of factors (or other goals). These factors are easily determined. Each factor is made up of sub-factors. The subfactors are based on expert opinion and data. This is where the student will spend much of his/her time, determining the subfactors and then weighting them as to their importance. The weighting of the importance of the factors will be done by experts and by various mathematical techniques. The weights will be used to determine linear equations, where the overarching goal is the dependent variable and the factors and/or subfactors are treated as independent variables. These linear equations will then give a measure of the degree of success of attaining the overarching goal.

Directed arrows from the factors to the overarching goal can be drawn to obtain what is called a directed graph. This can then be followed by drawing directed arrows from the subfactors to the factors resulting in a much larger directed graph. If one considers relationships between the subfactors and factors with directed arrows drawn accordingly, a mathematical structure is thus constructed. This structure is known as a network or a social network or a directed graph. It can be studied in its own right. Listed below are research projects from which the student may select. However, the student is not limited to these projects.

Research Projects

I. Nuclear Stability

Reducing Nuclear Threats and Preventing Nuclear Terrorism:
The overarching goal here is the development of a new strategy to protect the United States, its allies, and its friends from nuclear attack and from coercive pressures by states possessing nuclear weapons. The goals of the strategy include the following goals.

1. Prevent terrorists from acquiring and using nuclear weapons against the U.S. homeland or against U.S. friends or forces abroad.
2. Roll back North Korea’s nuclear weapons capability and head off Iranian edfforts to acquire nuclear weapons.
3. Discourage and prevent additional countries from acquiring nuclear weapons.
4. Maintain effective military forces, both nuclear and conventional, capable of deterring countries that already possess nuclear (or biological/chemical) weapons from using such weapons against the U.S., its allies, and friends or from using those capabilities to pressure or undermine U.S. friends and interests around the world.
5. Reduce the likelihood that nuclear weapons will be used whether by Russia, the U.S., or any other nuclear power as a result of accident or misrepresentation.
6. Ensure that any larger-scale expansion of civil nuclear power programs worldwide will proceed within the framework of new rules and procedures that can minimize the risks of proliferation to additional states and terrorists.

Each of the six above goals is supported by numerous U.S. Policies.

II. Economic Stability

The goal of economic stability is made up of five goals. The goal we will consider is
1. Economic Freedom
The goal of economic freedom is made up of the following ten goals

1. Business Freedom
2. Trade Freedom
3. Fiscal Freedom
4. Government Size
5. Monetary Freedom
6. Investment Freedom
7. Financial Freedom
8. Property Rights
9. Freedom from Corruption
10. Labor Freedom

III. Smart Power
The goal is to restore America’s inspirational leadership.
The goals making up this overarching goal are as follows:

1. Alliances, partnerships, and institutions: Rebuilding the foundation to deal with global challenges.
2. Global development: developing a united approach, starting with public health.
3. Public diplomacy: Improving access to international knowledge and learning.
4. Economic integration: Increasing the benefits of trade for all people.
5. Technology and innovation: Addressing climate change and energy insecurity.

IV. Hearing Impaired Children

1. Determine which tests of preschool, hard of hearing and deaf children are the best predictors of success when these students are mainstreamed in the public school system.
2. Determine which tests of preschool, hard of hearing and deaf students are the best indicators of the children in closing the language gap.
3. LENA Study (Language Environment Analysis). A recording device will be used in a parent-infant program to look for (1) children making more progress in both receptive and expressive language, (2) professionals having better information to use, and (3) to make parents more effective.

V. Applying Fuzzy Mathematics to Formal Modeling in Comparative Politics
Rational choice formal modelers have taken two approaches to address the gap between theory and empirical evidence. The first is to study the effect of different assumptions about the voting behavior of political actors. A second approach is to consider the effect of varying institutional designs. We will take a new approach. We will apply fuzzy set theory to formal models in comparative politics in order to incorporate vagueness and ambiguity about individual preferences. We have two goals: (1) to improve the capacity of formal models to generate a well-defined maximal set and (2) to improve the empirical validity of the predictions made by those models. The approach is similar to that of the uncovered set in that we deal with assumptions about individuals rather than institutions.

VI Creative Economy
The effect of the growing power of ideas and its impact on the economy will be modeled.

VII Health Sciences
Computer assisted medical diagnosis. The aspects, occurrence and confirmability of symptom-disease relationships are documented linguistically by medical experts or on the basis of medical database evaluations.

Diagnostic problem-solving using fuzzy abductive inference with degrees of manifestations.

Students involved in research projects with Dr. Clark and myself have gone on to continue their studies at prestigious schools. For example, two double majors in mathematics and political science have gone to Harvard University, one in graduate school in government and the other to Law School.

Industry is interested in students who have demonstrated the ability to successfully complete research projects of substantial length and to work well with others.

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