Projects For Undergraduate, Honors and Graduate Students

Introduction

My fundamental interests are in two areas: (1) modeling and simulation and (2) education. I consider them to be linked by problem solving issues; for example, problem-solving techniques are used to develop statements of models. I believe that research into such approaches as general systems theory will lead to better understanding of how to model.

The purpose of this page is to outline current areas of interests and current projects. Squirrel Works has its own page.

If you interested in these opportunities, then please read my page on conducting research. It contains helpful hints as well as a mirror into my personality.

I have compiled a set of topics that are useful in conducting my research.

General Systems and Systems Biology

Systems thinking started in ancient Chinese medicine. The history of systems thinking covers dynamical systems (Newton and Liebniz), statistical systems (statistical mechanics and thermodynamics), general systems (von Bertallanfy), and uncertain systems (Schweppe and Ferson). PhD projects abound in the mathematical foundations of general systems, bioinformatics, and systems biology. All such projects are interdisciplinary. The central question is one of modeling and simulation.

There are many different projects in this area. One is numerical experiment control, being explored by Carl Martin; Carl's project attempts to use artificial intelligence tchniques to control molecular dynamics codes. The remaining issues on this page are based on this viewpoint.

Visual Hybrid Modeling Systems: Problem Solving Environments

Problem-solving environments by that name have been around for a decade or more, but the idea is as old as computing. Visual problem-solving environments, like Modanna or Stella are examples of visual problem solving systems. In principle, every problem class can have specialized systems that "know" all there is to know about the class. The modeling system would have reasoning and VV&A capabilities.

This project is now joint undergraduate and graduate creative inquiry.

Undergraduate

Clemson University has decided that each undergraduate student should have at least two semesters of creative inquiry participation. I have a creative inquiry class that operates as a free, open source software development project called Skunk Works Software that starts with the Spring 2007 semester. Details are on the web site. The purpose of the project is to give students an opportunity to develop project and time management skills outside the technical curriculum.

Honors

Honors students may participate in Skunk Works Software. To receive Honors credit, the Honors student must assume a leadership role.

Graduate Students

Graduate students do not participate in the creative inquiry portion of the Skunk Works project. However, there are many issues of OSS development open to graduate students.

Computing in Uncertain Systems

This is related to the VV&A section. Models and simulations are now so complex that issues of uncertainty come into play. This means that such issues as the uncertainty of the exact values in input parameters must be address. There have been many systems proposed but the exact status of the area is not clear. Here are just some of the processes.

1. We need a g95 Fortran compiler. g95toC would suffice initially; even more interesting would be a g95 to Java Virtual Macine. Great MS project — with a little bit of work, a PhD project.
2. There is a new language being developed to support grid computing. PhD projects abound.
3. Really need Fortran to have a really good type system, similar to OCaml's and ML's. Microsoft has actually ventured into this area: PhD project. Throw in intervals and alternative arithmetic systems, and there are several PhD projects. Some MS projects as well.
4. The new g95 compiler must have data types for uncertain computing. At a minimum, we need intervals (as the current Sun f90 has), and some probabilistic arithmetics. PhD project
5. We need algorithms fo alternative arithmetic numerical methods. It would help to start on the question, "Just exactly where are we?" PhD project.
6. We need a compiler that can understand and use unit expressions. At least an MS project.
7. We need to collect / generate a library to support all uncertain computing paradigms. Multiple MS projects.
8. Mathematica implementation of fuzzy arithmetic. I have a GCL version of Mathematica created by Dr. Richard Fateman of Berkeley that I have permission to work with.

Uncertain systems can also relate to genetic algorithms and neural nets. Rose Lowe is completing her dissertation using genetic algorithms to generate rules for analyzing epidemiology data.

Verification, Validation, and Accreditation

Verification, validation, and accreditation (VV&A) are processes used to insure the correctness of models and simulations. These processes are important to both the Department of Defense and the Department of Energy. Clemson through my Institute for Modeling and Simulation is a leader in VV&A research.

1. General projects
   
   • Validation and verification of large scale systems. This project takes a collection of information gleaned from the Net and organize it into standard categories. The output of the project is paper, which should lead to a publication.
   • Testing of programs with numerical computations.
   • Verification of Programs (Program proofs).
   • Model Checking.
   • Reasoning with Uncertainty.
   • Risk Assessment and Management.
   • Experiment with common basic numerical functions to explore and then define adequate testing to accredit such routines.
     
2. Formal methods. Formal methods are proposed that should lead to requirements documents that can be manipulated. The hope is to eliminate the problems of natural language. This would lead to a paper.
   
3. Verification of simulations and numerical processes. This is a simple programming project: take everything you know about trigonometry and elementary algebra and show where is doesn't work in the computer. The output is a paper and the programs. Verification of floating point hardware with "paranoia". Paranoia is a program that verifies that the hardware is computing according to the IEEE 754 standard. This is a programming project. Experiment with a simple (and already constructed) model of the non-linear pendulum. The experiments are to test the behavior using random perturbations of the parameters and then perform standard statistical tests.

Interdisciplinary Design

Many industrial organizations must now mix computer systems with traditional engingeering systems. One example is the use of computers in automobiles. The proximity of BMW adds impetus to working with engineers to develop credible design techniques that satisfy science, mathematics, engineering, and computer science applications. The new Institute for Design on campus is actively considering all aspects of design.

Reasoning

Ted Doyle is just finishing his dissertation on the categoricity of refutation methods in classical and intuitionistic systems. The next step is to add quantifiers. PhD project.

I'd like for one or more graduate students to work on implementing a "production system" compiler that is a generalization of the ideas in expert systems. There's plenty of information available in the literature as far back as 1936.

Ken Kennedy is completing his dissertation in automatic programming using linguistic principles.

Education

My Programming Language Principles by Example is the culmination of a five year effort to develop an active-learning approach that fits well with computer/computational science classes. But education changes are just now beginning.

• Jennifer Parham is investigating a complete change in education away from propositional knowledge (good ol' facts) towards procedural knowledge.
• Dean Bushey is consider the strategic change in pedagogy and curriculum: rather than worry about freshman retention, we're asking "What are the traits of top-tier performers at five years after graduation." [Dean is now at the U. S. Air Force Academy as an instructor.]

These two projects are just the tip of the iceberg. There are projects as focused as changing one class and there are projects as interdisciplinary as focusing on the psychology of problem-solving. All problem-solving begins with modeling and so we come back to system biology. There are projects at all levels.