Johns Hopkins Whiting School of Engineering 1996 Annual Report [text version]

Whiting School of Engineering 1996 Annual Report

Mathematical Science
Keeping Secrets
Detecting Mines, Cells, and Stars
A Sample Answer
Department Facts

Keeping Secrets
More than 50 years ago, scientists working in the Axis war effort developed a device known as the Enigma machine. During most of World War II, the Axis powers used it with great success to encrypt military messages. Even with copies of instructions obtained by the French, the Allied forces could not crack Enigma’s elegant mix of alphabetic keyboard, rotors, reflector, and 26 lightbulbs. Finally, mathematician Alan Turing and others broke its code with the Bombe, a machine so named because of its ticking noises.

Cryptology and data security are just as relevant now as in wartime. Millions of messages travel electronic highways daily, and the challenge to keep sensitive information secret and authentic grows exponentially with the continual addition of material. In spring 1996, graduate student Lisa Evans assisted Professor Ed Scheinerman with the new course, Cryptology and Coding. “We felt that the theme of secure and reliable handling of digital information was very timely. Plus, we filled a gap at the intermediate level in discrete mathematics by offering a course in an applications-driven setting,” says Scheinerman. In addition to class work, students visited the National Security Agency’s (NSA) cryptology museum.

A second-year graduate student, Evans was the logical choice for the course’s first teaching assistant. During the last three summers, she has participated in cryptology internships at NSA. “I gained valuable experience by working on selected projects with linguists and others at NSA, and my results were presented in a technical paper at the end of each summer,” Evans says. “When I was ready to explore graduate schools, I wanted an education that would enhance my computer science and math background with engineering concepts. Johns Hopkins was my first choice.” Evans is leaning towards research in cryptology and is also exploring computational biology—with introducing the fascinating world of cryptology to engineering students providing a solid foundation for future investigations.

Detecting Mines, Cells, and Stars
There are approximately 100 million unexploded mine fields in the world. One out of every ten women will develop breast cancer in her lifetime. Do these statements seem unrelated? Think again, says Assistant Professor Carey Priebe. “Problems that differ at one level can become very similar at the mathematical modeling level,” says Priebe. And that’s exactly the case in statistical image analysis, one of his areas of expertise.

The Office of Naval Research (ONR) has funded Priebe’s project in mine field detection. At present, military personnel pore over images that consist of varied “backgrounds,” including beaches and brush. His challenge is to develop an automated model that characterizes the backgrounds and subsequently determines the likely location of minefields, which would decrease dramatically the number of images that need to be reviewed.

Radiologists and other medical professionals can also run into the problem of finding the veritable needle in a haystack when searching for breast cancer indicators. Priebe has used the same techniques to locate clusters of microcalcifications in X-ray mammography. The clusters show up as dots in the background of a mammogram and can indicate a precancerous condition. “The hardest thing to do,” Priebe comments, “is to develop a model that not only applies in the idealized case, but also works properly in the real world. A model, or theorem, must be ‘robust’ in the sense that it works under varying conditions, and it should demonstrate ‘continuity,’ in which a small change in one parameter changes the overall inference by a similarly small amount.”

Priebe’s research also has applications to the study of MRI and PET brain scans for understanding schizophrenia, finding galaxy clusters, and locating airplane runways and other targets of interest in aerial imagery. His enthusiasm for his work extends to a new undergraduate course he recently developed and taught in Statistical Image Modeling. The ten students in the class used their engineering skills and applied course concepts to complete individual projects, such as characterizing bone density. ONR recently granted Priebe a prestigious Young Investigator Award to continue his investigations.

A Sample Answer
Statisticians try to answer some pretty tough questions. What is the likelihood that an individual will develop colon cancer? Has a new drug increased the life expectancy of AIDS patients? What impact has overharvesting had on species indigenous to the Chesapeake Bay? The answers can have powerful consequences, from altering medical treatment and changing insurance guidelines to establishing new environmental regulations. True number-crunchers, statisticians are at home in many fields, yet the unifying aspect of their research is that—on some level—all staticians seek ways to study and interpret data. It is the diverse challenges presented to statisticians that attracted Assistant Professor Lancelot James to the discipline.

James is particularly interested in resampling methods. The concept behind resampling is to treat the study population as the “unknown” group and then make a statistical analysis based on a smaller group from within that population. This area of statistics uses computer-intensive methods to determine sample behavior of statistical estimators. Resampling is in contrast to more traditional approximation methods such as the familiar bell-shaped distribution that relies on an adequate sample size. James studies how the “weighted bootstrap” and “undersampling/jacknife” methods of resampling can produce more accurate results than other techniques. For example, in a large clinical study of patients with heart disease, individual subjects may have to leave prematurely or the study itself may be terminated before data gathering is completed. Therefore, the population at the end of the study may no longer be as large as the original group. Resampling methods like the bootstrap allow researchers to obtain statistically viable data from a much smaller population.

The general conclusion is that under certain model assumptions the bootstrap method performs better than corresponding “normal” approximation techniques. James seeks ways to increase the accuracy of resampling methods in complex situations, which include determining cases where the sample selected should be the same size as the original population. His study and validation of the procedures include statistical theory, probability, and other areas of mathematics supplemented by computer simulation.

Established 1972
Industrial engineering began at Hopkins in 1948, and in 1972 the Department of Operations Research and Industrial Engineering and the Department of Statistics merged to form the current department.

Phone 410-516-7198

Email math_sciences@jhu.edu

WWW http://brutus.mts.jhu.edu/

Students
1995-96 Academic Year
Graduate: 43
Undergraduate: 16

Faculty and Researchers
John C. Wierman, Chair
Cheng Cheng
Lenore J. Cowen
James A. Fill
Alan J. Goldman
Leslie A. Hall
Shih-Ping Han
Lancelot F. James
Daniel Q. Naiman
Jong-Shi Pang
Carey E. Priebe
Edward R. Scheinerman
Colin O. Wu

Research Areas
Discrete Mathematics
Mathematical Programming
Numerical Analysis
Operations Research
Probability
Statistics

Mathematical Science Keeping Secrets Detecting Mines, Cells, and Stars A Sample Answer Department Facts

Mathematical Science
Keeping Secrets
Detecting Mines, Cells, and Stars
A Sample Answer
Department Facts