Ralph B. D'Agostino, Sr.
Boston University
Title: Development, Validation And Transportability Of The Framingham Coronary Heart Disease Risk Prediction Functions (Case Study Of A Successful Exercise In Mathematical Statistical Methods)
Abstract: Coronary Heart Disease (CHD) risk prediction functions have been developed over the years by the Framingham Study investigators. Gender specific CHD risk functions have been produced that involve age, blood pressure, total cholesterol, HDL-Cholesterol, diabetes and smoking status. These functions employed categorical variables for all variables except age following the JNC-V (Hypertension) and NCEP (Cholesterol) guidelines. These functions have been validated within Framingham. Further, their performance on other populations has been investigated. These included consideration of the relation of individual risk factors to CHD (relative risk), the ability to discriminate between CHD cases and non-CHD cases and the ability to produce the correct absolute probability assessment (calibration) of the risk of CHD. We present the results of this investigation. The Framingham functions have validity and are transportable to whites and Blacks. With a simple adjustment for underlying level of risk they are transportable to groups of Japanese-Americans and Hispanics. The presentation illustrates an important contribution of Mathematical Statistical Methods to the fields of Epidemiology and Medicine. The talk will focus on both the statistical and medical aspects.
Bio: Ralph B. D'Agostino (Ph.D., Harvard, 1968) is Professor of Mathematics/Statistics, Public Health and Law at Boston University. He has over 30 years of experience in teaching statistics at all levels from the elementary service courses to advanced graduate courses. He is the recipient of the Metcalf Award for Teaching Excellence. His major fields of research are multivariate analysis, longitudinal studies, epidemiology, clinical trials and outcomes/effectiveness research. He is a fellow of the American Statistical Association and the Cardiovascular Epidemiology section of the American Heart Association. He has been affiliated with the Framingham Heart Study since 1981 and is presently Co-Principal Investigator of the Core contract and Director of data management and statistical analysis for the study. He has also been affiliated with the United States' Food and Drug Administration (FDA), Center for Drugs and Research (CDER) since 1974 as an Expert Consultant to the Biometrics Division, the Over-the-Counter Drugs Division, the Cardiovascular-Renal Drugs Division and the Gastrointestinal Drugs Division. Further, he has served on a number of Advisory Committees and was the Chair of the Nonprescriptive Drugs Advisory Committee (NDAC). He has twice been the recipient of the FDA's Commissioner's Special Citation (1981 and 1995). He is co-author/editor of four books: Factor Analysis: An Applied Approach, Goodness-of-Fit Techniques, Mathematical Models in Health Services Research, and Practical Engineering Statistics. He has served on the editorial board of the Journal of the American Statistical Association, Biostatistica, and Statistics in Medicine. He is presently the North American editor of Statistics in Medicine.
Marilyn Durkin
Bentley College
Title: Observations On The Dynamics Of The Complex Cosine-Root Family
Abstract: Many studies in complex dynamics focus on the Julia sets, or sets of chaotic orbits, for various functions. It is well known that the orbits of the critical values determine the structure of the Julia sets of critically finite functions. Much of the recent research has centered on functions with only one critical value (such as
or
), but what happens when a function has more than one critical value?
Is it possible for orbits of two different critical values to have
different eventual behavior, and, if so, how does this affect the structure of
the associated Julia set? In the
case of one such function,
, we see Julia sets with structures similar to both the quadratic and
exponential cases. Further, we can
predict when each of these structures will occur by plotting a bifurcation set
of all possible
- values. Here we see shadows of
the Mandelbrot set along with the surprising result of “Julia-like” sets
throughout the bifurcation set. This talk will progress from the basic ideas
behind iteration in the complex plane through the topics listed above.
If nothing else, there will be plenty of pretty pictures…Bio: Marilyn (Lynne) Durkin is currently the Chair of the Mathematical Sciences Department at Bentley College. As such, she doesn’t get as much time to pursue research as she once did. However, when time permits, her main areas of interest include discrete dynamical systems with emphasis on complex analytic dynamics, specifically Julia and bifurcation sets, application of dynamical systems techniques to analysis of financial time series, and the integration of dynamical systems and its applications into undergraduate and secondary curricula. She developed an undergraduate dynamical systems course for the general population at Bentley and has managed to teach it successfully for the last ten years. Many of the ideas in this course have been presented in articles and workshops directed to undergraduate and secondary faculty throughout the country.
Nancy Eaton
University of Rhode Island
Title: When Do Near Packings Exist?
Abstract: Let G, H, and K be graphs on n vertices. Suppose G’ is a subgraph of K isomorphic to G and H’ is a subgraph of K isomorphic to H such that G’ and H’ have no edges in common. Then (H’, G’) is a packing of H and G onto K. If G’ and H’ have only a matching in common, then (H’, G’) is a near packing of H and G onto K. We will see what conditions on G and H are known to guarantee existence of a packing or near packing of G and H onto the complete graph. We will also explore some conjectures.
Bio: Nancy Eaton is an Associate Professor at the University of Rhode Island. She received her B.A. degree from SUNY New Paltz in 1985 and her Ph.D. from Emory University in 1992. Her research area is Graph Theory. She has written papers and collaborated in the areas of Ramsey Theory, set representations of graphs, the random graph, and packings of graphs. She regularly presents papers at international conferences on combinatorics.
Susan L. Forman
Bronx Community College, CUNY
Bio: Susan L. Forman is Professor of Mathematics at Bronx Community College, The City University of New York (CUNY). While on extended leave from the College she served as Senior Program Officer for Education at the Charles A. Dana Foundation (1995-97) and as Director of College and University Programs for the Mathematical Sciences Education Board of the National Academy of Sciences (1992-95). Forman has served as First Vice-President of the Mathematical Association of America (1992-94), Chair of the Metropolitan Section of the MAA (1997-99), and President of the New York State Mathematics Association of Two-Year Colleges (1985-86). She received her PhD in mathematics education and research from Columbia University in 1980.
Cathy M. Frey
Norwich University
Title: Developing Mathematical Modules For The World Wide Web
Abstract: The World Wide Web has significantly changed the landscape of graduate and undergraduate education. Student access to the Internet makes distance-learning modules a preferred method of instruction for many students and faculty. Mathematics as a discipline has lagged behind this trend in education. The development of meaningful mathematical modules is critical to distributing mathematics education over the Web. This hands-on workshop will demonstrate websites that have been successful in delivering a variety of mathematical topics from a typical undergraduate Precalculus and Calculus course. The workshop will introduce the tools used to develop the demonstrated sites using Mathematica©, MathType© and JavaScript©. Participants will have an opportunity to develop a web page for presenting mathematics over the World Wide Web. To preview a site created with these methods look at http://www2.norwich.edu/frey/TaylorPolynomials/.
Bio: Cathy Frey has been teaching mathematics at Norwich University since 1985. Her areas of expertise are Actuarial Science and presenting mathematics over the World Wide Web. She has developed several web based instructional modules on a variety of topics covered in undergraduate mathematics courses. At the Joint National Mathematical Meetings in New Orleans this past January, Cathy presented her Taylor Polynomials Web Site at the contributed paper session entitled "Projects and Classroom Demonstrations that Make a Difference". At the Association for Vermont Independent Colleges Faculty and Staff Retreat in November of 2000, Cathy led the workshop entitled “Current AVIC Examples of Web-based Instruction”. She will be on an Independent Study Leave during the Fall semester of 2001, to further develop mathematical modules for the Web. Cathy graduated with a M.S. in Mathematics in 1985 and a B.S. in Mathematics 1983 both from the University of Vermont. She has also accumulated 175 of 200 credits necessary for Associateship in the Society of Actuaries.
Carolyn S. Gordon
Dartmouth College
Title: Isospectral Graphs And Surfaces: What Can You Hear?
Abstract: The spectrum of a finite regular graph is the eigenvalue spectrum of the associated adjacency operator. The spectrum of a surface is the eigenvalue spectrum of the associated Laplace operator. For example, if the surface is a plane domain, the eigenvalue spectrum corresponds to the characteristic frequencies of vibrations of the domain, viewed as a drumhead. We compare eigenvalue problems on graphs and surfaces and ask what the spectrum tells us about their geometry.
Bio: Carolyn Gordon received her B.S. degree from Purdue University in 1971 and her Ph.D. at Washington University in St. Louis in 1979. She served as a Lady Davis Postdoctoral Fellowship at the Technion and held faculty positions at Lehigh University and Washington University before moving to Dartmouth College in 1990, where she now holds the position of Benjamin Cheney Professor of Mathematics. Her research focuses on Riemannian geometry with emphasis on inverse spectral problems and on the geometry of Lie groups. She and David Webb were awarded a Chauvenet Prize for their article "You can't hear the shape of a drum" this past January. Her hobbies include Tai Chi and swimming, and her great joy is parenting her 7-year-old daughter.
Joe McKenna
University of Connecticut
Title: Thought Experiments With Mechanical Systems: Fun And Games With Rubber Bands And Springs
Abstract: In this talk, I will discuss many numerical experiments that model mechanical systems and which give rise to beautiful and unexpected periodic solutions. Many of these models are motivated by my research on suspension bridge oscillations. I will discuss the connections, and give suggestions for future undergraduate research on differential equations.
Bio: Joe McKenna was born in Dublin in 1948 and did his undergraduate work in University College, Dublin. He then completed his Ph.D. under Lamberto Cesari at the University of Michigan. His research is mainly in nonlinear partial and ordinary differential equations and especially their periodic solutions. Much of his recent work concerns large nonlinear oscillations in suspension bridges. This has been covered in many science magazines such as Discover, Science News, Inventions and Technology as well as several undergraduate textbooks on differential equations. He described some of this in a Monthly article in 1999, for which he received the Lester Ford Prize at Mathfest 2000. Having previously worked in the Universities of Wyoming and Florida and University College, Cork, he is currently Professor of Mathematics at the University of Connecticut.
V. Frederick Rickey
United States Military Academy