Chaos and Complexity Courses for Fall 1998, UW-Madison

Political Science 401 --- Evolutionary Models of Political Systems, Prof. Charles Franklin
Prereq.: None (but see below).
11:00--12:15 TuTh in 38 Agriculture Hall
Text: Selected readings (see below).
This course draws on recent work in the field of complex adaptive systems (CAS) to develop models of how the behavior of individuals interact to create social and political systems. This work draws heavily on notions from biology dealing with natural selection of successful behaviors and the dynamics of populations. Readings will consider substantive topics in American politics (political parties, campaign strategies), international relations (the development of cooperation among nations, emergence of new nation-states), comparative politics (the formation and collapse of parliamentary coalitions, origins of nationalism), and political theory (mechanisms of collective choice in democratic society). There will also be readings in the theory of complex adaptive systems, including an introduction to the genetic algorithm and computer models of social behavior. The class is appropriate for students in political science, sociology or economics interested in more formal and systematic models of politics, and for students in computer science, math or biology who wish to see social science applications of theories of CAS. A semester of calculus and an introduction to computer programming are helpful background, but are not required to do well in the course.

We will read substantial portions of the following books:

Computer Sciences 760 --- Machine Learning, Prof. Jude Shavlik
Prereq.: Comp. Sci. 540
11:00--12:15 TuTh in 1325 Comp. Sci. and Stat.
Text: Tom Mitchell, Machine Learning McGraw-Hill
Computational approaches to learning: including inductive inference, explanation-based learning, analogical learning, connectionism, and formal models. What it means to learn. Algorithms for learning. Comparison and evaluation of learning algorithms. Cognitive modeling and relevant psychological results. For more information, see Prof. Shavlik's page on the course.

Math 821 --- Advanced Topics in Real Analysis: Fluid Mechanics, Prof. Panagiotis Souganidis
Prereq.: Consent of instructor.
8:30-9:45 MF in 215 Ingraham
Text: See below.
The course is about various mathematical results on fluid mechanics such as incompressible and compressible Navier-Stokes. The course will begin with a description of the fundamental equations modelling newtonian fluids together with the basic approximating and simplified models. Then there will be a discussion of recent mathematical results on incompressible models. If time permits results about compressible models as well as asymptotic limits will be presented. The plan is to work through the last two books of P. L. Lions on this subject.

Statistics 860 --- Statistical Models, with Emphasis on Splines, Prof. Grace Wahba
Prereq.: Statistics majors, mathematical maturity to the level of a year of graduate work, and either multivariate analysis, or, some exposure to Hilbert spaces, or cons. instr. Those unfamiliar with Hilbert spaces will be asked to read the first 33 pages of Akhiezer and Glazman, Theory of Linear Operators in Hilbert Spaces, vol. I at the beginning of the course. Graduate students in CS, AOS and other physical sciences, engineering, economics and biostatistics may find some of the techniques studied here useful and are welcome to sit in, or take the course for credit if they have exposure to linear algebra, sufficient math background to read Akhiezer and Glazman, and are familiar with the basic properties of the multivariate normal distribution, as found, e. g. in Anderson, Multivariate Analysis, or Wilks, Mathematical Statistics. Otherwise, the development will be self-contained. If in doubt, please contact the instructor by e-mail or come to the first class.
4:00-5:15 TuTh in 1207 CS
Text: G. Wahba, Spline Models for Observational Data, SIAM (1990), and recent papers, tba.
This course is about various aspects of multivariate function estimation and statistical model building given scattered, noisy direct, and indirect data, mostly via the use of smoothing spline and reproducing kernel Hilbert space (rkhs) techniques. Use of public software will be included. Upon completing the course the student should be able to apply modern multivariate smoothing spline and related multivariate function estimation methods to medical, environmental, atmospheric and economic data sets. Open problems will also be discussed.
No prior knowledge of Hilbert space is required. Students who already have a background in rkhs (from Statistics 840) may take the course and do special reading assignments while the introductory material is covered.
  1. Background, introduction to the theory of reproducing kernel Hilbert spaces. Polynomial and thin plate splines, splines on the circle and sphere. Regression splines, partial splines, hybrid splines, ANOVA splines, thin plate splines, radial basis functions.
  2. Adaptive estimation of multiple smoothing and tuning parameters and the bias-variance tradeoff. Generalized cross validation, unbiased risk and maximum likelihood estimates for Gaussian and non-Gaussian data. Degrees of freedom for signal and the bias-variance tradeoff. Applications in penalized likelihood, Tihonov regularization, support vector machines, and wavelets.
  3. Model selection methods. Bayesian and bootstrap confidence intervals. Tests of the parametric null model hypothesis versus smooth alternatives. Applications to penalized GLIM models and generalized additive models for risk factor estimation.
  4. Numerical methods for medium sized to very large data sets. The randomized trace estimate for degrees of freedom for signal. Early termination of iterative methods as a form of regularization. Public software.
  5. Applications in medicine (risk factor modeling), environmental data analysis, economics, meteorology, machine learning, remote sensing (ill-posed inverse problems), and merging of observations and dynamical systems models (as in climate and numerical weather prediction) will be discussed, according to the interests of the class.

This will be a seminar-type course. There will be no sit-down exams. Students taking the course for credit will be expected to do one or two computer projects studying the behavior of some of the methods discussed on simulated or experimental data, and one or two projects in an area of application of their choice from (5) with a possible project being the presentation of a lecture in class on a recent paper or recent resarch.
Note: Wahba (1990) is on reserve at Wendt, Akhiezer and Glazman is on reserve in Wendt and the Math Library.

(Tue Apr 21 13:40:27 1998)

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