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
(CAS) to develop models of how the behavior of individuals interact to
social and political systems. This work draws heavily on notions from
dealing with natural selection of successful behaviors and the dynamics
populations. Readings will consider substantive topics in American
(political parties, campaign strategies), international relations (the
development of cooperation among nations, emergence of new
comparative politics (the formation and collapse of parliamentary
origins of nationalism), and political theory (mechanisms of collective
in democratic society). There will also be readings in the theory of
adaptive systems, including an introduction to the genetic algorithm
computer models of social behavior. The class is appropriate for
political science, sociology or economics interested in more formal and
systematic models of politics, and for students in computer science,
biology who wish to see social science applications of theories of CAS.
semester of calculus and an introduction to computer programming are
background, but are not required to do well in the course.
We will read substantial portions of the following books:
- Axelrod, Robert. 1984. The Evolution of Cooperation.
York: Basic Books.
- Axelrod, Robert. 1997. The Complexity of Cooperation.
Princeton: Princeton University Press.
- Cederman, Lars-Erik. 1997. Emergent Actors in World
Politics. Princeton: Princeton University Press.
- Epstein, Joshua M. and Robert Axtell. 1996. Growing
Societies. Washington DC: Broookings Institution Press.
- Holland, John H. 1992. Adaptation in Natural and
Systems. Cambridge: MIT Press.
- Holland, John H. 1995. Hidden Order. Reading
- Kauffman, Stuart A. 1993. The Origins of Order:
Self-Organization and Selection in Evolution. New York: Oxford
- Lightman, Alan. 1993. Einstein's Dreams. New
- Schelling, Thomas C. 1978. Micromotives and
Macrobehavior. New York: W.W. Norton.
- Simon, Herbert. 1996. The Sciences of the Artificial
edition. Cambridge MA: MIT Press.
- Computer Sciences 760 --- Machine
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
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
- Math 821 --- Advanced Topics in
Fluid Mechanics, Prof. Panagiotis
- 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
incompressible and compressible Navier-Stokes. The course will begin
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
two books of P. L. Lions on this subject.
- Statistics 860 --- Statistical
Emphasis on Splines, Prof. Grace
- Prereq.: Statistics majors, mathematical maturity to
the level of
a year of graduate work, and either multivariate analysis, or, some
Hilbert spaces, or cons. instr. Those unfamiliar with Hilbert spaces
asked to read the first 33 pages of Akhiezer and Glazman, Theory
Linear Operators in Hilbert Spaces, vol. I at the beginning of
course. Graduate students in CS, AOS and other physical sciences,
economics and biostatistics may find some of the techniques studied
and are welcome to sit in, or take the course for credit if they have
to linear algebra, sufficient math background to read Akhiezer and
are familiar with the basic properties of the multivariate normal
as found, e. g. in Anderson, Multivariate Analysis, or
Mathematical Statistics. Otherwise, the development
self-contained. If in doubt, please contact the instructor by e-mail or come to the first
4:00-5:15 TuTh in 1207 CS
Text: G. Wahba, Spline Models for Observational
SIAM (1990), and recent papers, tba.
This course is about various aspects of multivariate function
and statistical model building given scattered, noisy direct, and
data, mostly via the use of smoothing spline and reproducing kernel
space (rkhs) techniques. Use of public software will be included. Upon
completing the course the student should be able to apply modern
smoothing spline and related multivariate function estimation methods
medical, environmental, atmospheric and economic data sets. Open
also be discussed.
No prior knowledge of Hilbert space is required. Students who already
a background in rkhs (from Statistics 840) may take the course and do
reading assignments while the introductory material is covered.
- Background, introduction to the theory of reproducing
spaces. Polynomial and thin plate splines, splines on the circle and
Regression splines, partial splines, hybrid splines, ANOVA splines,
splines, radial basis functions.
- 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.
freedom for signal and the bias-variance tradeoff. Applications in
likelihood, Tihonov regularization, support vector machines, and
- Model selection methods. Bayesian and bootstrap
Tests of the parametric null model hypothesis versus smooth
Applications to penalized GLIM models and generalized additive models
- 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.
- Applications in medicine (risk factor modeling),
analysis, economics, meteorology, machine learning, remote sensing
inverse problems), and merging of observations and dynamical systems
in climate and numerical weather prediction) will be discussed,
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
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)
Chaos and Complex Systems Seminar Page