Instructors:  Reinhard Laubenbacher and Seth Sullivant

Time and Place:  Tuesdays, 4:30 - 7:00 PM,  SAMSI  First day:  September 2nd


Office hours:  Laubenbacher:    Sullivant:

Course Description:  This course will provide an introduction to the algebraic techniques that have emerged as useful tools in biology and statistics.  This course is intended to bridge the gap between abstract algebra and the application areas covered in the year-long program.  After providing an introduction to polynomial rings, ideals, and Grobner bases, we will survey a range of applications of these ideas.  Possible topics include:  Polynomial dynamical systems over finite fields and applications, graphical and hierarchical models, Markov bases for contingency table analysis, phylogenetic models and the space of trees, applications of tropical geometry, reverse engineering of biological networks, connections to experimental design.  Some of the lectures will be given by visitors to the SAMSI program.

Enrollment:  NCSU:  MA/ST 810E Section 2,   Duke:    ,  UNC:

Prerequisites:   Intended audience is graduate students in mathematics, statistics, and computational and mathematical biology.  We do not have any specfic prerequisites except for "mathematical maturity" and interest in applications. Please talk to the instructors if you are interested in attending.


Schedule of Lectures:

Date	Topic	Speaker
Sept 2	Polynomials, Ideals, Gröbner Bases	Seth
		Reinhard
Sept 9	Conditional Independence	Seth
	Introduction to Systems Biology	Reinhard
Sept 16	No Lectures:  Attend the Opening Workshop
Sept 23	Conditional Inference for Log-linear Models	Seth
	Discrete Models of Biological Networks	Reinhard
Sept 30	Markov Bases for Log-Linear Models	Seth
	Finite Dynamical Systems I	Reinhard
Oct 7	Graphical Models	Seth
	Finite Dynamical Systems II	Reinhard
Oct 14	Hidden Variable Models	Seth
	Reverse Engineering of Biological Networks	Reinhard
Oct 21	Likelihood Ratio Tests	Seth
	Reverse Engineering of Biological Networks	Reinhard
Oct 28	Bayesian Integrals	Seth
	Relations between discrete modeling frameworks: logical models, polynomial dynamical systems, Petri Nets	Reinhard
Nov 4
Nov 11
Nov 18
Nov 25
Dec 2	Student Presentations
Dec 9	Student Presentations

Further Reading:

M. Drton, S. Sullivant.    Algebraic statistical models, Statistica Sinica 17 (2007) 1273-1297.
L. Pachter, B. Sturmfels.   Algebraic Statistics for Computational Biology.  Cambridge University Press,  2005.
M. Drton, B. Sturmfels, S. Sullivant.  Lectures on Algebraic Statistics.  (In preparation).