Instructors:  Reinhard Laubenbacher and Seth Sullivant

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


Office hours: Tuesdays, 3:30- 4:30,  NISS Building   

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.

Assignments:  The assignment for the class will be to read three papers in the general area of "Algebraic methods in systems biology and statistics" and write short (2-3 page) summaries of each of the three papers.  Each student will also be expected to give a 20 minute presentation of one of the papers they have read, sometime during the course of the semester.  We will provide a list of papers to choose from during the second class meeting (September 9th), as well as instructions on how to prepare the summary.

Here is a file with assignment details:  homework.  Note that the first part is due on September 30th.

Here you can find copies of most of the papers:  papers.

Schedule of Lectures:

Date	Topic	Speaker
Sept 2	Overview Slides from Reinhard	Seth
		Reinhard
Sept 9	Polynomials, Ideals, and Varieties	Seth
	Gröbner bases	Reinhard
Sept 16	No Lectures:  Attend the Opening Workshop
Sept 23	Conditional Inference  (Section 1.1)	Seth
	Markov Bases of Log-linear Models (Sections 1.2 & 1.3)	Seth
Sept 30	Markov Bases II	Seth
	The relationship between biological network inference and design of experiments  Slides	Reinhard
Oct 7	Markov Bases III:  Connections with Algebra	Seth
	Data Discretization & Minimal Wiring Diagrams   Slides	Reinhard
Oct 14	Finite Dynamical Systems	Reinhard
		Reinhard
Oct 21	Conditional Independence (Section 3.1)	Seth
	Finite Dynamical Systems II    Slides	Reinhard
Oct 28	Graphical Models (Section 3.2)	Seth
		Reinhard
Nov 4	Parametrizations of Graphical Models (Section 3.3)	Seth
	Using Graphical Models	Seth
Nov 11	Phylogenetic Models  (Part of Section 4.1)	Seth
	Tree spaces	Megan Owen
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.  Oberwolfach Seminars, Birkhauser, 2009.
R. Laubenbacher, B. Stigler.   Design of experiments and biochemical network inference.
Ben Wells   How to use 4ti2 on a PC.