Algebraic Methods in Systems Biology and Statistics

Fall 2008

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
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
Oct 21 Conditional Independence (Section 3.1) Seth
Finite Dynamical Systems II    Slides Reinhard
Oct 28 Graphical Models (Section 3.2) Seth
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.