Teaching

Many complex systems are hard to describe and understand because they are composed of large numbers of elements interacting in a non-ordered way. A good example is cellular biology; diverse cellular components (genes, proteins, enzymes) participate in various reactions and regulatory interactions, forming a robust system. A very useful representation of complex systems is given by graphs (or networks), where we denote the components with nodes and their interactions by edges. The properties of these interaction graphs can then be analyzed by graph theoretical and statistical mechanics methods and this information can lead to important conclusions about the dynamics of the system.

Lecture Notes for Spring 2009
(lecture notes will appear after each class)

Lecture Notes from Spring 2008

Lecture Notes from Spring 2007

Topics

1. elements of graph theory: node degree, distances between nodes, clustering,
   node betweenness, subgraphs, directed graphs
2. random graph theory
3. network models and theory: lattices, small-world networks,scale-free networks, evolving networks
4. network robustness and vulnerability
5. percolation and flow processes on networks
6. introduction to cellular networks: gene regulatory networks, signal transduction networks, metabolic networks; methods of network inference
7. modeling reaction networks: elements of chemical kinetics
8. signal transduction network models
9. modeling gene regulatory networks using continuous and discrete dynamics