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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.
Courses
- PHYS580: Elements of Network Science and its Applications (graduate), Fall
2011, Fall 2012
- PHYS497/BIOL497 Systems Biology and Networks (undergraduate), Spring 2011, Spring
2012, Spring 2013
- PHYS597: Graphs and Networks in Systems Biology (graduate), Spring 2004- 2009,
Fall 2009, Fall 2010
Lecture Notes
 Topics
 elements of graph
theory: node degree, distances between nodes, clustering,
node betweenness, subgraphs, directed graphs
- random graph theory
- network models and theory: lattices, small-world networks,scale-free networks, evolving networks
- network robustness and vulnerability
- percolation and flow processes on networks
- introduction to cellular networks: gene regulatory networks, signal transduction networks, metabolic
networks; methods of network inference
- modeling reaction networks: elements of chemical kinetics
- signal transduction network models
- modeling gene regulatory networks using continuous and discrete dynamics
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