|Math 303 - Complex Networks|
Peter Sheridan Dodds
Complex networks crucially underpin much of the real and synthetic world. Networks distribute and redistribute information, water, food, and energy. Networks can be constituted by physical pipes, embodied in relationships carried in people's minds, or manifested by economic interdependencies.
In the past decade, building on work in a wide range of disciplines, many (but certainly not all) advances have been made in understanding all manner of com- plex networks such as the World Wide Web, social and organizational networks, biochemical networks, and transportation networks. In this special topics course, we will explore this evolving field of complex networks by reading and discussing seminal and recent papers, and developing mathematical and algorithmic results where they exist. The level will be graduate/advanced undergraduate.
Topics to be covered (more or less):
* Structure and form of complex networks including physical branching networks (river networks and cardiovascular networks), neural networks, social networks, the Internet, the world wide web, transportation networks, and organizations.
* distribution versus redistribution networks.
* properties of networks including degree distributions, clustering, motifs, various measures of betweenness, modularity, the role of randomness, network dynamics, and multiscale structures.
* community detection algorithms.
* bipartite networks.
* partly random networks as models of real world networks.
* generating function techniques.
* universal models including scale-free networks, p-star networks, and generative models.
* small-world networks.
* impedance and flow in networks.
* connections between delivery networks and energy usage in organisms.
* search in networks as facilitated by network structure and search methods.
* folksonomy and tagging.
* generalized notions of contagion in networks.
* network epidemiology and fad spreading.
Math/Csys 300 is a prereq (not 301 as incorrectly stated in the catalog).
Familiarity with differential equations, difference equations, standard calculus, linear algebra, statistical methods.
Proficiency in coding (C, Matlab, Perl, Python) will be beneficial (and indeed necessary) for certain projects but is not required.
Not specific to any particular application domain
|Frequency: Once a year|
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