ECE 498 LV - Network Science: Dynamics and Flow (Spring 2017)

Instructor: Lav Varshney (office hours, Thursday 12:30-2:00pm, 314 CSL and by appointment)

Lectures: Tuesday and Thursday, 11:00am, 4070 Electrical and Computer Engineering Building

Adjacency matrix of C. elegans connectome (Varshney, et al., 2011)	Volume of taxi rides in Manhattan on average Tuesday at 4PM, March 2009, http://www.binaryspark.com/heytaxi	Backbone of the flavor network (Ahn, Ahnert, et al., 2011)

• Can we predict the behavior of the nematode C. elegans by looking at the connectivity pattern of its neurons?
• Can we characterize the pulse of life in New York City by looking at flows of taxi cabs?
• Can we design flavorful culinary recipes by understanding knowledge on shared flavor compounds in ingredients?

By taking an engineering perspective on network science, we can address these problems; more traditional problems in communications, computing, and power; and more!

Catalog Description: Network science studies connections and flows among interacting objects, and the dynamic evolution of these structures. This course will cover the mathematics of networks, drawing on an emerging set of principles and techniques that originate in engineering theory, physics, biology, and the social sciences. The goal is to equip students with conceptual tools for understanding complex network systems. Examples taken primarily from neuronal, knowledge, and infrastructure networks.

Suggested Prerequisites: ECE 210, ECE 313, MATH 286, MATH 415, or their equivalents. Programming in matlab and/or python.

Textbook: M. E. J. Newman, Networks: An Introduction, Oxford University Press, 2010. Note that further readings and lecture notes will be provided through the course website.

Grading: Homework [including data/programming assignments] (35%), midterm exam (20%), final exam (20%), group project [open-ended topics, written report, and in-class conference-style presentations] (25%).  Graduate students enrolled for 4 credits will complete an additional individual research project.

Syllabus, Syllabus Attachment

Homework

• Homework 0 (released January 15, due January 17 in class)[solutions, see Lecture 1 slides]
• Homework 1 (released January 17, due January 24 in class)[solutions]
• Homework 2 (released January 24, due January 31 in class)[solutions]
• Homework 3 (released January 31, due February 7 in class)[solutions]
• Homework 4 (released February 7, due February 14 in class)[solutions]
• Homework 5 (released February 14, due February 21 in class)[solutions]
• Homework 6 (released February 24, due March 7 in class)[solutions]
• Homework 7 (released March 14, due March 28 in class)[solutions]
• Homework 8 (released March 31, due April 11 in class)[solutions]
• Homework 9 (released April 11, due April 18 in class)[solutions]
• Homework 10 (released April 18, optional and not specifically due)[solutions]

Exams

• Exam 1 (March 9) [solutions]

​Final Project

• [guidelines] [feedback form]

Course Schedule

Topics:

• Introduction to networks and their mathematical abstraction
• Empirical study of networks and important design questions in application domains
  • infrastructure networks—electricity, water, communications
  • neuronal networks—human connectome and connectome of small organisms
  • knowledge networks—citation, semantic, etc.
• Fundamentals of network theory
  • mathematical representations, components, paths, degrees, walks
  • software for network analysis
• Dynamics of networks
  • review of differential equations, difference equations, linear systems theory
  • review of (scalar) nonlinear dynamics
  • network dynamics
  • epidemics
  • synchronization
• Flow on networks
  • shortest paths
  • maximum flow
  • bottleneck flow
  • multicommodity flow
• Measures and metrics
  • centrality, from principles of dynamics and flow
• Network visualization
  • Laplacian graph drawing
• Random networks​
  • Erdos-Renyi graphs, exponential random graphs, and scale-free networks