Do you ever wonder how seeming successfully ants forage for rich sources of food, bees move a beehive to more suitable locations, flocks of birds fly in formation? How come a tree falling in Ohio causes fifty five million people in the Northeast of the US and Canada to loose their electrical power? Why the actions of a few in an once in the financial district in London impact so significantly the World financial markets? Why do critical infrastructures, e.g., cellular and mobile networks, fail in times of crisis, when they are most needed? How do bot-nets spread and compromise millions of computers in the internet? Can companies understand the viral behavior of their three million (did you say eighty million) (mobile) customers? These and others are background and motivational examples that guide us in this course whose goal is the study of relatively dumb agents that sense, process, and cooperate locally but whose collective, coordinated activity leads to the emergence of complex behaviors. Among others, the course will develop basic tools to understand: i) the modeling of these highly networked, large scale structures (e.g., colonies of agents, networks of physical systems, cyber physical systems ii) how to predict the behavior of these networked systems iii) how to derive and study the properties (e.g., convergence and performance) of distributed algorithms for inference and data assimilation. The course will develop graph representations and introduce tools from spectral graph theory, will cover the basics from queueing theory, Markov point processes, and stochastic networks to predict behaviors under several types of stress conditions and asymptotic regimens, and will explore consensus algorithms and several classes of distributed inference algorithms operating under infrastructure failures (intermittent random sensor and channel failures,) different resource constraints (e.g., power or bandwidth,) or random protocols (e.g., gossip.) The course is essentially self-contained. There will be a mix of homework, midterm exams, and projects. Students will take an active role by exploring examples of applications and applying network science concepts to fully develop the analysis of their preferred applications.
Pre-requisites: Probability theory.