Topics will vary from semester to semester. See Computer Science Division announcements.

Networks play a central role in our social and economic lives. They affect our well-being by influencing the information we receive, products we choose to buy, economic opportunities we enjoy, and diseases we catch from others. How do these networks form? Which network structures are likely to emerge in society? And how does the structure of the network impact the dynamics of the spread of an innovation or infection? This course tries to survey the mathematical results developed in the last few years on analyzing the structure of popular random networks, as well as the understanding of processes on them, with particular emphasis on epidemics. In addition it will touch on a recently very popular subject, the non-parametric modeling of a large graph via a graphon, and the related notion of graph limits. The course is loosely based on the text book “Random Graph Dynamics” by Rick Durrett (https://services.math.duke.edu/~rtd/RGD/RGD.pdf), updated to what has happened since its publication, including the topics of graphons and graph limits, plus a larger emphasis on epidemics, as well as a short introduction to the topic of the spread of information and innovation. Additional literature, including original research papers, will be provided during the course. Prerequisites: The course is open to graduate students with a good level of mathematical maturity and a strong background in probability (including some knowledge of Martingales, Markov Chains, and basic notions of stochastic processes), as well as some basic background in graph theory and differential equations. Topics: Random Graph Models and Structure of Large Networks (50-60%): • Erdos-Renyi random graphs: cluster growth, formation of the giant connected component, diameter • Models with community structure: Stochastic block model and topic models • Non-parametric models: graphons, graph limits, estimation • Differential privacy on Networks • Scale-free graphs: random graphs with a fixed degree distribution, preferential attachment model and Polya urns Epidemics Models and their Behavior (about 25%): • Basic compartmental models (SIS, SIR, etc.) • Differential Equation Approach: R0, exponential growth, size of an epidemic • Mathematically rigorous derivation of Differential Equations from the underlying dynamic model

This class has pre-requisites! Read them in the class description. If you have concerns about your qualifications for the class, please contact the professor.

URL for the class is: https://people.eecs.berkeley.edu/~borgs/CS294-179/

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