Sparsest Cut and Concurrent Flow

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Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.