Random Field Ising Model on Graphs

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Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.

Graph Theory: Girth and Independence

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Cavity Method: Mean Field Theory

Explores the Cavity Method in Mean Field Theory, analyzing spins in an external field within a graph.

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Networks, Flows

Covers the definition of flow in a network and flow calculation.

Assembly: Physics of Manufacturing

Discusses the importance of assembly in manufacturing and covers common couplings, stability, and spatial vectors.

Minimum Spanning Trees: Prim's Algorithm

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