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Fixed Points in Graph Theory
Focuses on fixed points in graph theory and their implications in algorithms and analysis.
Differentiable Functions and Lagrange Multipliers
Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.
Max Flav-Min Cut in Directed Graphs
Covers the concept of maximum flow-minimum cut in directed graphs with capacity constraints.
Szemerédi Regularity Lemma
Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.
Graph Theory Fundamentals
Covers the fundamentals of graph theory, including vertices, edges, degrees, walks, connected graphs, cycles, and trees, with a focus on the number of edges in a tree.
Graph Algorithms II: Traversal and Paths
Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.
Interlacing Families and Ramanujan Graphs
Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.
Model Selection and Local Geometry
Explores model selection challenges in causal models and the impact of local geometry on statistical inference.
Sparsest Cut and Concurrent Flow
Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.
Consensus Algorithms: Weight Assignment and Applications
Explores the design of graph weights for consensus and applications in sensor networks.