Lectures related to Networked Control Systems: Graph Theory and Stochastic Matrices

Explores properties of matrices, irreducibility, and graph connectivity in networked control systems.

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

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

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

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

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Explores the application of matrices and eigendecompositions in networks.

Covers graphical models for probability distributions and factor graphs representation.

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Introduces elementary graph algorithms, focusing on Breadth-First Search and Depth-First Search.

Explores consensus in networked control systems through graph weight design and matrix properties.

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Introduces graph theory basics, graph representation methods, and traversal algorithms like BFS and DFS.

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

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

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

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