Lectures related to Networked Control Systems: Opportunities

Graphical Models: Representing Probabilistic Distributions

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

Networked Control Systems: Properties and Connectivity

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

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.

Minimum Spanning Trees: Prim's Algorithm

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

Cheeger's Inequalities

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

Networked Control Systems: Coordination Among Agents

Explores coordination among agents in networked control systems through graph theory and real-world examples.

Graph Theory and Network Flows

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

Networked Control Systems: Challenges and Opportunities

Explores challenges and opportunities in networked control systems, covering LTI systems, delays, packet drops, and consensus.

Statistical Analysis of Network Data

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

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

Interlacing Families and Ramanujan Graphs

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

Szemerédi Regularity Lemma

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

Expander Graphs: Properties and Eigenvalues

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

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Convergence of Random Walks

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

Graphs: Properties and Representations

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

Networked Control Systems: Graph Theory and Stochastic Matrices

Explores graph theory, stochastic matrices, consensus algorithms, and spectral properties in networked control systems.

Cavity Method: Mean Field Theory

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

Shortest Path Algorithms: BFS and Dijkstra

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