Lectures related to Networked Control Systems: Properties and Connectivity

Graphical Models: Representing Probabilistic Distributions

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

Networked Control Systems: Graph Theory and Stochastic Matrices

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

Networked Control Systems: Opportunities

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

Irreducible Matrices and Strong Connectivity

Explores irreducible matrices and strong connectivity in networked control systems, emphasizing the importance of adjacency matrices and graph structures.

Matrices and Networks

Explores the application of matrices and eigendecompositions in networks.

Expander Graphs: Properties and Eigenvalues

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

Networked Control Systems: Laplacian Matrix and Consensus

Explores the Laplacian matrix and consensus in networked control systems.

Laplacian Matrix: Properties and Examples

Explores the Laplacian matrix, time-varying consensus theorems, and balanced graphs in networked control systems.

Graphs: BFS

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

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Spectral Graph Theory: Introduction

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

Isogenic Graphs: Spectral Analysis and Mathematical Applications

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

Consensus in Networked Control Systems

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

Interlacing Families and Ramanujan Graphs

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

Pseudorandomness: Expander Mixing Lemma

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

Graph Algorithms: Modeling and Representation

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Graph Representation and Traversal

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

Networked Control Systems: Challenges and Opportunities

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

Convergence of Random Walks

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

Statistical Analysis of Network Data

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