Lectures related to Networked Control Systems: Properties of Laplacian Matrices

Spectral Clustering: Theory and Applications

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

Isogenic Graphs: Spectral Analysis and Mathematical Applications

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

Interlacing Families and Ramanujan Graphs

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

Interlacing Families and Ramanujan Graphs

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

Networked Control Systems: Graph Theory and Stochastic Matrices

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

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.

Expander Graphs: Properties and Eigenvalues

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

Spectral Graph Theory: Introduction

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

Convergence of Random Walks

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

Cheeger's Inequality

Explores Cheeger's inequality and its implications in graph theory.

Laplacian Matrix: Properties and Examples

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

Building Ramanujan Graphs

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Networked Control Systems: Opportunities

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

Matrix Tree Theorem

Explores the Matrix Tree Theorem and its application in calculating spanning trees in graphs.

Statistical analysis of network data

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

Matrices and Networks

Explores the application of matrices and eigendecompositions in networks.

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.

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Graph Algorithms II: Traversal and Paths

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