Lectures related to Markov Chains and Algorithm Applications

Markov Chains: Applications and Analysis

Explores Markov chains, focusing on the coloring problem and algorithm analysis.

Markov Chains: Applications and Sampling Methods

Covers the basics of Markov chains and their algorithmic applications.

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Belief Propagation for Graph Coloring

Explores Belief Propagation for graph coloring and its convergence properties.

Probability & Stochastic Processes

Covers applied probability, stochastic processes, Markov chains, rejection sampling, and Bayesian inference methods.

Graph Coloring: Theory and Applications

Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.

Information Theory: Basics

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Graph Coloring: Random vs Symmetrical

Compares random and symmetrical graph coloring in terms of cluster colorability and equilibrium.

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.

Graph Coloring and Directed Cycles

Explores graph coloring, directed cycles, LLL algorithm applications, and element dependencies in graphs.

Graph Theory Basics

Introduces graph theory basics, Ramsey theory, and graph coloring concepts.

Graph Algorithms II: Traversal and Paths

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

Graph Coloring: Basics and Applications

Covers the basics and applications of graph coloring, including balancing vectors and achieving perfect fairness.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Cheeger's Inequalities

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

Minimum Spanning Trees: Prim's Algorithm

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

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Graph Theory: Girth and Independence

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.

Networked Control Systems: Opportunities

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

Graph Theory and Network Flows

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