Markov Chains: Applications and Sampling Methods

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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.

Monte Carlo Techniques: Sampling and Simulation

Explores Monte Carlo techniques for sampling and simulation, covering integration, importance sampling, ergodicity, equilibration, and Metropolis acceptance.

Markov Chains and Algorithm Applications

Covers the application of Markov chains and algorithms for function optimization and graph colorings.

Graph Coloring and Directed Cycles

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

MCMC Examples and Error Estimation

Covers Markov Chain Monte Carlo examples and error estimation methods.

MCMC with Metropolis

Covers the implementation of Markov Chain Monte Carlo (MCMC) with the Metropolis algorithm for sampling from posterior distributions.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Graph Theory Basics

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