Percolation: Random Graph Models

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Graph Coloring and Directed Cycles

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

Percolation: Bond Percolation

Covers bond percolation on a square lattice, discussing percolation phases, critical threshold, mean cluster size, and critical point scenarios.

Statistical analysis of network data

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

Phase Transitions: Percolation in 2D Networks

Explores phase transitions through percolation in 2D 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.

Belief Propagation

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

Statistical Analysis of Network Data

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

Probability & Stochastic Processes

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

Graph Models and Brain Connectomics

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.

Conditional Statements & Graph Theory

Covers conditional statements and graph theory, including proof techniques and concepts related to graphs, paths, connectivity, and gossip protocols.