I am attending a School on Network Science at ECE, IISc, organized as part of the IMI, and funded by ICTS. I jotted down some points for revision/future look-up.

References

Topics

**[Dr Ayalvadi Ganesh]**__Networks, Rumours, and Epidemics__References

- Grimmett and Frieze
- Damon Mosk-Aoyoma and Devavrat Shah. Distributed Computation of Separable Functions. IEEE Trans. Info. Theory. 2008
- Consensus. de Groot et al.
- Voter model. Hassin and Peleg, James Cruise and Ganesh Ayalvadi
- Wright-Fisher model, Morale model
- Wisdom of Crowds. Golub and Jackson
- Acemoglu, Dahleh, Lobel, Ozdaglar
- Kermack and McKendrick. Epidemic model using ODEs
- Ganesh Ayalvadi, Moussalie, Tousley. Effect effect of network topology on epidemic spread. IEEE InfoComm. 2005
- Draief, Ganesh, Moussalie. thresholds for Virus Spread on Nertworks. Ann. Appl. Prob. 2008

- Coupon Collector Problem
- Stochastic Domination, Strassen's Theorem
- Markov Chains---irreducible, aperiodoc, ergodic, balance equations, invariant distribution, etc.
- Markov Process (continuous time)
- Poisson Process---thinning
- Martingales, stopping time, Optional Stopping Theorem
- Binary Entropy function, Conditional entropy
- Random walks---coalescing RW
- Coupling from the past in MCMC
- Erdos-Renyi graphs, scale-free graphs, expander/ing graphs, unimodular graphs
- Linear recurrences, harmonic functions
- Lattices---infinite lattice
- Perron-Frobenius Theorem---sprectral radius, Perron eigenvalue
- Eigenvalue of e^A, where A is a matrix
- Generalized isoperimetric constant

**Ising Models**[Andrea Montanari]Topics

- Hammersley-Clifford Theorem
- Inclusion-Exclusion Principle
- Union bound
- Measures, Concentration
- Gibbs sampling, MCMC, Metropolis
- Constrastive Divergence (Hinton)
- Glauber Markov Chain
- tanh, atanh---properties
- "One-dimensional recursion"
- Inequalities---Markov, Chebyshev, ...
- Sterling number---as related to enumerating number of graphs with p vertices and Cp edges
- Belief propagation, Generalized BP
- Contraction (on graphs)

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