Thursday, January 5, 2012

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.

Networks, Rumours, and Epidemics [Dr Ayalvadi Ganesh]
  • 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]
  • 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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