MH_on_HC

Metropolis-Hastings MH algorithm to simulate the Ising model for brain connectome.

This algorithm finds the critical temperature of the Human Connectome or any other network by inserting the connectivity matrix J.

Prerequisites

This program requires a fast computer due to the iteration inside each Monte Carlo step.

Description

To execute the algorithm, open main.m. It contains three functions:

• N_critical_T.m: This function find numerically an estimated value of the critical temperature (TC) in order to define a range of temperature for the algorithm.
• one_metropolis_step.m: This function correspond to one Metropolis step for flipping N spins selected randomly.
• visualization.m: This function is optional, it just visualizes the curve of Susceptibility vs Temperature.

Usage

Enter the next statement in Command Window of Matlab:

main

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Reference list

Newman, E. M. J., & Barkema, G. T. (2001). "The Ising model and the Metropolis algorithm. In Monte Carlo Methods in Statistical Physics" (pp. 45–87). Oxford, UK: Oxford University Press.

Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J., & Sporns, O. (2008). "Mapping the Structural Core of Human Cerebral Cortex". PLoS Biology, 6(7), e159.

License

MIT