Multistability-Paper

Description

This repository contains all code necessary to produce the figures of the paper:

Breffle J, Mokashe S, Qiu S, Miller P. 2023. Multistability in neural systems with random cross-connections. Biol Cybern. 117(6):485–506. doi:10.1007/s00422-023-00981-w.

Journal link: https://doi.org/10.1007/s00422-023-00981-w
Link to publicly available view-only version: https://rdcu.be/dujJP

The repository includes separate codes for simulations of finite systems, for mean-field analysis of infinite systems, and for solving approximate analyses of finite systems with binary neural response functions.

Figure-by-figure instructions

Figure 1: Single-unit response functions, $f(x)$, produce bistability at $s=1$

• ./figure-code/FI_curves.m produces panels A-C

Figure 2: All activity regimes can be observed in a single random network

• ./figure-code/example_net_dynamics.m produces panels A-D with the setting "figSim = 'fig2';"
• ./figure-code/perturb_nets_run_sim.m produces the data for panel E
• ./figure-code/perturb_nets_plot_sim.m plots the data for panel E

Figure 3: Smaller networks are multistable at larger $g$ values

• ./figure-code/simulation-code/sim_rand_nets.m produces the data for panels B-F with appropriate parameter selection
  • Set options as instructed in the "%% Sim options" section
• ./figure-code/example_net_dynamics.m produces panel A with the setting "figSim = 'fig3';"
• ./figure-code/same_nets_across_g.m plots the data for panels B-F

Figure 4: Multistability across phase space

• ./figure-code/simulation-code/sim_rand_nets.m produces the data for all tanh and logistic unit panels with appropriate parameter selection
  • Set options as instructed in the "%% Sim options" section
• ./figure-code/simulation-code/sim_rand_nets_binary.m produces the data for all binary unit panels with appropriate parameter selection - Set options as instructed in the "%% Sim options" section
• ./figure-code/grid_sim_plotting.m plots the data produced by the simulation codes

Figure 5: Zipf's Law from data and from sampling a log-normal distribution

• all codes are found in the ./Zipf_Figure_Codes/ folder

Figure 6: Infinite limit calculations with logistic f-I curves

• all codes are found in the ./Inf_Logistic_Codes/ folder
• the code inf_logistic_grid.m should run if the other functions are in the same directory
• the code plot_phase_diagram.m should produce the figure so long as its input file is adjusted to match the output file of inf_logistic_grid.m

Figure 8: Probability of multistability in finite circuits

• erf_code_binary_units1.m produces continuous analytic curves
• binary_net_sim_count.m produces simulated data points

Figure 9: Infinite limit calculations for binary response curves

• erfApprox_maxk_infN.m produces the analytic results
• the binary simulation code of Figure 5 or 8 can be adapted to produce Figure 9C

Appendix figures

Figure 10: The dynamic regimes of individual networks changes as $g$ is scaled

• ./figure-code/simulation-code/sim_rand_nets.m produces the data with appropriate parameter selection
  • Set options as instructed in the "%% Sim options" section
• ./figure-code/same_nets_across_g_classes.m plots the data for panels B-F

Figure 11: Simulation results for networks with increasing $N$ converge to the infinite-$N$ analytic results

• ./figure-code/rmsrates_across_g.m creates each panel individually
  • Change the value of figSim to create each panel

Figure 12: Phase diagram for networks with tanh units

• Created as in Figure 6 with the specified parameter values

Figure 13: Impact of the criterion for multistability in networks with logistic units

• Created as in Figure 6 with the specified parameter values

Figure 14: Impact of the criterion for multistability in networks with tanh units

• Created as in Figure 6 with the specified parameter values

Usage notes

• The simulation code can run either locally or on a slurm computing cluster with an array of 100 jobs.
• The ./figure-code/simulation-code/*.sh files run the code on a slurm cluster with each job running one network at each parameter point.
• Data produced by the cluster needs to be combined into a single file with ./figure-code/process_HPCC_sim.m to be plotted by the analysis scripts
• ./figure-code/functions/myPlotSettings.m sets the figure settings for each figure
• ./figure-code/functions/AppendFileNum.m ensures existing data is not overwritten