DOI: 10.5061/dryad.2m85h
title: Data from: Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations

description: Network models are routinely downscaled compared to nature in terms of
 numbers of nodes or edges because of a lack of computational resources,
 often without explicit mention of the limitations this entails. While
 reliable methods have long existed to adjust parameters such that the
 first-order statistics of network dynamics are conserved, here we show
 that limitations already arise if also second-order statistics are to be
 maintained. The temporal structure of pairwise averaged correlations in
 the activity of recurrent networks is determined by the effective
 population-level connectivity. We first show that in general the converse
 is also true and explicitly mention degenerate cases when this one-to-one
 relationship does not hold. The one-to-one correspondence between
 effective connectivity and the temporal structure of pairwise averaged
 correlations implies that network scalings should preserve the effective
 connectivity if pairwise averaged correlations are to be held constant.
 Changes in effective connectivity can even push a network from a linearly
 stable to an unstable, oscillatory regime and vice versa. On this basis,
 we derive conditions for the preservation of both mean population-averaged
 activities and pairwise averaged correlations under a change in numbers of
 neurons or synapses in the asynchronous regime typical of cortical
 networks. We find that mean activities and correlation structure can be
 maintained by an appropriate scaling of the synaptic weights, but only
 over a range of numbers of synapses that is limited by the variance of
 external inputs to the network. Our results therefore show that the
 reducibility of asynchronous networks is fundamentally limited.
description: Simulation
 databinary/asymm/dist_Kin_scale: data on E-I network of Ginzburg neurons for Fig. 1C. binary/asymm/mcculloch_pitts: data on binary E-I network with population-specific connection probability for Fig. 5. binary/symm: data on binary E-I network with population-independent connection probability, scaled to preserve zero-lag covariances, for Fig. 6. spiking/E_I_LIF_network: data on scaling of network of leaky integrate-and-fire neurons with population-independent connection probability, preserving correlations, for Fig. 7. spiking/inhibitory_LIF_network: data on single-population network of inhibitory leaky integrate-and-fire neurons, for Fig. 2. spiking/microcircuit_param_scan: data on scaling of microcircuit model of Potjans & Diesmann (Cereb Cortex, 2014) with and without regard for covariances, for Figs. 3 and 4.data.tar.gzPython scripts for analysis and plottingfig1.py, fig2.py, fig3.py, fig4.py, fig5.py, fig6.py, fig7.py: reproduce the figures of the paper using the data and additional figure files in this repository. binary_network_asymm.py, binary_network_symm.py, g_gamma_K_scaling.py, ginzburg_network_dist_Kin_scale.py, inhibitory_LIF_network.py: NEST simulation scripts for random recurrent networks. parameters_binary_asymm.py, parameters_binary_symm.py, parameters_ginzburg.py, parameters_inhibitory_LIF_network.py: corresponding parameter files. hambach_run_g_gamma_K_scaling.py, hambach_run_inhibitory_LIF_network.py, hambach_run_sim_dist_Kin_scale.py: scripts for running the corresponding simulations on a cluster. h5py_wrapper.py: for storing and loading h5 files. plotfuncs.py, plot_utils.py, ps_manip.py: general plotting scripts. ginzburg_theory.py, ginzburg_theory_distKin.py, hawkesnet.py, siegert.py: contain functions for computing covariances and related quantities. microcircuit_analysis.py: functions for loading and analyzing data from simulations of the Potjans and Diesmann (Cereb Cortex, 2014) microcircuit model. microcircuit: folder containing NEST simulation scripts for the Potjans and Diesmann microcircuit model.py.tar.gzAccessory figure filesfig_scaling_framework.json: configuration file for Fig. 1. relevant_scales.eps, why_scaling.eps, scaling_as_subsampling.eps: diagrams included in Fig. 1. redistributing_synapes.eps: diagram included in Fig. 6. spiking_network_scaling_diagram.eps: diagram included in Fig. 7.figures.tar.gzSimulation data - submission 2binary/asymm/dist_Kin_scale: data on E-I network of Ginzburg neurons for Fig. 1C. binary/asymm/mcculloch_pitts: data on binary E-I network with population-specific connection probability for Fig. 3. binary/symm: data on binary E-I network with population-independent connection probability, scaled to preserve zero-lag covariances, for Fig. 6. spiking/E_I_LIF_network: data on scaling of network of leaky integrate-and-fire neurons with population-independent connection probability, preserving correlations, for Fig. 7. spiking/inhibitory_LIF_network: data on single-population network of inhibitory leaky integrate-and-fire neurons, for Fig. 2. spiking/LIF_network_rate_comparison: data on E-I network of leaky integrate-and-fire neurons with different firing rates, for Fig. 5. spiking/microcircuit: data on scaling of microcircuit model of Potjans & Diesmann (Cereb Cortex, 2014), for Fig. 4.data2.tar.gzPython scripts for analysis and plotting - submission 2fig1.py, fig2.py, fig3.py, fig4.py, fig5.py, fig6.py, fig7.py: reproduce the figures of the paper using the data and additional figure files in this repository. binary_network_asymm.py, binary_network_symm.py, g_gamma_K_scaling.py, ginzburg_network_dist_Kin_scale.py, inhibitory_LIF_network.py, LIF_network_rate_comparison.py: NEST simulation scripts for random recurrent networks. parameters_binary_asymm.py, parameters_binary_symm.py, parameters_g_gamma_K_scaling.py, parameters_ginzburg.py, parameters_inhibitory_LIF_network.py, parameters_LIF_network_rate_comparison.py: corresponding parameter files. hambach_run_g_gamma_K_scaling.py, hambach_run_inhibitory_LIF_network.py, hambach_run_LIF_network_rate_comparison.py, hambach_run_sim_dist_Kin_scale.py: scripts for running the corresponding simulations on a cluster. h5py_wrapper.py: for storing and loading h5 files. plotfuncs.py, plot_utils.py, ps_manip.py: general plotting scripts. corr_hawkes_like.py, ginzburg_theory.py, ginzburg_theory_distKin.py, hawkesnet.py, siegert.py: contain functions for computing covariances and related quantities. microcircuit: folder containing NEST simulation scripts for the Potjans and Diesmann microcircuit model.py2.tar.gzAccessory figure files - submission 2fig_scaling_framework.json: configuration file for Fig. 1. relevant_scales.eps, why_scaling.eps, scaling_as_subsampling.eps: diagrams included in Fig. 1. redistributing_synapes.eps: diagram included in Fig. 6. spiking_network_scaling_diagram.eps: diagram included in Fig. 7.figures2.tar.gz