Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2013 Nov 14;9(11):e1003311. doi: 10.1371/journal.pcbi.1003311

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© 2013 Habenschuss et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

PMC Copyright notice

A. Typical spike response of the microcircuit model based on [30] comprising 560 stochastic point neurons. Spikes of inhibitory neurons are indicated in red. B. Fast convergence of a marginal for a representative layer 5 neuron (frequency of “on”-state, with ) to its stationary value, shown for two different initial Markov states (blue/red). Statistics were obtained for each initial state from trials. C. Gelman-Rubin convergence diagnostic was applied to the marginals of all single neurons (simple states, ). In all neurons the Gelman-Rubin value drops to a value close to 1 within a few , suggesting generally fast convergence of single neuron marginals (shown are 20 randomly chosen neurons; see panel E for a summary of all neurons). The shaded area below 1.1 indicates a range where one commonly assumes that convergence has taken place. D. Convergence speed of pairwise spike coincidences (simple states (1,1) of two neurons, 20 randomly chosen pairs of neurons) is comparable to marginal convergence. E. Summary of marginal convergence analysis for single neurons in C: Mean (solid) and worst (dashed line) marginal convergence of all 560 neurons. Mean/worst convergence is reached after a few . F. Convergence analysis was applied to networks of different sizes (500–5000 neurons). Mean and worst marginal convergence of single neurons are hardly affected by network size. G. Convergence properties of populations of neurons. Dotted: multivariate Gelman-Rubin analysis was applied to a subpopulation of 30 neurons (5 neurons were chosen randomly from each pool). Solid: convergence of a “random readout” neuron which receives spike inputs from 500 randomly chosen neurons in the microcircuit. It turns out that the convergence speed of such a generic readout neuron is even slightly faster than for neurons within the microcircuit (compare with panel E). A remarkable finding is that in all these cases the network size does not affect convergence speed.

Inline graphic — A. Typical spike response of the microcircuit model based on [30] comprising 560 stochastic point neurons. Spikes of inhibitory neurons are indicated in red. B. Fast convergence of a marginal for a representative layer 5 neuron (frequency of “on”-state, with ) to its stationary value, shown for two different initial Markov states (blue/red). Statistics were obtained for each initial state from trials. C. Gelman-Rubin convergence diagnostic was applied to the marginals of all single neurons (simple states, ). In all neurons the Gelman-Rubin value drops to a value close to 1 within a few , suggesting generally fast convergence of single neuron marginals (shown are 20 randomly chosen neurons; see panel E for a summary of all neurons). The shaded area below 1.1 indicates a range where one commonly assumes that convergence has taken place. D. Convergence speed of pairwise spike coincidences (simple states (1,1) of two neurons, 20 randomly chosen pairs of neurons) is comparable to marginal convergence. E. Summary of marginal convergence analysis for single neurons in C: Mean (solid) and worst (dashed line) marginal convergence of all 560 neurons. Mean/worst convergence is reached after a few . F. Convergence analysis was applied to networks of different sizes (500–5000 neurons). Mean and worst marginal convergence of single neurons are hardly affected by network size. G. Convergence properties of populations of neurons. Dotted: multivariate Gelman-Rubin analysis was applied to a subpopulation of 30 neurons (5 neurons were chosen randomly from each pool). Solid: convergence of a “random readout” neuron which receives spike inputs from 500 randomly chosen neurons in the microcircuit. It turns out that the convergence speed of such a generic readout neuron is even slightly faster than for neurons within the microcircuit (compare with panel E). A remarkable finding is that in all these cases the network size does not affect convergence speed.