The influence of burst duration on pattern formation.

<p><b>A.</b> Examples of synaptic strength evolution over time. Numbers along the top indicate the input burst duration in seconds. <b>B.</b> Mean power spectra, normalized by the peak power in each spectrum, of the final connectivity patterns in simulations using burst durations of 0.03 s (blue), 0.3 s (orange), and 3.0 s (black). <b>C.</b> Robustness of the periodic connectivity pattern to different burst durations. Reference power spectra are taken from simulations with a burst duration of 0.1 s. Black: robustness measures for each burst duration. Pink: theoretical robustness measure, based on the concentration of power at <i>k</i>* in <math><mrow>Re<mo stretchy="false">[</mo><mi>κ</mi><mo>~</mo><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></math>, normalized to the theoretical robustness for a burst duration of 0.1 s. <b>D.</b> Examples of <math><mrow>Re<mo stretchy="false">[</mo><mi>κ</mi><mo>~</mo><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></math> for burst durations of 0.03 s (blue), 0.3 s (orange) and 3.0 s (black). The negative lobe in the black curve extends beyond the horizontal axis and has been cut for clarity. <b>E.</b> Spatial frequencies of connectivity patterns that developed in simulations as a function of the burst duration (black circles and error bars: mean ± SEM). Grey line: predicted spatial frequencies. The sawtooth fluctuations at longer burst durations correspond to the emergence of new dominant peaks in <math><mrow><mi>κ</mi><mo>~</mo><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow></math>, which is compressed towards lower spatial frequencies as the burst duration is increased. <b>F.</b> Theoretical robustness as a function of burst duration for asymmetric STDP rules with <i>τ</i>₊ = 20 ms (pink) and <i>τ</i>₊ = 50 ms (green).