Network-wide oscillations can enhance or suppress the predicted levels of spike synchrony.

<p>(A) Dependence of <math><mrow>log<msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub></mrow></math> on the difference in preferred phases between two neurons, as computed using models with and without an oscillatory factor. Purple and cyan arrows indicate two different Δ(Φ_<i>pref</i>)s. (B) Bootstrap-generated distribution of <math><mrow>log<msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub></mrow></math> values under the null hypothesis of log<i>ζ</i>₁₂ = 0. Arrowhead shows the value of <math><mrow>log<msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub></mrow></math> computed by the simplified model. Thus, a significantly larger number of synchronous spikes is observed than predicted by the model lacking an oscillatory factor (<math><mrow>log<mo stretchy="false">(</mo><msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>057</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>013</mn></mrow></math>, <i>p</i> value = 0.0025). (C) Including an oscillatory factor in the model yields an accurate prediction of the observed number of synchronous spikes (<math><mrow>log<mo stretchy="false">(</mo><msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>006</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></math>, <i>p</i> value = 0.6775). (D, E) Same as (B,C) for different preferred phases that lead to significantly lower synchrony than predicted when an oscillatory factor is not included in the model (D: <math><mrow>log<mo stretchy="false">(</mo><msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>013</mn></mrow></math>, <i>p</i> value = 0.0025; E: <math><mrow>log<mo stretchy="false">(</mo><msub><mi>ζ</mi><mo>^</mo><mn>12</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>009</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>015</mn></mrow></math>, <i>p</i> value = 0.2700). (F) Dependence of the power on number of trials and <i>ζ</i>. The mean firing rate is 25 Hz. The red and green lines indicate choices of <i>ζ</i> and <i>N</i> for which the power equals 0.8, based on simulation and theory respectively. (G) Same as (F), but the mean firing rate is 10 Hz.