Our simulation is based on a random network 
of neurons implemented as McCulloch-Pitts neurons 
The discrete time evolution for each neuron is given by the input function Ii
(t) and the output function Ei
(t) with a threshold value of Θi
−60 mV for the generation of an action potential (AP), and with constant c denoting the change in postsynaptic potential triggered by the arrival of an AP at the synaptic cleft 
. Firing neurons either cause a hyperpolarisation or depolarization of ± (0.2 mV–1 mV) 
. For sake of simplicity, we assume a value of ±0.5 mV for the effect of inhibitory and excitatory postsynaptic potentials on the cell membrane and set c
0.5. The effects of a single AP on the postsynaptic membrane potential is not strong enough to generate an AP since the membrane potential returns to its resting potential of −70 mV after a few milliseconds 
. The net effect of spatial summation depends on various parameters 
. In the model, we assume a linear spatial and temporal summation.
Whether the synapses are of the inhibitory or the excitatory type is coded in the randomly generated adjacency matrix aij
. The number of synapses depends on the connection probability in the network which in turn determines the average node degree k of each neuron in the network 
. Existing experimental results could be explained best for k
120. shows the connection probability p resulting in k
120 for different network sizes. These theoretical considerations are substantiated by microscopic analysis of mammal cortical tissue indicating a connection probability of p
0.12 for a cluster of 1,000 neurons and a ratio of 80
20 between excitatory and inhibitory synapses 
Connection probability and network size.
For determining the stimulus intensities, we assume that a single TMS pulse triggers the simultaneous depolarization of neurons 
. Numerical analysis of our network revealed a mean change of 1.25 mV of the synaptic potential per neuron for k
120. Thus, we set the TMS induced disturbance to 160%, 240%, 320% and 400% of the mean change of the synaptic potential which corresponds to a change of 2 mV, 3 mV, 4 mV, 5 mV. One can think of that as the increase caused by the simultaneous spiking of either 4 neighbours (TMS-INTENSITY 4), 6 neighbours (TMS-INTENSITY 6), 8 neighbours (TMS-INTENSITY 8) or 10 neighbours (TMS-INTENSITY 10) 
. These values guarantee stable oscillatory behaviour of the network after the TMS stimulation for all network sizes. The TMS stimulation itself is applied within a period of 7.99 s, beginning at 8,000 s and lasting to 15,999 s. The simulation output is defined as the sum of the output Ei
(t) of all neurons at time t which corresponds to macroscopic properties like the LFP or the surface EEG and will be called equivalent local field potential (eLFP). For the processing of the output ρ(t) () of the model, we selected one segment of 1 s ending immediately before the first (PRE) and one segment of 1 s beginning after the last stimulation (POST). For all combinations of the model parameters TMS-INTENSITY and TMS-FREQUENCY we calculated 20 independent runs, each of the runs incorporating a new, random adjacency matrix (this lead to 4 * 6
24 models times 20 independent runs which leads to 480 model runs). In rare cases ρ(t) showed limit cycle behaviour for certain model runs, which were treated as missing values. In this case the independent run was excluded from the statistics. This left us with 17 independent runs as a source of variance of ρ(t). As the variance originates from the adjacency matrix, which reflects individual interconnection of the neurons, we argue that this would also reflect variations of the network likely to be found in different cortical columns within the same individual or even across individuals.
Typical time course of the output function ρ(t) of the neural network 500 ms before the stimulation (PRE) and 500 ms after the last TMS pulse (POST) for the two intensities TMS-INTENSITY 6 and TMS-INTENSITY 10.
The spectral power of the output ρ(t) is calculated using the Fast-Fourier-Transform (FFT) and averaged within the common frequency bands (delta: 0.5–4 Hz, theta: 4–8 Hz, alpha: 8–12 Hz, beta: 12–24 Hz, gamma: 24–48 Hz). The estimates of the band power are statistically analysed using STATISTICA 6.1. We perform a repeated measures ANOVA with band power as dependent variable for the 17 runs (random factor), the repeated measures factor TIME (2 steps: PRE, POST), and 3 fixed factors: TMS-FREQUENCY (6 steps: 0.5 Hz, 1 Hz, 2 Hz, 5 Hz, 10 Hz, 20 Hz), TMS-INTENSITY (4 steps: 4, 6, 8, 10) and FREQUENCY-BAND (5 steps: delta, theta, alpha, beta, gamma).