Probability distribution <i>W</i>_<i>G</i> in function of the individual payoff <i>π</i>_<i>i</i>, as defined in Eq 1, considering four different values of <i>π</i>_<i>g</i> (see the legend).

<p>The black dotted line separates the ‘group phase’ from the ‘individual phase’, i.e. the values of <i>W</i>_<i>G</i> supporting the conservation of groups and those that lead to the emergence of individual behaviors.</p

Average number of breaking groups < <i>B</i>(Δ<i>T</i>) > in the time interval Δ<i>T</i>.

<p>The legend indicates, for each line, the considered group size <i>G</i>. <b>a</b>) Results achieved with <i>L</i> = 3. <b>b</b>) Results achieved with <i>L</i> = 25. <b>c</b>) Comparison between results achieved with <i>L</i> = 3 and <i>L</i> = 25. Results have been averaged over different simulation runs.</p

Density of groups <i>ρ</i>_<i>g</i> in function of the ‘individual payoff’ <i>π</i>_<i>i</i>, for different spin vectors of length <i>L</i>, on varying the group size <i>G</i>.

<p><b>a</b>) <i>G</i> = 2. <b>b</b>) <i>G</i> = 10. <b>c</b>) <i>G</i> = 25. <b>d</b>) <i>G</i> = 50. Results have been averaged over different simulation runs.</p

Phase diagram of the population, with groups of size <i>G</i> versus the ‘individual payoff’ <i>π</i>_<i>i</i>, on varying the length of the spin vectors <i>L</i>.

<p>Yellow indicates the ‘group phase’, while Blue the ‘individual phase’. <b>a</b> <i>L</i> = 3 and <b>b</b> <i>L</i> = 10. The pictorial representation on the left aims to show groups of different size <i>G</i>, that we can observe in nature. Results have been averaged over different simulation runs.</p

Example of the parameters required to define the methods for an experiment on 5 variables.

<p>In the second column the instantaneous effects are neglected both for targets and conditioning. In the third column we set instantaneous effects for some drivers and the respective targets. For example, when the target is 1, instantaneous effects are taken into account for driver 2 (first two rows, right column, parameter <i>idDrivers</i>) and conditioning variable 3 (first row, right column, parameter <i>idOtherLagZero</i>).</p><p>Example of the parameters required to define the methods for an experiment on 5 variables.</p

Simulated system.

<p>Interactions between the variables of the simulated system.</p

ROC curves for all methods for the non-linear system.

<p>The curves are obtained reporting the results obtained gradually increasing the time series length simulated according to 14 from 128 to 1024 points.</p

TE values versus the number of significant realizations, non-linear system.

<p>For time series of 512 points simulated according to 13, the links retrieved by the different methods are reported. The five simulated links are red; those who are not present in the model are blue.</p

TE matrices for human EEG recordings.

<p>Matrices of Transfer Entropy among the 76 intracranial contacts implanted in an epileptic subject. Contacts 1 to 64 belong to a cortical grid, contacts 65 to 76 to two strips implanted in deeper structures. Transfer Entropy values are obtained with three approaches to non-uniform embedding considering ten seconds of brain activity in the pre-ictal phase (top panels) and ictal phase (bottom panels). The color scale reflects Transfer Entropy values, the shading is inversely proportional to the significance: brighter colors correspond to more significant values.</p

How to set the input parameters: an example.

<p>How to set the input parameters: an example.</p