*2.1. Participants*

This study was carried out in accordance with the latest version of the Declaration of Helsinki [42] and approved by the mandatory Ethics Committees requested by Swiss Federal Authorities, following the constitutional article (art. 118b Cst) of 8 March 2010 and the Federal Act involving Human Beings on 30 September 2011 (revised 1 January 2014). The ADHD patients were recruited either in the Psychiatric Department of the University Hospital of Lausanne or at a psychiatrist's practice in collaboration with the Lausanne University Hospital after an initial screening appointment to ensure that they were fulfilling the criteria defined by the DSM-IV-TR for inattentive, hyperactive/impulsive or mixed subtypes [43]. Subjects with comorbid disorders and subjects taking medications were excluded from this study. We selected 65 young adults between 18 and 30 years old in the two groups of study, controls (*NCTRL* = 37) and ADHD patients ( *NADHD* = 28). Notice that control participants were recruited in the same age-range of the patients and with a similar social and educational background. Controls were screened prior to the experimental session to ensure that they would not report any disorder or exclusion criteria mentioned in the authorization released by the Ethics Committees. All participants were requested to fill French versions of the adult ADHD self-report scale (ASRS) and the Conners' adult ADHD rating scales-self seport: screening version (CAARS-S:SV) [44–46] two weeks prior the begin of the protocol. All participants received a monetary compensation following the scale approved by the mandatory Ethics Committees (Commission cantonale d'ethique de la recherche sur l'être humain, code 101/12) requested by Swiss Federal Authorities.

#### *2.2. Working Memory Task*

In this study the WM task consisted in two variants of the dual *n*-back task aimed at testing the divided attention [47,48]. Briefly, the task is the following. At each trial, an auditory and a visual cue were presented simultaneously during 500 ms, with an interstimulus interval (ISI) set to 3000 ms. The level of difficulty of the task is referred as *n*-back. The participants were asked to memorize the dual modality cues in order to compare the current auditory and visual stimuli with those presented *n*-trials back in time with the value *n* always the same for auditory and visual stimuli. In the conditions under which the current stimulus is not the same as the cue presented *n*-trials earlier, no response was requested by the participants. The participants had to press the "A" key for any visual stimulus matching the same stimulus presented *n*-trials back in time and/or the "L" key for any auditory stimulus matching the same stimulus presented *n*-trials back in time. If the participants did not respond within the fixed ISI, the trial was accounted as no response. Immediately after the response, a green light was switched on for correct response, otherwise a red light indicated a mistake. If "no response" was the correct choice, the green light switched on at the end of the ISI. In the case of baseline level, the difficulty of the task was set to *n* = 1. Figure 1 illustrates the dual *n*-back task at level *n* = 2 of difficulty.

In the case of adaptive level, the difficulty *n* of the task was adjusted as a function of the performance. The whole task consisted of 20 blocks of 20 + *n* trials with the same level of difficulty. An increase by 1 in the level of difficulty in the next block was triggered by a performance of less than three mistakes in each modality. With levels of difficulty higher than 1, a decrease by 1 in the level was triggered by five or more errors cumulated in any modality. The total duration of the working memory task was approximately half an hour.

**Figure 1.** Level *n* = 2 of the dual *n*-back task. Each stimulus was composed by an auditory and a visual cue presented during 500 ms. This means the participants had to compare the third stimulus (S3) with the first one (S1), S4 with S2, S5 with S3, and so on. For the first correct response (R1), no stimuli matched those presented two trials back in time and no key press was requested. For R2, both auditory and visual stimuli matched the target (S4 identical to S2, green arrow)), such that both "A" and "L" key were pressed. For R3, only the auditory stimulus matched the target (red arrow) and only the "L" key was pressed. For R4, only the visual stimulus matched the target (blue arrow) and only the "A" key was pressed. Notice that in this example only correct responses are illustrated.

#### *2.3. Working Memory Training Protocol*

In a pre-training session, at the laboratory, all participants played the adaptive version of the dual *n*-back task. At this session, the participants performed the WAIS-IV (Wechsler Adult Intellicence Scale-Fourth Edition) digit span subtest from the Wechsler adult intelligence scale, which requires participants to sequentially order the numbers (i.e., backward and forward digit span sequencing) presented by the examiner [49], the forward span of the Corsi block-tapping task, which is a visuospatial short-term memory task [50] and the attentional network test (ANT) [51]. The analysis of ANT will be presented in another paper. The WM training started the day after the pre-training session. At home, the participants played the dual *n*-back task by mean of an Internet remote connection to a server with protected access. The strict requirement was to complete at least 18 training sessions within a month. Randomly assigned participants in both controls and ADHD group were requested to perform a WM training either with a fixed baseline level of difficulty, i.e., dual 1-Back, or with a performance-dependent adaptive *n*-level of difficulty. A post-training session similar to the pre-training session was scheduled at the end of WM training [48]. All participants played the adaptive version of the dual *n*-back task at the post-training session. Please notice that all the analyses in this paper refer to the data acquired during the pre-training and the post-training sessions.

#### *2.4. Probability Gambling Task*

The probability gambling task (PGT) used in this study was derived from a modified Gneezy–Potters' task [48,52]. In summary, at the beginning of each trial an amount of 20 points was endowed to each participant. At each trial, the participant had to choose the amount wagered (as illustrated by Figure 2). The probability to win was set to 1/3, which meant a gain equal to 4× the gamble. In the event of a loss, at the end of the trial, the participant loses the entire amount wagered for that trial and keeps the rest of the initial endowment (which was always equal to 20). If the bet was equal to 16, then at the end of the trial the participant would receive 4 points in the event of a loss (i.e., 4 = (20 − 16)) and 68 points in case of a win (i.e., = (20 − 16)+(4 × 16)). Notice that in this study the participant was just informed that the outcome of the bet was determined without any feedback on the amount earned, on the contrary of another study published elsewhere [41]. The click on the selected value of the bet with a mouse button is used as the triggering event for the electrophysiological analysis.

**Figure 2.** Probabilistic gambling task. A trial started when the participant pressed the spacebar (event S in the timeline), followed (20 milliseconds later) by a screen with a message request to select the gamble. This screen stayed on until a response was made by clicking on the selected value of gamble (event 0). The response time was determined by the interval between that message and the selection of gamble. This button click (event 0) was used as triggering event for the electrophysiological analysis. A fixed interval of 4000 ms followed until the end of the trial with the same screen and with the highlighted selected gamble.

#### *2.5. EEG Recording and Analyses*

EEG was recorded using using 64 scalp Ag/AgCl active electrodes with impedances kept below 5 kΩ and referenced to the linked earlobes (ActiveTwo MARK II Biosemi EEG System, BioSemi B.V., Amsterdam, The Netherlands) mounted on a headcap (10/20 layout, NeuroSpec Quick Cap). Two pairs of bipolar electrodes were used to record ocular movements. EEG signals were recorded at 1024 Hz sampling frequency (24 bit resolution) and band-pass filtered between 0.05 Hz and 200 Hz. The selection of the amount to gamble (Figure 2, event 0) detected by a button-click was used to trigger the event-related potentials (ERPs). BrainVision Analyzer 2.0.4 (Brain Products, Gilching, Germany) was used for ERP preprocessing and removal of ocular artefacts by Infomax Independent Component Analysis (*ICA*) [53]. The ERP trials were cut into epochs starting 500 ms before and ending 1000 ms after the trigger. The interval of 500 ms prior to trigger onset was used for baseline correction. After removal of the trials characterized by easily identifiable artefacts, the epochs were visually inspected for contamination by residual minor artefacts. Artefact-free trials were filtered with lower cutoff at 0.1 Hz and upper cut-off at 30 Hz (−12dB/octave). Participants with less than 15 segments

in any of the two recordings were excluded from this study. Analyses on the individual average whole-scalp ERP signals were performed with the software Cartool [54]. Those tests were applied with Bonferroni correction for the number of electrodes with a *p* value threshold at 0.05 [55].
