**1. Introduction**

The information necessary for complex cognitive tasks, which require the expectation that a relevant stimulus is remembered, must be encoded and maintained in working memory (WM) with

a prior selective attention that is necessary to ignore irrelevant information for further processing. Patients diagnosed with attention deficit/hyperactive disorder (ADHD) are characterized by poor WM, poor concentration, high impulsivity, tendency to excessive talking, impairement in maintaining focused attention and a multiple range of associated disorders [1–4]. Limited or untidy attentional resources in ADHD patients would reduce the anticipation of ensuing stimuli to be remembered and the amount of information that can be encoded [5,6]. Impaired selective attention processes during encoding information in WM and the resulting WM deficits have been observed in ADHD patients in association with altered functional connectivity of cortical and subcortical networks involving, in particular, the prefrontal cortex (PFC) [7–10]. Besides, neurophysiological evidence show that improvement in WM performance is achieved by invariant and distributed neuronal dynamics in the PFC [11].

A growing body of evidence shows that a few weeks of WM training for children and adults suffering from ADHD has positive behavioral and cognitive effects [12–15], Transfer effects reported after WM training [16,17] sugges<sup>t</sup> that such training could be an alternative therapeutic approach to drugs for ADHD patients [18–20]. However, some comprehensive reviews and meta-analyses draw a more skeptical conclusion [21–24]: the training has a limited efficacy, the generalization and the duration of the effects are questionable, and the underlying neurophysiological processes remain unclear.

It is known that WM deficits are associated with impaired decision making in individuals with substance addictions and alcohol-dependency [25,26]. Risky decision making in an experimental task, the Iowa gambling task, is poorly performed by ADHD patients [27,28] and WM impairments characterizing ADHD were suggested to moderate the expression of risky decision-making in patients affected by this disorder [29–31]. Indeed, ADHD patients often choose riskier options with unfavorable outcomes in economic and financial settings [32,33]. More generally, substance use disorders, pathological gambling, and ADHD [26,34–36], as well as healthy participants charged with a high WM load [37], shared deficits in tasks associated with ventral prefrontal cortical dysfunction. On the one hand, the structural abnormalities observed in young adults with ADHD sugges<sup>t</sup> complex audio-visual, motivational, and emotional dysfunctions [38]. The dual *n*-back task, on the other hand, is a WM training task in which the participants have to remember two independent sequences of audio-visual stimuli and must identify when an auditory or visual stimulus matches the one that appeared *n* trials back [39,40].

In the current work, we extend our previous study with EEG recordings, which showed differences in brain dynamics between controls and young adult patients with ADHD during the performance of a probabilistic gambling task [41]. Our working hypothesis is that WM training with the Dual *n*-back task is acting on a top-down modulation of the attentional processes with participation of prefrontal and parietal areas as sources of the efferent control signals. In the current study, we present new evidence that WM training affects selectively the activity of prefrontal cortex of young adult ADHD during a probabilistic gambling task. The P1-like waveform, elicited by the choice of the amount wagered, was restored in ADHD patients after WM training with the *adaptive level* variant of the Dual *n*-back task. We interpret this finding as an improvement of early higher-level mechanisms of attentional control in ADHD after adaptive training. In controls, the level of difficulty of WM training tended to affect late components of the event-related potentials (ERPs) mainly located at parietal areas.

#### **2. Materials and Methods**
