Seventy-five individuals were recruited for the present investigation (33 patients with schizophrenia and 42 healthy controls) in the context of regular consultation at a university hospital in southwest France. All participants provided written informed consent and the study was approved by the national ethics review committee. The Mini International Neuropsychiatric Interview French Version 5.0.0 (MINI, Sheehan et al. ) was used to confirm or rule out DSM-IV-TR diagnoses. Patients met criteria for schizophrenia, were receiving antipsychotic medications and were evaluated as clinically stable outpatients by a staff psychiatrist. Healthy control participants were identified through community postings and were recruited in the absence of lifetime psychotic disorder, lifetime bipolar disorder, and lifetime substance dependence, as well as no other current DSM-IV-TR axis I disorder. All participants were also required to be free from conditions or disability incompatible with the use of a smartphone or any contraindication for an MRI examination.
After verification of eligibility criteria, participants completed a clinical and neuropsychological assessment battery (see below for details) and were then trained to operate a study-dedicated smartphone (Samsung Galaxy S with a 10.6 cm screen, 12-point font size). Following successful completion of this training, they were given a smartphone to carry with them for 1 week and were instructed to respond to five electronic surveys per day. The surveys occurred at random intervals within 5 equal time epochs from morning to evening (approximately every 3 h). A mobile color-word interference test of cognitive performance that was similar to the Stroop test was administered at the end of two of the five daily surveys (for a more detailed description, see below). The average duration of electronic surveys was approximately 5 min. The subsample of individuals who also received an MRI examination did so rapidly (approx. 48 h) before completing clinical testing and EMA. Participants received compensation up to 100 euros in purchase vouchers for the completion of both the EMA and MRI phases of the study.
Clinical and neuropsychological assessment battery
Mini International Neuropsychiatric Interview French version 5.0.0 
The MINI is a brief structured diagnostic interview (median: 15 min), exploring the main clinical disorders of DSM-IV, including substance dependence comorbidity.
Positive and negative syndrome scale 
French version (Lépine et al. 1989). This scale is a hetero-evaluation scale of psychopathological symptoms observed in patients with psychotic syndromes, especially individuals with schizophrenia, based on 30 items ranging from 1 (absent) to 7 (extreme). It allows to calculate the scores of three dimensions: positive symptoms (7 items), negative symptoms (7 items) and general psychopathology (16 items). This scale is administered to patients only.
The Stroop paradigm is a common procedure for measuring executive functions, notably cognitive inhibition. The test is composed of three parts: a word page (color words printed in black ink), a color page (color hues printed in rectangle) and a competing word-color page (e.g., the word ‘red’ printed in blue ink). Each page contains five columns of ten items. Participants were instructed to read the maximum number of words (word page) and name the maximum ink colors as quickly as possible, in 45 s.
EMA surveys and mobile cognitive tests
The EMA surveys included questions about physical location, activity, and mood states at the moment of survey completion, as well as concerning the experience of positive psychotic symptoms since the previous EMA survey. Psychotic symptoms were those validated by previous EMA investigations [7, 39] and included five questions concerning delusions of being spied on, mind reading, thought insertion, thought broadcasting, and having special powers. An additional question assessed the experience of visual or auditory hallucinations. Psychotic symptoms were assessed within each of the five daily electronic questionnaires. The presence of any psychotic symptom at each electronic assessment was defined as endorsement of at least one of these six questions. In other words, the presence or absence of at least one of the psychotic symptoms (as a binary variable) was the main outcome of the behavioral experiment. The mobile test of cognitive performance was similar to the interference trial of the Stroop Test and provided participants with a list of 16 color words (four lines each of “Yellow”, “Red”, “Blue”, and “Green”) and in different colors (also Yellow, Red, Blue, Green). No word was written in the color that matched the meaning of the written word (i.e., the word “Blue” would appear in the colors of red, yellow, and green, but not in blue). The order of words and colors was randomized, and each word and color appeared once per line. Participants were instructed to say the ink color of each word aloud as quickly as possible. Participants were provided a maximum of 60 s to complete the task. When the participants completed this naming, they were instructed to press the ‘finished’ button displayed on the screen that would stop the timing of test. The mobile color-word interference test was presented at the end of two of the five daily electronic questionnaires (providing a maximum of 14 distinct mobile test scores). To avoid biases associated with test repetition or time of the day, fourteen unique versions of the test were administered during the week in an order that was counterbalanced across the different time epochs of the day. Responses were audio recorded on the study smartphones, and each audio file was imported into Audacity® software to determine the precise time needed to complete the task, in seconds. This duration corresponds to the time elapsed between the first word spoken and the last word spoken in relation to the task. Each audio file was listened to and scored independently by two trained raters. Inter-rater reliability for this coding procedure was above r = 0.90. As this test resulted in relatively few errors, the time to complete the mobile color-word interference test was used as the primary measure of cognitive performance.
Based on the present sample, an initial publication examined compliance rates, fatigue effects, training effects and convergent validity . Compliance with the self-report EMA interviews was high for all participants, with 95% of the possible assessments being completed by both controls and patients in the context of their daily lives (resulting in 1654 observations). Examination of compliance with mobile cognitive tests revealed that 88% and 83% of the mobile letter-word generation assessments were completed by controls and patients, respectively. No fatigue effects were observed considering that there was no variation in the number of missing observations occurred as a function of day of the study. Concerning practice effects, defined as the time needed to complete the color-word interference test, a significant decrease was observed as a function of study duration for both groups. Finally, analyses found significant correlations between the mobile test and the traditional Stroop test for both groups, indicating that both measure the same underlying construct.
Brain imaging data were collected using a 3.0 Tesla GE MRI system with a 32-Channel MRI Head Coil. Anatomical MRI volumes were acquired using a sagittal three-dimensional T1-weighted (Repetition Time = 8.5 ms, Echo Time = 3.2 ms, flip angle = 11°, FOV = 256 mm × 256 mm, voxel size = 1 mm × 1 mm × 1 mm, Slice Thickness = 1 mm, 176 slices). The resting-state functional images were collected using a single-shot echo-planar sequence (RT = 2.2 s, ET = 27 ms, flip angle = 80°, FOV = 192 mm × 192 mm, voxel size = 3 mm × 3 mm × 3.5 mm, 42 axial slices). For the resting-state scan, participants were instructed to keep their eyes closed, to not fall asleep and to not think about anything in particular.
Analyses of predicting the occurrence of positive symptoms were conducted only on the sample of patients with schizophrenia. Prospective within-day associations between cognitive performance and psychotic symptoms were analyzed using hierarchical linear and nonlinear modeling . Data were time-lagged so that time to complete the color-word interference test at any given assessment (T0) predicted the presence of psychotic symptoms at the subsequent assessment on the same day (T1). All analyses adjusted for the status of the T outcome variable as measured at the T0 assessment. Bernoulli models were used for dichotomous outcomes (presence or absence of psychotic symptoms). Multiple or exploratory analyses were avoided in light of the a priori hypothesis concerning the impact of cognitive performance on the subsequent occurrence of psychotic symptoms. Figure 1 presents an illustration of the EMA methodology, where red arrows indicate the prospective, within-day association between momentary cognitive performance and later-occurring symptoms. These daily coefficients (or arrows) are then aggregated across days for each individual before being averaged for the sample as a whole.
fMRI data pre-processing and graph analysis
Neuroimaging data in this investigation were based on pre-processing performed using the latest version of FMRIPREP , a Nipype-based tool. For each subject, the T1-weighted (T1w) volume was corrected for intensity non-uniformity (INU) using ANTs N4BiasFieldCorrection v2.1.0  and skull-stripped using ANTs antsBrainExtraction v2.1.0 (using the OASIS template). Spatial normalization to the ICBM 152 Nonlinear Asymmetrical template version 2009c  was performed through nonlinear registration with the antsRegistration tool of ANTs v2.1.0 , using brain-extracted versions of both T1w volume and template. Brain tissue segmentation of cerebrospinal fluid (CSF), white-matter (WM) and gray-matter (GM) was performed on the brain-extracted T1w using fast50 FSL v5.0 . Functional data were slice time-corrected using 3dTshift from AFNI v16.2.07  and motion-corrected using mcflirt (FSL v5.0.9, ). Distortion correction was performed using an implementation of the TOPUP technique  using 3dQwarp (AFNI v16.2.07 ). This was followed by co-registration to the corresponding T1w using boundary-based registration  with nine degrees of freedom, using flirt (FSL). Motion correcting transformations, field distortion correcting warp, BOLD-to-T1w transformation and T1w-to-template (MNI) warp were concatenated and applied in a single step using antsApplyTransforms (ANTs v2.1.0). Six head-motion parameters along with WM and CSF mean signals were used as noise regressors within a GLM framework. In addition, ICA-based Automatic Removal Of Motion Artifacts (AROMA) was used to generate aggressive noise regressors as well as to create a variant of data that is non-aggressively de-noised . Spatial smoothing was avoided following , and bandpass filtering (0.008–0.1 Hz) was performed. Many internal operations of FMRIPREP use Nilearn , principally within the BOLD-processing workflow.
Graph analysis was performed using PyNets (https://github.com/dPys/PyNets). First, for each participant, BOLD signals were extracted from 13 ROIs included in the AAL2 atlas and that fall under an Executive Control Network (ECN) mask created from the intrinsic connectivity 7-Network Yeo atlas . To illustrate the application of graph theory to the Executive Control Network, the data for one example participant were reconstructed by PyNets and are provided in Fig. 2. The Pearson correlation between pairwise ROIs was calculated to create the correlation adjacency matrix for each participant. A proportional threshold strategy was performed to prune negative and weak connections that might be spurious and preserve a percentage of the strongest positive connections . A range of proportional thresholds was used based on previous literature [0.35–0.5] (i.e. the top [35–50%] of the edges of the graph survive thresholding). Binarization was not performed and weighted graph metrics were calculated. Several well-known graph metrics were computed to characterize the participant-level ECN: Global Efficiency, Average Local Efficiency, Small-worldness, Degree Assortativity Coefficient, Average Clustering, Average Shortest Path Length, Graph Number of Cliques, Transitivity, Modularity, and Coreness . The different metrics are calculated from elementary properties of the graphs, including degree (the number of links of a given node), path (the sequence of edges connecting a set of successive nodes) and length (the number of edges constituting the path).
Finally, a two-level statistical model was then constructed using hierarchical linear and nonlinear modeling to explore the correlations between average prospective relationships of cognition and positive symptoms during EMA period and graph theory metrics of the Executive Control Network. The first level included variability in time-lagged EMA ratings of cognitive performance (time, measured in seconds, to complete a color-word interference test) and its association with later positive symptoms, nested within persons. The second level included between-person variability in the person-level index of connectivity (graph theory indexes: Global Efficiency, Average Local Efficiency, Smallworldness, Degree Assortativity Coefficient, Average Clustering, Average Shortest Path Length, Graph Number Of Cliques, Transitivity, Modularity, Coreness). This two-level model indicated association between average prospective relationships of cognition and positive symptoms during EMA period and an index of connectivity. In other words, this model would identify cross-level interactions, which would indicate that the within-person and prospective associations between cognitive performance and symptoms varied as a function of individual difference in graph theory indices.