# Differences in Performance of ASD and ADHD Subjects Facing Cognitive Loads in an Innovative Reasoning Experiment

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## Abstract

**:**

**the multiscale entropy (MSE)**, in the 14 channels (‘brain regions’). MSE, a nonlinear information-theoretic measure of complexity, was computed to extract a feature that quantifies the complexity of the EEG.

**Behavior-Partial Least Squares Correlation, PLSC**, is the method to detect the correlation between two sets of data, brain, and behavioral measures.

**-PLSC**, a variant of PLSC, was applied to build

**a functional connectivity**of the brain regions involved in the reasoning tasks.

**Graph-theoretic measures**were used to quantify the complexity of the functional networks. Based on the results of the analysis described in this work, a mixed 14 × 2 × 3 ANOVA showed significant

**main effects of**

**group factor**and

**brain region* syllogism**

**factor**, as well as a significant

**brain region* group interaction**.

**There are significant differences between the means of MSE (complexity) values at the 14 channels of the members of the ‘pathological’ groups of participants, i.e., between ASD and ADHD, while the difference in means of MSE between both ASD and ADHD and that of the control group is not significant. In conclusion, the valid–invalid type of syllogism generates significantly different complexity values, MSE, between ASD and ADHD. The complexity of activated brain regions of ASD participants increased significantly when switching from a valid to an invalid syllogism, indicating the need for more resources to ‘face’ the task escalating difficulty in ASD subjects. This increase is not so evident in both ADHD and control.**Statistically significant differences were found also in the behavioral response of ASD and ADHD, compared with those of control subjects, based on the principal brain and behavior saliences extracted by PLSC. Specifically, two behavioral measures, the emotional state and the degree of confidence of participants in answering questions in Aristotle’s valid–invalid syllogisms, and one demographic variable, age, statistically and significantly discriminate the three groups’ ASD. The seed-PLC generated

**functional connectivity networks**for ASD, ADHD, and control, were ‘projected’ on the regions of the

**Default Mode Network (DMN)**, the ‘reference’ connectivity, of which the structural changes were found significant in distinguishing the three groups. The contribution of this work lies in the examination of the relationship between brain activity and behavioral responses of healthy and ‘pathological’ participants in the case of cognitive reasoning of the type of Aristotle’s valid and invalid syllogisms, using PLSC, a machine learning approach combined with MSE, a nonlinear method of extracting a feature based on EEGs that captures a broad spectrum of EEGs linear and nonlinear characteristics. The results seem promising in adopting this type of reasoning, in the future, after further enhancements and experimental tests, as a supplementary instrument towards examining the differences in brain activity and behavioral responses of ASD and ADHD patients. The application of the combination of these two methods, after further elaboration and testing as new and complementary to the existing ones, may be considered as a tool of analysis in helping detecting more effectively such types of disorders.

## 1. Introduction

#### 1.1. The Structure of Aristotle’s Syllogism and Its Relation to Cognitive Processes

- A: All X are Y
- I: Some X are Y
- E: No X is Y
- O: Some X are not Y

**valid reasoning**). In his famous work ‘ORGANON—Prior analytics’ [19,20], the great philosopher presents a series of statements (the ‘building blocks’) in the process of reasoning that leads to a valid conclusion with absolute certainty. The

**dual processing**model for the logical reasoning [25,26,27], is developed to help understand how the brain functions when a subject is ‘engaged’ in this type of reasoning. A natural question that is generated is whether Aristotle’s valid and invalid syllogism induce the same or different mental processes in the brain. This is a current, still open, and challenging research question, aiming at shedding light on the fundamental operation of reasoning, in its two extreme conditions. A work related to the study of EEG activity in different brain regions in the case of healthy participants exposed in valid and paradoxes syllogisms has been analyzed in the work of our team [28,29,30].

#### 1.2. Syllogistic Reasoning, Linguistic, and Visuo-Spatial Systems and Executive Function (EF)

**Executive function (EF)**is a severe term used to explain the maintenance of effective goal-directed behaviors such as cognitive, emotional, and physical self-control, all referred to as

**mental control processes**. Working memory, planning, cognitive flexibility, response inhibition, and fluency are all functions of the EF, and play a crucial role in performing complex cognitive processes. It seems natural therefore to consider these dimensions of EF as related to the cognitive loads induced by the Aristotle’s syllogisms that involve or ‘activate’ some of the above EF. As we describe below, EF is measured by specific multidimensional psychometric instruments that all include the emotional control construct, used also in the current work. Since the main aim of this paper is to detect the shared information (correlation-association) between brain activity in various regions and behavioral data, the knowledge of the brain regions that are strongly ‘linked’ to EF is of high importance in our work in seeking similar strong link between Aristotle’s reasoning process and brain regions.

**basal ganglia**,

**thalamus,**and

**prefrontal cortex**as well as prefrontal areas of the

**frontal lobe**, are all important regions helping EFs perform cognitive processes [35]. Plenty of research shows that basic brain regions that are responsible for EF are those that are affected by ADHD and ASD [36,37], a fact that is supported by the deficits in EF shown in patients with neurodevelopmental disorders such as ASD and ADHD [38,39]. Symptoms of those deficits recorded in ADHD referring to response inhibition and working memory deficit [40] while in ASD referring to primary deficit in flexibility and planning [41].

**Behavior Rating Inventory of Executive Function (BRIEF**), which uses parents’ ratings of their children’s performance of daily executive tasks [42].

**Emotional control,**is one of the 19 cognitive dimensions of BRIEF used in the work of [43], an application of PLSC to explore the relationship between cognitive ability patterns and the differences in local brain anatomy measured by MRI. In the present paper, the emotional control dimension is also included in the behavior matrix, but taken from another instrument, the

**SAM (Self-Assessment Manikin),**[44] (see Section 2.4.2 and in Supplementary Materials). The reason for selecting the emotional control in the behavioral data matrix is its high correlation with five of the 19 most important constructs in testing the overall cognitive ability of an individual, namely the monitor (0.59), organize material (0.35), plan/organize (0.51), working memory (0.45), and initiate (0.55), with numbers indicating the correlation [43].

#### 1.3. Complexity and MSE in Normal and ‘Pathological’ Conditions

#### 1.4. Emotional Regulation (ER) or Control in ASD and ADHD

## 2. Materials and Methods

#### 2.1. The Workflow

#### 2.2. Participants

#### 2.3. EEG Recordings

#### 2.4. Tasks Description. The Aristotle Experiment

#### 2.4.1. Stimuli and Procedures Stimuli

#### 2.4.2. Behavioral Data and Procedure

#### 2.5. The Partial Least Square Correlation (PLSC) Method

_{n}between each condition-wised sub-matrix (X

_{n}, Y

_{n}) is stacked one below the other to form the total-combined correlation matrix R, which finally is decomposed by Singular Value Decomposition, SVD. The behavior matrix Y contains the same variables in both studies, one demographic (age) and two neuropsychological (emotional state and level of confidence of participants. The rows of Y are the same participants as in matrix X and its columns are the participants’ age, and values of emotional state and confidence level. Both X and Y are centered (the mean is subtracted) and normalized within each group n (X

_{n}and Y

_{n}are centered and normalized independently, so the sum of squares of a column in say ASD is equal to 1). The matrix of correlations for each group n is computed as ${\mathit{R}}_{\mathit{b}\mathit{e}\mathit{h}\mathit{a}\mathit{v}\mathit{i}\mathit{o}\mathit{r}}={\mathit{Y}}_{\mathit{b}\mathit{e}\mathit{h}\mathit{a}\mathit{v}\mathit{i}\mathit{o}\mathit{r},\mathit{n}}^{\mathit{T}}{\mathit{X}}_{\mathit{n}}$. This matrix is the input to the SVD. ${\mathit{R}}_{\mathit{b}\mathit{e}\mathit{h}\mathit{a}\mathit{v}\mathit{i}\mathit{o}\mathit{r}}$ contains the correlation of each of the j = 14 EEG or MSE values (at each channel) in X with each of the k = 3 behavioral measures (age, emotional state, confidence) in Y within each of the N = 3 conditions or ASD, ADHD, and control groups. Thus, R will contain N × K rows and J columns, as shown below:

**U**is the N × K row and L column matrix of the saliences for the behavioral measures, with L the rank of ${\mathit{R}}_{\mathit{b}\mathit{e}\mathit{h}\mathit{a}\mathit{v}\mathit{i}\mathit{o}\mathit{r}}$, and Δ the diagonal matrix of singular values, and finally,

**V**the J × L matrix of the saliences of the brain activity.

**U**matrix of behavioral saliences indicate EEG- (or MSE-) dependent differences in the brain–behavior correlation, or equivalently the interaction of the experimental conditions with the behavioral measures. Brain saliences

**V**reflect EEG-dependence differences in the brain behavior correlation.

**U**, reflecting the differences in the behavior. According to [1], in order to assess the reliability of the brain–behavior association, confidence intervals must be estimated.

**U**against each behavioral variable is needed (see Section 3, results). In order to express the saliences in terms of brain activity and behavior, the original matrices

**X**and

**Y**are projected onto their respective saliences, and this projection creates the latent variables that are linear combinations of

**X**and

**Y**. PLSC searches for latent variables that express the largest amount of shared information of

**X**and

**Y**(i.e., latent variables with maximal covariance).

**Lx**of

**X**and

**L**of

_{Y}**Y**are computed from the aforementioned respective saliences. To recall,

**L**is called Brain Scores and

_{x}**L**behavior sores, and both matrices have I rows and

_{Y}**L**columns. The Brain Scores are given by

**L**. The latent variables for behavior per group is given by the product of the rows of

_{x}= XV**Y**and

**U**corresponding to each group. The combined behavior scores are formed by concatenating the group-wise behavior scores, so the latent variable for the n-th group is given as follows:

**L**matrix is finally formed as ${\mathit{L}}_{\mathit{Y}}=\left(\begin{array}{c}{\mathit{L}}_{\mathit{Y},1}\\ {\mathit{L}}_{\mathit{Y},2}\\ {\mathit{L}}_{\mathit{Y},3}\end{array}\right)$.

_{Y}**L**and

_{x}**L**is not done with the typical way. We can use however PCA style plots, as shown in the results section, which can help us in observing how the first and second brain scores separates the participants in ASD, ADHD, and control groups from each other, and similarly how the first and second behavior scores does the same thing. Permutation tests are also performed, as described below, to enhance the reliability of the results and extend them to the population. Figure 3, the ‘construction’ of all the matrices and sub-matrices involved in the PLSC application on the data of the current study.

_{Y}_{X}and Z

_{Y}, respectively. The following relation describes the common information in the two matrices

_{R}

_{,}in centered and normalized form). Z

_{R}is the variable that is used further in this analysis, and its SVD decomposition is written

_{R}, then U is a J x L orthonormal matrix of left singular vectors, V is the K × L orthonormal matrix of right singular vectors, and Δ is L × L diagonal matrix (the off-diagonal elements of Δ are all 0). The elements of diag{Δ} are the singular values (with ordering from larger to smallest). The eigenvalues (the squared singular values) describe the variance of the data extracted by the components. The matrices of singular vectors U and V in the PLSC ‘vocabulary’ are called saliences [1,92]. To correspond these variable with those in PCA (Principal Component Analysis), the matrices UΔ and VΔ are ‘equivalent’ to principal (factor) scores [105]. The original variables Z

_{X}and Z

_{Y}, in PLSC, are combined linearly to create pairs of latent variables (each pair has one latent variable from Z

_{X}and one from Z

_{Y.}The latent variables of Z

_{X}and Z

_{Y}are given by

_{X}= Z

_{X}U and L

_{Y}= Z

_{Y}V

_{X}is called brain scores, and matrix L

_{Y}is called behavior or design scores.

_{X}and Z

_{Y}, respectively, called latent variables, denoted l

_{X}and l

_{Y,}computed as ${\mathit{l}}_{\mathit{X}}={\mathit{Z}}_{\mathit{X}}\mathit{u}$ and ${\mathit{l}}_{\mathit{Y}}={\mathit{Z}}_{\mathit{Y}}\mathit{v}$, respectively, and have maximal covariance, expressed as follows:

_{X}and Z

_{Y}, the coefficients have unit norm

_{X}and L

_{Y}that contain the coefficients of the linear transformations, which are given as follows:

_{X}and L

_{Y}attains the maximum possible value, and when l = 2, the covariance between L

_{X}and L

_{Y}has also the maximum possible value, but now under the constraints that the second pair of the latent variables are orthogonal. The relationships between the jth column of X and the kth column of Y is measured by the scalar product of these two columns. Due to centering of these matrices, as mentioned above, the scalar product gives the covariance between the two columns. The product reflects the correlation between them, when in addition to the centering, the columns are also normalized (transformed to z-scores). Since correlation and covariance do not depend on the order of the variables, they are not directional, so the roles of X and Y are symmetric and the analysis concentrates on shared information [88]. Once more, PLSC computes latent variables with maximal covariance.

#### 2.5.1. Common Inertia in PLSC and Significance of Inferences in PLSC and Permutation Test

_{total}

**Δ**), and L is the number of nonzero singular values of R.

_{perm}, reflects now only random associations of the original data (due to randomization of rows in X), and the SVD analysis in (2) is repeated again, giving new singular values. We note here that SVD on the original R corresponds to fixed effect model. The overall index of effect ${\mathit{I}}_{\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}}$ (i.e., the common inertia) is computed repetitively for a large number of times (in our case 10,000 times). Then, the probability distribution is ${\mathit{I}}_{\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}}$. If the common inertia computed for the sample is rare (for example <5%), then this index is statistically significant (the test actually corresponds to an omnibus test that tests the overall effect).

#### 2.5.2. Brain Functional Connectivity Analysis via Seed-PLSC within the Default Model Network (DMN). ASD and ADHD Abnormalities in DMN’s Connectivity

#### DMN

#### Seed-PLS Functional Connectivity and DMN

_{seed}is the matrix formed by the columns of X corresponding to channels F3 and F4. According to the methodology, these two columns are removed now from the X matrix, which now becomes X

_{seed}. Because of these two changes in X and Y, we obtain a new correlation matrix, the R

_{seed}, which now contains the correlation of each of the j-2 MSE values in X

_{seed}with each of the k seed MSEs in Y

_{seed}within each of the n = 3 conditions (ASD, ADHD, control). The R

_{seed}correlation matrix becomes

_{seed}) and the MSE values in X

_{seed}represents their functional connectivity. The pattern of this connectivity can be illustrated by plotting the saliences for the brain V into a glass brain to show how strongly the seed MSE values correlate with the rest of the brain. The matrix U of the seed saliences indicate the differences in the seed MSEs across experimental conditions. Thus, in a similar way as in the behavior-PLSC one, a separate plot of each column of U against each seed MSE shows how the experimental conditions (here the different groups) interact with the seed MSEs. The results of the application of seed-PLSC are presented in Section 3.3.

#### 2.5.3. Graph-Theoretic, Functional Connectivity Measures Applied on Seed Brain Salience Matrix V

#### Multiscale Entropy MSE

_{E}) over several timescales on coarse-grained data [47,48]. Sampling entropy measures the order or irregularity of a signal. Let the EEG signal be presented as $=\left\{{\mathit{x}}_{1},{\mathit{x}}_{2},\dots ,{\mathit{x}}_{\mathit{N}}\right\}$, then S

_{E}is defined as

#### ${S}_{E}$ is computed for each time-series ${\mathit{y}}_{\mathit{j}}^{\left(\mathit{\tau}\right)}$

**Figure 5.**(

**a**) The procedure for coarse-graining (Adapted from Costa et al. [47]). (

**b**) Comparison of MSE curves (linear x y scales) for the three stochastic noises and three EEGs at channel 5 (indicative), for the invalid type of syllogism, and for the three groups of subjects (control, ASD, and ADHD). (

**c**) MSE curves vs. time scales, in log–log scales, for subject #23 and channel 8, for invalid type of syllogism. The red line set the borders of frequency bands (gamma, beta, alpha, theta, and delta). (Taken from Papaioannou A. et al. [155]).

## 3. Results

#### 3.1. Mixed ANOVA and Multi-Dimensional Chi Square Analysis of MSE Values

_{(2,60)}= 3.564, p = 0.034). The Mauchly’s test of sphericity W = 0.022 is significant (p = 0.000), so the assumptions behind the normal within-subjects ANOVA are violated, thus the reported F is epsilon corrected and the p value is also the corrected p value.

_{(13,780}= 12.677, p = 0.000), and the channel * group interaction is also significant (F

_{(26,780)}= 2.677, p = 0.000). The syllogism main effect is not significant, F

_{(1,60)}= 2.263, p = 0.138. Also, the syllogism* group interaction is not significant, F

_{(2,60)}= 0.985, p = 0.379. The channels* syllogism interaction is not significant, F

_{(13,780)}= 0.983, p = 0.466. Finally, the channels* syllogism*group interaction is not significant, F

_{(26,780)}= 1.103, p = 0.329

^{2}), in order to quantify how large each effect is. The significant main effect of channels has η

^{2}= 0.174, indicating that this variable, when removing the effects of the other variables and interactions, explains 17.4% of the variance. Similarly, the significant two-way interaction of channels * group has η

^{2}= 0.082 and explains 8.2% of the variance. No other effects are significant.

#### 3.1.1. Behavioral Performance: X^{2} Multidimensional Test

^{2}= 31.08, df = 14, p = 0.05). Also, there is a significant relationship between arousal emotion and education (Χ

^{2}= 72.76, df = 21, p = 0.000). We observed also a significant relationship between control emotion and the left- or right-handed feature (Χ

^{2}= 35.00, df = 12, p = 0.000). No associations were found between emotion dimensions and all groups for the invalid syllogism. Figure 7, Figure 8 and Figure 9 depict the variation of the above interactions with group. We comment below on these findings, referring to relevant literature for support. Based on Figure 7 and Table 8, which shows the self-reported scores of the participants on the valence and arousal dimensions of their emotional state during the reasoning tasks, we have constructed Figure 7c, the 2-D plot of the circumplex model of affect [100,101]. From the plot, we observe three distinct clusters: (a) the ASD valid–invalid characterized by low valence medium arousal and medium valence medium arousal respectively, (b) the ADHD valid and invalid, characterized by low valence high arousal (LVHA), and (c) the control valid–invalid, with low valence, high arousal (LVHA).

#### 3.2. Behavior-PLSC and Seed-PLS Results

#### 3.2.1. Brain Saliences Scores

**valid**and

**invalid**syllogism, respectively.

#### 3.2.2. Behavior Saliences Scores: Age-Group, Emotion State-Group, and Level of Confidence-Group Interactions

#### 3.2.3. Projections of the Brain–behavior Correlation Matrix on Channels. The ‘Heat Map’

#### 3.2.4. Projection of the Brain Saliences Matrix V on Channel (Brain) Locations

#### 3.3. Results of Seed-PLS for Functional Connectivity

**a**) , and the Brain saliences matrix V reflecting the activated regions of the brain due to seed regions F3 and F4 activations, for the invalid syllogism, (b).

- F3: Left dorsal lateral Prefrontal Cortex (l-DLPFC)
- F4: Right dorsal lateral Prefrontal Cortex (r-DLPFC)
- Middle distance between of AF3 and AF4: medial PFC (mPFC) (a proxy)
- Middle distance between P7 and P8: Precuneus/posterior cingulate (PCC) (a proxy)
- P7: Left lateral parietal (l-LP)
- P8: Right lateral parietal (l-LP)
- T7: Left inferior Temporal (l-infT) (T7 a proxy)
- T8: Right inferior Temporal (r-infT) (T8 a proxy)

## 4. Discussion and Conclusions

## Supplementary Materials

**a**), Distribution of I_(total_perm) (10000 permutations), for the case of MSE feature, valid type of syllogism (

**b**). Table S1: Demographics of group of participants, used in the mixed ANOVA and X2 analysis, Table S2: Descriptive statistics of all variables involved in the mixed ANOVA and X2 analysis, Table S3: MANOVA analysis, Results of multivariate tests of the channel*group and channels*syllogism interactions. Manova tests (e.g Wilk’s lamda) > 0.14 show large effects, Table S4: Results of the test of spherisity in the mixed ANOVA analysis. Since W=0.022 is significant, the reported F value is epsilon corrected, Table S5: Results of mixed ANOVA to test within-subjects effects, for MSE values, Table S6: Independent ANOVA ANALYSIS, as support to the mixed ANOVA, Table S7: Estimated marginal means for group factor, Table S8: Estimated marginal means for Channels factor, Table S9: Estimated marginal means for Syllogism factor, Table S10: Mixed ANOVA iteractions effects groups*channels, Table S11: Mixed ANOVA iteractions effects groups*syllogism, Table S12: Mixed ANOVA iteractions effects channels*syllogism, Table S13: Mixed ANOVA iteractions effects groups*channels*syllogism.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) An indicative workflow. Our approach (path) is from raw data to preprocessing, Multi Scale Entropy (MSE) in combination with Partial Least Square Correlation, applied on CBD (Cognitive-Behavioral-Demographic) data. (

**b**) A work flow of PLSC for analyzing brain and behavioral data in the current study. Entropy values (MSE) were extracted from EEGs and used as input to PLSC (Study B).

**Figure 3.**Construction of matrices X, Y, and extracted correlation matrix R. The observations (mean of EEG or MSE per subject) are arranged according to 3 conditions (ASD, ADHD, and control). X, Y are normalized within condition. The matrix of correlations R

_{n}between each condition-wised sub-matrix (X

_{n}, Y

_{n}) are stacked one below other to form the total-combined correlation matrix R, which finally is decomposed by singular value decomposition, SVD.

**Figure 6.**Marginal means of complexity (MSE), for each group of participants for valid and invalid syllogisms. When passing from valid to invalid cognitive load in the ASD group, the complexity increases.

**Figure 8.**Arousal dimension of emotion scores versus education levels of participants in the groups.

**Figure 9.**Control dimension of emotion scores versus handedness (right or left-handed participants) in the groups.

**Figure 10.**Time series of average MSE values at channels per subject, extracted from EEGs recorded at participant’s scalp, when they are exposed in a cognitive load induced by a

**valid**syllogism.

**Figure 11.**(

**a**) Time series of average MSE values at channels per subject, extracted from EEGs recorded at participant’s scalp, when they are exposed in a cognitive load induced by an

**invalid**syllogism. (

**b**) Plot of squared singular values and percentage of the total variance explained. The first four singular values explain about 95% of the variance. It shows actually the effect of dimensionality reduction attained by the action of the SVD on the Correlation matrix R. Case: Valid syllogism. (

**c**) Plot of squared singular values and percentage of the total variance explained. The first four singular values explain about 95% of the variance. It shows actually the effect of dimensionality reduction attained by the action of the SVD on the correlation matrix R. Case: invalid syllogism.

**Figure 12.**(

**a**) Plot of first and second brain scores (latent variables), based on the average per subject MSE, for

**valid**type of syllogism. (

**b**) Plot of first and second

**behavior**(Design)

**scores**(

**latent variables**), based on the average per subject MSE, for

**valid**type of syllogism.

**Figure 13.**(

**a**) Plot of first and second

**brain scores**(

**latent variables**), based on the average per subject MSE, for

**invalid**type of syllogism. (

**b**) Plot of first and second

**design scores**(

**latent variables**), based on the average per subject MSE, for

**invalid**type of syllogism.

**Figure 14.**(

**a**) 1st behavior salience,

**valid**syllogism. The 1st behavior salience reveals the difference ASD and the other groups for age (‘maturation effect’) and the difference between control and other groups for percent of certainty (or degree of confidence). No difference was found in emotional state for all groups. (

**b**) 1st behavior salience,

**invalid**syllogism. The 1st behavior salience reveals the difference ASD and the other groups for age (as in the valid case) and the difference between control and other groups for percent certainty and difference between ASD and the other two groups in the emotional state.

**Figure 15.**(

**a**) 2nd behavior salience,

**valid**syllogism. (

**b**) 2nd behavior salience, invalid syllogism. This salience reveals the difference between ADHD (strong negatively correlated) from ASD and control for age, no differences in emotional state, and difference between ASD and other two groups for percent certainty, having also different signs in correlation.

**Figure 16.**Heat map of the correlation matrix

**R**between brain and behavior matrices for the

**valid**syllogism.

**Figure 17.**Heat map of the correlation matrix

**R**between brain and behavior matrices for the

**invalid**syllogism.

**Figure 18.**(

**a**) Plot of saliences for brain matrix

**V**(right singular vectors) row-wise. Each plotted row corresponds to a channel and depicts how the MSE dependent differences in brain–behavior correlations weigh on that channel, in the case of

**valid**syllogism. (

**b**) Plot of saliences for brain matrix

**V**(right singular vectors) row-wise. Each plotted row corresponds to a channel and depicts how the MSE dependent differences in brain–behavior correlations weight on that channel, in the case of invalid syllogism.

**Figure 19.**Location of intense behavior by group interaction effects (correlations >0.40), in both valid and invalid syllogism.

**Figure 20.**Plot of first seed salience vs. seeds 1 and 2 (MSE values at F3 and F4, respectively), for all groups, in the valid syllogism.

**Figure 21.**Plot of second seed salience vs. seeds 1 and 2 (MSE values at F3 and F4, respectively), for all groups, in the valid syllogism.

**Figure 22.**Heat map of the brain salience matrix V extracted by SVD of correlation matrix R between brain X and seed Y matrices, for the valid syllogism.

**Figure 23.**Heat map of the brain salience matrix V extracted by SVD of correlation matrix R between brain X and seed Y matrices, for the invalid syllogism.

**Figure 24.**Measures of centrality of the network generated by the brain salience matrix V, for the valid syllogism. The rows and columns of V are the nodes of the network, while the links correspond to elements of the weight matrix W (normalized V and taking its elements with a threshold = 0.20, i.e., retaining the 20% of the strongest links).

**Figure 25.**Adjacency matrix of the network generated by the brain salience matrix V, for the valid syllogism. The rows and columns of V are the nodes of the network, while the links correspond to elements of the weight matrix W (normalized V and taking its elements with a threshold = 0.20, i.e., retaining only the 20% of the strongest links). The density of the network is 0.400.

**Figure 26.**Measures of centrality of the network generated by the brain salience matrix V, for the invalid syllogism. The rows and columns of V are the nodes of the network, while the links correspond to elements of the weight matrix W (normalized V and taking its elements with a threshold = 0.20, i.e., retaining the 20% of the strongest links).

**Figure 27.**Adjacency matrix of the network generated by the brain salience matrix V, for the invalid syllogism. The rows and columns of V are the nodes of the network, while the links correspond to elements of the weight matrix W (normalized V and taking its elements with a threshold = 0.20). The density of the network is 0.370.

**Figure 28.**Plot of first seed salience, vs. seeds 1 and 2 (MSE values at F3 and F4, respectively), for all groups, in the invalid syllogism.

**Figure 29.**Plot of second seed salience, vs. seeds 1 and 2 (MSE values at F3 and F4, respectively), for all groups, in the invalid syllogism.

**Figure 30.**(

**a**) Brain saliences matrix V reflecting the activated regions of the brain due to seed regions F3 and F4 activations, for the valid syllogism. (

**b**) Brain saliences matrix V reflecting the activated regions of the brain due to seed regions F3 and F4 activations, for the invalid syllogism.

**Figure 31.**(

**a**) The seven major brain functional networks (from Raichle M., 2001, freely available in ftp://imaging.wustl.edu/pub/raichlab/restless_brain, accessed on 8 November 2021) [148], used in this work to correspond our activated regions, due to seeds F3 and F4, with regions of the above major brain networks. (

**b**) Connectivity network generated via seed-PLSC approach, when using electrodes F3 and F4 as seeds, for the case of valid syllogism. Lines of different colors correspond to different groups of participants, indicating which other electrodes are activated during the valid syllogism. The seeds have been chosen as the brain regions involved in emotion regulation and goal-specific working memory during a cognitive task (here the valid syllogism), based on the literature review. The lines connecting the F3 and F4 seed electrodes with the rest of electrodes are based on the seed brain salience matrix V heat map values (>0.3), Figure 22 and Figure 23, for valid and invalid cases, respectively. (

**c**) Connectivity network generated via seed-PLSC approach, when using electrodes F3 and F4 as seeds, for the case of invalid syllogism. Lines of different colors correspond to different groups of participants, indicating which other electrodes are activated during the valid syllogism. The seeds have been chosen as the brain regions involved in emotion regulation and goal-specific working memory during a cognitive task (here the valid syllogism), based on the literature review. The lines connecting the F3 and F4 seed electrodes with the rest of electrodes are based on the seed brain salience matrix V heat map values (>0.3), Figure 22 and Figure 23, for valid and invalid cases, respectively.

Channel Index | Channel Name | Location |
---|---|---|

1 | AF3 | Anterio-frontal, left |

2 | F7 | Frontal-temporal, left |

3 | F3 | Frontal, left |

4 | FC5 | Frontal-central, left |

5 | T7 | Temporal, left |

6 | P7 | Parietal, left |

7 | 01 | Occipital, left |

8 | 02 | Occipital, right |

9 | P8 | Parietal, right |

10 | T8 | Temporal, right |

11 | FC6 | Frontal-central, right |

12 | F4 | Frontal, right |

13 | F8 | Frontal-temporal, right |

14 | AF4 | Anterio-frontal, right |

A | B |
---|---|

Denying the Antecedent | Affirming the Consequent |

Major Premise: If A then B Minor Premise: not Conclusion: Therefore not B | Major Premise: If A then B Minor Premise: B Conclusion: Therefore A |

Example If George beat the game already, then he is a great gamer. George did not beat the game already Therefore, George is not a great gamer | Example If George beat the game already, then he is a great gamer. George is a great gamer Therefore, George beat the game already |

Study | Brain Activity Data | Demographic &Behavioral Data |
---|---|---|

63 participants (21 for each group, ASD, ADHD, and control) | Average MSE at 28 channel -syllogism combinations, per subject | Age, % of certainty in answers, mean of emotional state. |

**Table 4.**Results of mixed ANOVA to test the between-subjects effects of group factor (ASD, ADHD, and control) for MSE values (dependent variables).

Tests of Between-Subjects Effects | ||||||
---|---|---|---|---|---|---|

Transformed Variable: Average | ||||||

Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared |

Intercept | 937.863 | 1 | 937.863 | 3881.298 | 0.000 | 0.985 |

group | 1.722 | 2 | 0.861 | 3.564 | 0.034 | 0.106 |

Error | 14.498 | 60 | 0.242 |

**Table 5.**Results of mixed ANOVA to test the within-subjects effects for MSE values (dependent variables).

Tests of Within-Subjects Effects | |||||||
---|---|---|---|---|---|---|---|

Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared | |

Channels | Sphericity Assumed | 1.210 | 13 | 0.093 | 12.677 | 0.000 | 0.174 |

Greenhouse-Geisser | 1.210 | 7.816 | 0.155 | 12.677 | 0.000 | 0.174 | |

Huynh-Feldt | 1.210 | 9.397 | 0.129 | 12.677 | 0.000 | 0.174 | |

Lower-bound | 1.210 | 1.000 | 1.210 | 12.677 | 0.001 | 0.174 | |

Channels*group | Sphericity Assumed | 0.511 | 26 | 0.020 | 2.677 | 0.000 | 0.082 |

Greenhouse-Geisser | 0.511 | 15.631 | 0.033 | 2.677 | 0.001 | 0.082 | |

Huynh-Feldt | 0.511 | 18.794 | 0.027 | 2.677 | 0.000 | 0.082 | |

Lower-bound | 0.511 | 2.000 | 0.256 | 2.677 | 0.077 | 0.082 | |

Error (Channels) | Sphericity Assumed | 5.728 | 780 | 0.007 | |||

Greenhouse-Geisser | 5.728 | 468.940 | 0.012 | ||||

Huynh-Feldt | 5.728 | 563.832 | 0.010 | ||||

Lower-bound | 5.728 | 60.000 | 0.095 | ||||

Syllogism | Sphericity Assumed | 0.092 | 1 | 0.092 | 2.263 | 0.138 | 0.036 |

Greenhouse-Geisser | 0.092 | 1.000 | 0.092 | 2.263 | 0.138 | 0.036 | |

Huynh-Feldt | 0.092 | 1.000 | 0.092 | 2.263 | 0.138 | 0.036 | |

Lower-bound | 0.092 | 1.000 | 0.092 | 2.263 | 0.138 | 0.036 | |

Syllogism*group | Sphericity Assumed | 0.080 | 2 | 0.040 | 0.985 | 0.379 | 0.032 |

Greenhouse-Geisser | 0.080 | 2.000 | 0.040 | 0.985 | 0.379 | 0.032 | |

Huynh-Feldt | 0.080 | 2.000 | 0.040 | 0.985 | 0.379 | 0.032 | |

Lower-bound | 0.080 | 2.000 | 0.040 | 0.985 | 0.379 | 0.032 | |

Error(Syllogism) | Sphericity Assumed | 2.441 | 60 | 0.041 | |||

Greenhouse-Geisser | 2.441 | 60.000 | 0.041 | ||||

Huynh-Feldt | 2.441 | 60.000 | 0.041 | ||||

Lower-bound | 2.441 | 60.000 | 0.041 | ||||

Channels*Syllogism | Sphericity Assumed | 0.020 | 13 | 0.002 | 0.983 | 0.466 | 0.016 |

Greenhouse-Geisser | 0.020 | 8.369 | 0.002 | 0.983 | 0.450 | 0.016 | |

Huynh-Feldt | 0.020 | 10.173 | 0.002 | 0.983 | 0.458 | 0.016 | |

Lower-bound | 0.020 | 1.000 | 0.020 | 0.983 | 0.325 | 0.016 | |

Channels*Syllogism*Group | Sphericity Assumed | 0.045 | 26 | 0.002 | 1.103 | 0.329 | 0.035 |

Greenhouse-Geisser | 0.045 | 16.737 | 0.003 | 1.103 | 0.347 | 0.035 | |

Huynh-Feldt | 0.045 | 20.345 | 0.022 | 1.103 | 0.340 | 0.035 | |

Lower-bound | 0.045 | 2.000 | 0.002 | 1.103 | 0.338 | 0.035 | |

Error(Channels*Syllogism) | Sphericity Assumed | 1.214 | 780 | 0.002 | |||

Greenhouse-Geisser | 1.214 | 502.122 | 0.002 | ||||

Huynh-Feldt | 1.214 | 610.361 | 0.002 | ||||

Lower-bound | 1.214 | 60.000 | 0.020 |

**Table 6.**Post hoc tests for each dependent variable. Pairwise comparisons for all combinations of the group factor (independent variable).

Multiple Comparisons | |||||||
---|---|---|---|---|---|---|---|

95% Confidence Interval | |||||||

(I)group | (J)group | Mean Difference (I−J) | Std. Error | Sig. | Lower Bound | Upper Bound | |

LSD | ASD | ADHD | −0.075549196 * | 0.0286686642 | 0.011 | −0.132895063 | −0.018203330 |

normal | −0.027149080 | 0.0286686642 | 0.347 | −0.084494947 | 0.0301996786 | ||

ADHD | ASD | 0.075549196 * | 0.0286686642 | 0.011 | 0.018203330 | 0.132895063 | |

normal | 0.048400116 | 0.0286686642 | 0.097 | −0.008945751 | 0.105745983 | ||

normal | ASD | 0.027149080 | 0.0286686642 | 0.347 | −0.030196786 | 0.084494947 | |

ADHD | −0.048400116 | 0.0286686642 | 0.097 | −0.105745983 | 0.008945751 | ||

Bonferroni | ASD | ADHD | −0.075549169 * | 0.0286686642 | 0.032 | −0.146158774 | −0.004939619 |

normal | −0.027149080 | 0.0286686642 | 1.000 | −0.097758658 | 0.043460497 | ||

ADHD | ASD | 0.075549196 * | 0.0286686642 | 0.032 | 0.004939619 | 0.146158774 | |

normal | 0.048400116 | 0.0286686642 | 0.290 | −0.022209462 | 0.119009694 | ||

normal | ASD | 0.027149080 | 0.0286686642 | 1.000 | −0.043460497 | 0.097758658 | |

ADHD | −0.048400116 | 0.0286686642 | 0.290 | −0.119009694 | 0.022209462 |

Emotion Dimension (SAM) | X^{2} Value | df | Asympt. Sig. (2-Sided) |
---|---|---|---|

Arousal Emotion * group (Valid) | 31.08 | 14 | 0.005 |

Arousal Emotion * education (Valid) | 72.76 | 21 | 0.000 |

Control Emotion * Left or Right Hand | 35.00 | 12 | 0.000 |

**Table 8.**Statistics of valence and arousal scores of participants that are used in plotting the 2-D circumplex model of affect, Figure 7c.

Valid Syllogism | |||||
---|---|---|---|---|---|

Valence | Group | Mean | Median | Min | Max |

ASD | 4.14 | 4.00 | 1 | 8 | |

ADHD | 4.29 | 4.00 | 1 | 9 | |

Control | 3.00 | 2.00 | 1 | 7 | |

Arousal | ASD | 5.38 | 5.00 | 2 | 9 |

ADHD | 7.29 | 7.00 | 4 | 9 | |

Control | 7.81 | 8.00 | 3 | 9 | |

Invalid Syllogism | |||||

Valence | Group | Mean | Median | Min | Max |

ASD | 5.10 | 5.00 | 2 | 9 | |

ADHD | 4.29 | 4.00 | 1 | 9 | |

Control | 4.00 | 4.00 | 1 | 8 | |

Arousal | ASD | 5.62 | 5.00 | 2 | 9 |

ADHD | 6.76 | 7.00 | 3 | 9 | |

Control | 7.62 | 8.00 | 3 | 9 |

**Table 9.**Squared singular values extracted from SVD on matrix R, and their cumulative percent of explaining the total variance of R, for valid and invalid syllogism.

Valid | Invalid | ||
---|---|---|---|

Singular Value (Squared) | Cumulative % of Variance Explained | Singular Value (Squared) | Cumulative % of Variance Explained |

4.185 | 70.30 | 6.73 | 77.65 |

0.608 | 80.52 | 0.67 | 85.38 |

0.509 | 89.07 | 0.46 | 90.75 |

0.336 | 94.72 | 0.39 | 95.30 |

0.157 | 97.35 | 0.16 | 97.21 |

0.074 | 98.60 | 0.10 | 98.44 |

0.047 | 99.40 | 0.08 | 99.44 |

0.022 | 99.77 | 0.04 | 99.96 |

0.013 | 100.00 | 0.00 | 100.00 |

**Table 10.**Notable high correlations (>0.40) between pair of brain–behavior measures (extracted from brain saliences matrix V).

Valid Syllogism | Invalid Syllogism | ||||
---|---|---|---|---|---|

Channel | Behavior-Group Interaction | Correlation Coefficient | Channel | Behavior-Group Interaction | Correlation Coefficient |

AF3 | Age*ADHD | −0.572 | AF3 | Confidence*Control | −0.562 |

FC5 | Confidence*ADHDConfidence*Control | 0.521 0.519 | F7 | Emotion*ADHD | −0.590 |

T7 | Confidence*ASD | −0.715 | F3 | Emotion*ASD | 0.473 |

P7 | Confidence*ADHD | 0.582 | T7 | Age*ADHD | 0.641 |

O2 | Emotion*ADHD | −0.640 | P7 | Age*Control | 0.551 |

T8 | Age*Control | 0.600 | O1 | Confidence*ADHD | −0.408 |

F4 | Emotion*Control | 0.456 | O2 | Confidence*ASD | 0.528 |

F8 | Confidence*Control | −0.434 | T8 | Confidence*ADHD | −0.561 |

AF4 | Emotion*ASD | 0.547 | FC6 | Emotion*ADHD | 0.490 |

F4 | Emotion*Control | 0.746 | |||

F8 | Emotion*ASD | −0.574 |

**Table 11.**(

**a**) Singular values and explained variance from seed-PLS for the valid syllogism. (

**b**) Singular values and explained variance from seed-PLS for the invalid syllogism.

(a) | |
---|---|

Valid Syllogism | |

Squared Singular Values | Total Variance Explained, % |

41.183 | 98.43 |

0.330 | 99.22 |

0.197 | 99.69 |

0.105 | 99.94 |

0.019 | 99.99 |

0.002 | 100.00 |

(b) | |

Invalid Syllogism | |

Squared Singular Values | Total Variance Explained, % |

28.476 | 94.44 |

0.903 | 97.43 |

0.370 | 98.66 |

0.224 | 99.41 |

0.100 | 99.74 |

0.076 | 100.00 |

**Table 12.**Linking major brain systems’ regions [144] to activated regions (channels) of the present study.

Valid Syllogism | Invalid Syllogism | |||||
---|---|---|---|---|---|---|

Brain Network | ASD | ADHD | Control | ASD | ADHD | Control |

Default Mode | AF4, P8 | AF4 | P7, P8 | AF3, AF4, P8 | AF4 | P7, P8 |

Visual | O1 | O1 | O1, O2 | O2 | O1, O2 | O1 |

Sensorimotor | T7 | T7 | T8 | T7 | T8 | |

Auditory | T7 | T7 | T8 | T7 | T8 | |

Dorsal Attention | O1, P8 | O1, P8, T7 | P7, P8, O1, O2, T8 | O2, P8, FC5, FC6 | T7, O1, O2 | FC6, T7, O1, P8, T8 |

Salience | T7 | T7 | T8 | T7 | T8 | |

Executive Control | F7, F8 | F8 | F8 | F7 | F7, F8 | F7 |

**Table 13.**Intensity of connections of brain regions located in different and in the same hemispheres for the

**valid**syllogism.

Intensity of Connections of Brain Regions Located in Different Hemispheres | ||
---|---|---|

ASD Valid | ADHD Valid | Control Valid |

AF3 to P8: 0.311 | F3 to AF4: −0.446 | F3 to T8: 0.509 |

F4 to F7: 0.313 | F4 to FC5: −0.374 | F3 to F8: −0.401 |

F4 to O1: −0.361 | F4 to P7: 0.5186 | |

Intensity of Connections of Brain Regions Located in the Same Hemispheres | ||

F3 to AF3: 0.288 | F3 to FC5: 0.403 | F3 to FC5: 0.314 |

F3 to F7: 0.283 | F3 to T7: 0.306 | F3 to O1: −0.518 |

F3 to T7: 0.242 | F3 to O1: −0.304 | F4 to AF4: 0.360 |

F3 to O1: 0.293 | F4 to FC6: 0.319 | F4 to O2: 0.409 |

F4 to F8: 0.582 | F4 to P8: −0.299 | F4 to P8: −0.364 |

**Table 14.**Intensity of connections of brain regions located in different and in the same hemispheres for the

**Invalid**syllogism.

Intensity of Connections of Brain Regions Located in Different Hemispheres | ||
---|---|---|

ASD Invalid | ADHD Invalid | Control Invalid |

F3 to P8: 0.307 | F3 to O2: −0.532 | F3 to P8: 0.458 |

F3 to FC6: 0.321 | F3 to AF4: 0.454 | F3 to FC6: −0.354 |

F3 to F8: 0.356 | F3 to F8: 0.407 | F4 to P7: 0.387 |

F4 to T7: 0.614 | ||

F4 to O1: 0.520 | ||

Intensity of Connections of Brain Regions Located in the Same Hemispheres | ||

F3 to AF3: 0.304 | F3 to F7: 0.137 | F3 to F7: −0.382 |

F3 to FC5: 0.317 | F4 to F8: 0.058 | F3 to O1: −0.387 |

F4 to AF4: −0.413 | F4 to T8: −0.652 | |

F4 to F8: 0.656 | F4 to FC6: 0.445 | |

F4 to O2: −0.336 |

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**MDPI and ACS Style**

Papaioannou, A.; Kalantzi, E.; Papageorgiou, C.C.; Korombili, K.; Bokou, A.; Pehlivanidis, A.; Papageorgiou, C.C.; Papaioannou, G.
Differences in Performance of ASD and ADHD Subjects Facing Cognitive Loads in an Innovative Reasoning Experiment. *Brain Sci.* **2021**, *11*, 1531.
https://doi.org/10.3390/brainsci11111531

**AMA Style**

Papaioannou A, Kalantzi E, Papageorgiou CC, Korombili K, Bokou A, Pehlivanidis A, Papageorgiou CC, Papaioannou G.
Differences in Performance of ASD and ADHD Subjects Facing Cognitive Loads in an Innovative Reasoning Experiment. *Brain Sciences*. 2021; 11(11):1531.
https://doi.org/10.3390/brainsci11111531

**Chicago/Turabian Style**

Papaioannou, Anastasia, Eva Kalantzi, Christos C. Papageorgiou, Kalliopi Korombili, Anastasia Bokou, Artemios Pehlivanidis, Charalabos C. Papageorgiou, and George Papaioannou.
2021. "Differences in Performance of ASD and ADHD Subjects Facing Cognitive Loads in an Innovative Reasoning Experiment" *Brain Sciences* 11, no. 11: 1531.
https://doi.org/10.3390/brainsci11111531