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What do anatomical properties of the brain reveal about the ontology of human cognitive abilities?

Daniel Kristanto1, Xinyang Liu2,3, Werner Sommer4, Andrea Hildebrandt2,5*#, Changsong Zhou1,6*# 1: Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong 2: Department of Psychology, Carl von Ossietzky Universität Oldenburg, 26129 Oldenburg, Germany 3: Shanghai Key Laboratory of Brain Functional Genomics (Ministry of Education), School of Psychology and Cognitive Science, East China Normal University, 200062 Shanghai, China 4: Department of Psychology, Humboldt University at Berlin, Berlin, Germany, Department of Psychology, Zhejiang Normal University, Jin Hua, China 5: Research Center Neurosensory Science, Carl von Ossietzky Universität Oldenburg, Germany 6: Department of Physics, Zhejiang University, 310000 Hangzhou, China

*Corresponding authors.

E-mail addresses: [email protected] (A. Hildebrandt), [email protected] (C. Zhou).

# Senior authors

Abstract

Over the past decades, the neuropsychological science community has endeavored to determine the number and nature of distinguishable human cognitive abilities. Based on covariance structure analyses of inter-individual performance differences in multiple cognitive tasks, the ability structure has been substantiated with sufficient consensus. However, there remains a crucial open question that must be answered to develop unified theoretical views and translations toward neuropsychological applications: Is the cognitive ability structure ascertained at the behavioral level similarly reflected in the anatomical and functional properties of the brain? In the current study, we explored the cognitive ability structure derived from positive and negative networks

1 reflected by the brain’s anatomical properties (thickness, myelination, curvature, and sulcus depth) that were found to be associated with performance in 15 cognitive tasks. The derived neurometric ontological structure was contrasted with the entities of psychometric ontology. Overall, we observed that the brain-derived ontological structures are partly consistent with each other, but also show interesting differences that complement the psychometric ontology. Moreover, we discovered that brain areas associated with the inferred abilities are segregated, with little or no overlap between the abilities. Nevertheless, they are also integrated as they are densely connected by white matter projections with an average connection density higher than the brain connectome. The consistency and differences between psychometric and neurometric ontologies are crucial for theory building, diagnostics, and neuropsychological therapy, which highlights the need for their simultaneous and complementary consideration.

Keywords: Cognitive ontology, individual differences, neuroanatomical properties of the brain, brain networks, segregation and integration

Introduction

Broadly accepted cognitive ontologies are crucial for unified neuro-psychological theories, cognitive diagnostics and mental health therapy. Over the past decades, research on human cognition and intelligence, aimed at describing, measuring, and classifying abilities and unveiling their ontological structure, has mainly been based on inter-individual covariations of performance across multiple tasks. Since the synthesis model known as Cattell–Horn–Carroll (CHC) theory of cognitive abilities was compiled and disseminated (1), there has been a widespread consensus on the psychometric ontology of intelligence, notwithstanding some caveats (2). According to the CHC model, stratum I comprises individual differences in a large number of cognitive tasks that require maximal performance in terms of speed or/and accuracy. Stratum II incorporates broad latent (not directly observable but task-derived) abilities, e.g., fluid reasoning (Gf), comprehension knowledge (Gc, also called crystallized intelligence), short-term memory (Gsm), long-term storage and retrieval (Glr), and cognitive processing speed (Gs). These broad, domain-specific abilities are all positively associated with each other. The CHC model accounts for this positive manifold by assuming a general factor of intelligence (g) at stratum III. A somewhat separate literature on ontological entities of human intelligence concerns executive functions (EF). Most suggestions

2 about the ontological entities of EF derived from psychometric tasks encompass working memory, shifting, and inhibition (e.g., (3)).

Cognitive neuroscience is a much younger discipline than the psychometrics of intelligence and investigates among others the anatomical properties and neural mechanisms underlying the ontological entities of human cognition. Early studies focused on stratum I, aiming at understanding the neuroanatomical basis and neurofunctional mechanisms underpinning the mastery of specific cognitive tasks. Following this research direction, several studies adopted connectome-based predictive modeling (4, 5), a method to map brain properties and performance scores on specific cognitive tasks (6–9). As a further step toward generalization, latent cognitive abilities in stratum II of the CHC model were mapped to brain structure and activity (10–17). Such studies are highly valuable for generating neuroanatomical and neurofunctional explanations of the psychometric ontological entities of cognition beyond specific tasks. However, the quest for brain-derived ontological entities of cognition has recently gained prominence, such that the psychometric entities are not be taken as granted but rather explored in a bottom-up fashion, i.e., from the brain to psychological constructs (18).

The cognitive neuroscience community has thus far not sufficiently appreciated the psychometric desiderata—expressed already by Cronbach and Meehl (1955)—of not conflating psychological constructs with their operational measures (19). That is, a task is only a task and ontological entities of cognition must be determined by analysis beyond single tasks. Consequently, modern cognitive neuroscience approaches to derive ontological entities of cognition must use multiple tasks to explore distinct indicators of anatomical and functional properties of the brain to support the existence of stratum II ontological entities of cognition (the top-down approach), and also to mine the brain to derive ontological entities that do not take psychometric entities for granted (the bottom-up approach, see (20)).

The availability of large-scale, multivariate cognitive neuroscience databases enables such an alternative bottom-up approach, which involves the exploration of potential ontological entities of human cognition on the basis of brain properties (21). For example, Bolt and colleagues investigated which cognitive entities are revealed by brain activation patterns observed when performing a series of cognitive tasks (22). However, they did not systematically discuss the consistency and disparity between their brain-derived ontology and those established in

3 psychometrics. We argue that such direct comparisons are necessary to better substantiate the ontology of human cognition, which should accommodate both the covariance structures of task performance and the brain networks producing these abilities (20, 23).

The present study contributes to the establishment of a formal ontology for psychology, cognitive neuroscience, and their applied disciplines by adopting a bottom-up approach (see (20)). We explored the cognitive ontology derived from the brain’s anatomical properties, including thickness, myelination, curvature, and sulcus depth, which are associated with performance in 15 psychometric tasks. Moreover, we went beyond existing approaches by comparing the derived cognitive ontologies with the psychometric ontology revealed by the same tasks. Specifically, we investigated the extent to which brain-derived ontologies as reflected by shared brain areas across the 15 cognitive tasks (stratum I) are consistent with or distinct to the established psychometric ontologies at stratum II of the CHC model. Next, as suggested in the literature (20), we expected that the ability-related brain areas would be segregated, to support differentiation between the inferred cognitive ontologies. Furthermore, we investigated how the ability-related brain areas are coupled via the underlying network connectivity to form the positive manifold underlying the general intelligence that is captured at stratum III of the CHC model.

Results

Our overall methodological framework is illustrated in Fig. 1. We first identified task- related brain areas based on linear associations between brain properties (thickness, myelination, curvature, and sulcus depth) and task performances collected by the Washington University and University of Minnesota Consortium’s (WU-Minn) Human Connectome Project (HCP; see Materials, Table 1, and SI Appendix Table S1 for the task descriptions and further details). Next, we quantified the overlap between task-related brain areas with these different anatomical properties, by using an Intersect Over Union (IOU) index to create IOU matrices. These matrices were then subjected to exploratory factor analysis (EFA) to obtain a brain-derived cognitive ontology. This ontology was descriptively compared with the psychometric ontology derived from covariances across the same cognitive tasks. In addition, we identified overlapping brain areas associated with the different entities of the brain-derived ontology (henceforth referred to as

4 ability-related brain areas) and investigated the underlying anatomical network connections between those areas (see Methods).

Fig. 1. Summary of our methodological framework illustrating the systematic procedures (blue arrows) and the aims (red arrows).

Task-related brain areas. The task-related brain areas consisting of positive and negative networks (according to the Multi-Modal Parcellation (MMP) atlas (24)) were identified by thresholding correlations between anatomical properties of the brain and performance scores on 15 tasks across individuals (see Methods). Fig. S1, supported by Table S2 (labels of the brain areas in the MMP atlas) and Table S3 (task-related brain areas according to the MMP atlas; see SI Appendix), depicts the brain areas related to each task, together with their hemisphere-specific distributions in positive and negative networks. It additionally illustrates the contributions of different brain properties to the task-related brain areas. Importantly, all of the task-related brain areas, including positive and negative networks, covered approximately 80% of the entire cortex. Overall, eight tasks (Gc1, Gm1, Gm2, EF1, EF2, EF3, Gs3, and Gs4) covered more brain areas in the negative networks than in the positive networks. On average, there were ~10% of the overall task-related brain areas where different anatomical properties of the same area diverged into positive and negative correlations with performance. With respect to the brain’s anatomical properties associated with cognitive performance (Fig. S1B), we observed that sulcus depth made the strongest contribution to the task-related brain areas, outperforming the other properties in 10

5 of the 15 tasks, while myelination was the only property that contributed more strongly to the negative network than to the positive network.

Cognitive ontologies derived from psychometric performance versus the brain’s anatomical properties. We created three matrices, illustrated in Fig. 2, based on which we explored psychometric and brain-derived cognitive ontologies (see Methods). The correlation matrix (Fig. 2A) was obtained by pairwise correlations of performance scores across all cognitive tasks, and enabled exploration of the psychometric ontology. The IOU matrices indicate the pairwise overlap of task-related brain areas for all tasks allocated to the positive networks (Fig. 2B) and the negative networks (Fig. 2C), and enabled exploration of the neurometric ontology.

First, we factor analyzed the correlation matrix of task performance scores using confirmatory factor analysis (CFA) to provide a descriptive reference of the psychometric ontology in line with the CHC model (see Methods), for comparison with the brain-derived ontologies. In keeping with previous analyses of the HCP data for the same 15 tasks (10, 11), we estimated five domain-specific abilities as psychometric ontological entities—namely, reasoning, comprehension knowledge, memory, executive function, and mental speed—corresponding to those listed in Table 1. Domain-specific ability factors were allowed to correlate with each other. To account for task specificity, three residual correlations between two pairs of EF tasks and one pair of Gs tasks were necessary. These indicators reflect two different conditions of the same tasks, and thus task specificity is obvious by design. The five correlated factors model well fitted the matrix of task performance associations (see SI Appendix Table S4, illustrating the statistical evaluation of the model fit). The standardized factor loadings for all domain-specific abilities were statistically significant, but their magnitude varied across ontological entities (see SI Appendix Table S5). The correlations between domain-specific abilities ranged from .26 to .79, with the smallest correlation observed between EF and Gc and the largest between Gf and Gc and between EF and Gs. This pattern of correlations between psychometric ontological entities of cognition is consistent with the vast literature on human intelligence.

Fig. 2. (A) Correlation matrix of task performance scores. (B) Positive Intersect Over Union (IOU) matrix. (C) Negative IOU matrix.

Second, using CFA, the structures mimicking the cognitive ontological entities established for the performance scores were fitted to the positive and negative IOU matrices. As summarized in SI Appendix Table S4, the fit of both models was poor. Furthermore, the model parameter estimates indicated that the five-factor structure of the psychometric ontology was not reflected in the IOU matrices. This was mainly because Gf, Gc, and Gm were highly correlated and not differentiable by the IOUs. Thus, we concluded that task-related brain areas revealed substantially different cognitive ontological entities to those derived from task performance scores.

Given that the factorial structure derived from psychometrics did not hold for the IOU matrices indicating overlap of task-related brain areas, we next explored the factorial structure of the positive and negative IOU matrices using EFA (see Methods). As depicted in SI Appendix Fig. S2, scree plots and parallel analyses indicated that a three-factor structure best explained the structure of the positive IOU matrix, whereas the negative IOU matrix was best described by a five-factor solution. The number of factors was also supported by the results of 휒2-difference tests between sequential nested models, which were defined by a stepwise increase in the number of factors to account for the structure of the IOU matrix (see SI Appendix Table S6). As indicated in SI Appendix Table S4, the final EFA solutions had a good fit. Thus, the loading patterns of these solutions can be descriptively compared with the psychometric ontological structure. Fig. 3 provides a schematic graphical summary of this comparison.

Fig. 3A displays the loading pattern characterizing the reference psychometric ontological structure. Fig. 3B is a simplified schematic representation of the positive IOU matrix structure (solid lines). Additionally, the complete factor loading matrix estimated by the EFA on the positive

7 IOU matrix is displayed in SI Appendix Table S7. Not obviously interpretable loadings are displayed as broken lines in Fig. 3B. However, as indicated in SI Appendix Table S7, these loadings are much weaker than those displayed as solid lines. Thus, the loading pattern suggests a first factor (Accuracy during cognitive effort) that reflects shared brain properties associated with rather difficult tasks scored by performance accuracy (covering Gf1, Gf2, Gf3, Gc1, and Gc2), a second factor (EF) that represents shared brain properties relevant for executive function tasks (covering EF1, EF2, EF3, and EF4), and a third factor (Gs) of mental speed-related brain areas shared by easy cognitive tasks scored by the swiftness of responses (covering Gs1, Gs2, Gs3, and Gs4). Compared with the psychometric ontology, the neurometric ontology derived from the positive IOU matrix of task-related brain areas revealed a partly consistent but less differentiated ability structure.

Fig. 3C is a simplified schematic representation of the neurometric ontology derived from the negative IOU matrix (solid lines). The complete factor loading matrix estimated by the EFA applied to the negative IOU matrix is provided in SI Appendix Table S8. The loading pattern is different from that indicated by the positive IOU matrix. The broken lines in Fig. 3C indicate not obviously interpretable loadings (see SI Appendix Table S8, which illustrates that these loadings are much weaker than those displayed as solid lines). Thus, the loading pattern suggests a five- factor structure partly in line with the psychometric ontology, encompassing Gf (Gf1, Gf2, and Gf3), Gc (Gc1 and Gc2), Inhibition (EF3 and EF4), Switching (EF1 and EF2), and Gs (Gs1, Gs2, Gs3, and Gs4).

Note that the positive and negative IOU matrices analyzed above were computed by applying a threshold of p < .05 to the correlations between brain properties and task performance. Importantly, the above identified ontological entities were found to be robust when using a stricter threshold of p < .01 (see SI Appendix, Supplementary Results and Table S9).

Fig. 3. Comparison between the psychometric and neurometric cognitive ontologies. (A) Psychometric ontology based on 15 tasks. (B) Neurometric ontology derived from the positive Intersect Over Union (IOU) matrix of task-related brain areas. (C) Neurometric ontology derived from the negative IOU matrix of task-related brain areas. Details on model fit and loading estimates are provided in SI Appendix Tables S4–S8. The solid lines indicate the ontological structure used for further analysis, while the broken lines indicate the non-interpretable but very weak loadings.

Brain areas corresponding to the inferred neurometric ontological entities. We further identified the brain areas corresponding to the neurometric cognitive entities, which we termed ability-related brain areas. These areas were defined as the overlapping task-related brain areas of all cognitive tasks subsumed under a given entity. For instance, the entity Gs derived from the positive IOU matrix (Fig. 3B) is reflected by the tasks Gs1, Gs2, Gs3, and Gs4. Thus, the ability- related brain areas corresponding to Gs are the brain areas common to the tasks Gs1, Gs2, Gs3, and Gs4. An exception held for Gs in the ontological structure derived from the negative networks: as no brain areas overlapped across all of the four Gs tasks, the ability-related brain areas were determined by those common to three (out of four) tasks.

Fig. 4A–B illustrates the ability-related brain areas using the MMP atlas (24) for all cognitive ontological entities (see SI Appendix, Supplementary Results and Table S10 for detailed information of the areas). Brain areas related to the entities derived from the positive IOU matrix were mostly in the inferior parietal cortex, posterior cingulate cortex, anterior cingulate, and the medial prefrontal cortex. The cognitive ability-related areas derived from the negative IOU matrix

9 were dominated by parts of the anterior cingulate and medial prefrontal cortex, the superior parietal cortex, and the lateral temporal cortex. To evaluate the functional relevance of these areas, we assigned the ability-related brain areas to corresponding resting-state networks (RSNs) (25), as depicted in Fig. 4C–D. The RSNs were determined using a clustering method applied to the resting-state functional connectivity profile of each brain region (25). In general, we found that there was overlap of all RSNs and accuracy during cognitive effort-related brain areas, but only the default mode network (DMN) and the somatosensory and motor (SM) network overlapped with Gs-related brain areas. For EF, we found that the frontoparietal and salience (FP and SAL) networks, in addition to the DMN and SM networks, overlapped with the ability-related brain areas. Gc and switching derived from the negative IOU were associated with all RSNs, whereas Gf and inhibition lacked associations with the SAL network. For Gs, only the DMN and SM networks were covered. We discuss these findings further below.

As the ability-related areas are supposed to be segregated across ontological entities, we also quantified the exclusiveness of ability-related brain areas by computing their pairwise overlap using the IOU index (see Methods), as shown in Fig. 4E. We found relatively little overlap across the ability-related brain areas, with most overlaps present between Inhibition and Switching (IOU index = .278) and between Gf and Gc (IOU index = .2). All of these weak overlaps were demonstrated by the ontological entities derived from the negative networks. In contrast, we found that the Gs entity in both the positive and negative neurometric ontologies had the least brain-area overlap with other ontological entities. Corresponding entities in the positive and negative ontologies revealed relatively little overlap of brain areas. For example, EF in the positive ontology only had a small overlap with Inhibition and Switching (IOU index = .02) but no overlap was present in the negative ontology. Moreover, Gs-related brain areas were not overlapped between ontological structures derived from the positive and negative networks. These results show that the ability-related brain areas are well segregated among the entities of the neurometric ontology.

Fig. 4. Brain areas corresponding to the ontological entities (A) derived from the positive Intersect Over Union (IOU) matrix and (B) derived from the negative IOU matrix. (C) and (D): Distribution of the ability-related brain areas for (A) entities derived from the positive IOU matrix and (B) entities derived from the negative IOU matrix in seven resting-state networks (RSNs). The RSNs are attention (ATT), frontoparietal (FP), default mode (DMN), visual (VIS),

11 limbic (LIM), somatosensory and motor (SM), and salience (SAL). (E) The pairwise overlaps computed from the IOU index of the ability-related brain areas.

Anatomical connectivity analysis of the ability-related brain areas. Next, we analyzed the network connectivity underlying the segregated ability-related brain areas using fiber-based structural connectivity obtained by probabilistic tractography averaged across individuals (see Methods). The ability-related brain areas as defined above for each ontological entity were considered as core areas, whereas the union of all task-related brain areas of the corresponding ontological entity, excluding the core, were considered as extended areas. We examined two levels of connections: (i) the connections between the core areas; and (ii) the connections between the extended areas. Both connectivity levels can be applied within areas of the same ontological entity and between entities.

We applied network density thresholds of 10%, 20%, and 50% of the strongest connections in the weighted group-averaged connectivity matrix to identify existing connections (binary 0 or 1). For each level of connections (core and extended areas), we obtained the connection density as the ratio between the number of existing connections and the number of possible connections. Under all thresholds, the connection density of the core areas is clearly larger and that of extended areas is clearly smaller than the average connection density of the whole brain network (Fig. 5B). This finding indicates that although the ability-related brain areas are segregated in their regional anatomical properties, they are densely connected by white matter projections, such that their average connection density is greater than that of the brain connectome.

Fig. 5. Comparison of the anatomical connection density between the ability-related brain areas (core areas) and the other task-related areas (extended areas). (A) Connection density within and between cognitive entities included in the neurometric ontology compared with the whole structural connectivity network with a 20% threshold. (B) The

12 average connection density of core areas across different entities and all extended areas at different network density thresholds (10%, 20%, and 50%, horizontal dotted lines) in the whole structural connectivity network.

Discussion

This work explored the cognitive ontology reflected in the task-related anatomical properties of the cortex, and compared this ontology with the widely established psychometric ontology summarized in the CHC model. We began by confirming the ontological structure of human cognition based on psychometric task performance. To explore neurometric ontologies, we created IOU matrices reflecting the overlap of task-related brain areas identified from the correlation between the brain’s anatomical properties and task performance across individuals. Next, we investigated whether the established psychometric ontology is also reflected in the brain’s anatomical properties and fitted a model reflecting the psychometric ontology to the derived IOU matrices. However, the psychometric ontology did not fit well to the IOU matrices. To mine the best fitting neurometric ontology, we applied EFAs to the IOU matrices and found that the positive IOU matrix was best reflected by three factorial entities, whereas the negative IOU matrix required five entities. We further identified the brain areas related to the inferred cognitive ontological entities derived from the positive and negative IOU matrices. Interestingly, the ability-related brain areas demonstrated competing features: On the one hand, they were segregated, as there was little overlap of the ability-related brain areas between entities. On the other hand, they were integrated, as their structural connectivity was denser than the average connection density of the brain connectome. Next, we discuss the three main findings related to the aims depicted in Fig. 1.

Consistencies and differences in psychometric versus neurometric ontologies. We found that neurometric ontologies align to some extent with psychometric ontologies. The most evident consistency is that Gs is an entity in both the positive and negative IOU matrices. In addition, the EF entity reflected in the positive IOU matrix is consistent with EF in the psychometric structure. Furthermore, the psychometric Gf and Gc entities perfectly matched the neurometric Gf and Gc derived from the negative IOU matrix. These similarities are remarkable, because the dependent measures subjected to factor analyses (performance speed and accuracy versus associated anatomical properties of the brain) are arguably extremely different in nature. It

13 can thus be concluded that there is a partially robust isomorphy between cognitive ontologies derived from behavior and their associated anatomical properties of the brain. This validates parts of the CHC ontological structure of human cognition from a neurometric point of view.

However, we also observed interesting and – crucially – interpretable differences between psychometric and neurometric ontologies. First, the positive IOU matrix did not reflect a separation between Gf and Gc. We thus termed the overarching ontological entity as accuracy of cognitive effort. This unified Gf and Gc is in line with Cattell’s view on general intelligence encompassing these two facets of cognition (26). A strong relationship between Gf and Gc was also previously expressed in terms of skill acquisition (27) and emotional intelligence (28). Second, it was also interesting to find that switching and inhibition could be distinguished by the negative IOU matrix, which are often treated as one overarching entity (EF) in psychometrics. However, the segregation of switching and inhibition is consistent with at least one previous study that confirmed the separability of these cognitive entities under the umbrella of EF, based on a factor analysis of task performances (3).

Another difference between psychometric and neurometric ontologies was consistent for both the positive and negative IOU matrices: Gm was not identified as an independent cognitive entity based on task-related brain areas. Note that memory task-related brain areas were scattered into different neurometric ontological entities (i.e., accuracy of cognitive effort and EF in case of the positive IOU matrix, and Gf and Gs when analyzing the negative IOU matrix). This may indicate that brain areas associated with Gm are complex and widely distributed, such that they may not be quantifiable by neuroanatomical properties alone (29, 30). However, detailed analyses of task-related brain areas in terms of these properties facilitated understanding of the brain network underlying Gm, which overlaps with the networks associated with accuracy of cognitive effort and Gs.

Specifically, we argue that these results indicating similarity and explainable dissimilarity between psychometric and neurometric cognitive ontologies are compelling, considering that we explored only a limited number of anatomical properties of the brain. These findings have the potential to prompt further psycho-neuro-informatics studies to explore the cognitive ontology using an even broader range of anatomical and functional properties of the brain. From a more general perspective, we emphasize that the present comparative approach, focusing either on

14 similarity or dissimilarity, is highly valuable for exploring whether ontological entities derived from psychometrics (stratum II in the CHC model) translate into brain anatomy and function (23). The potential translation is of theoretical importance, and is also relevant for neuropsychological diagnostics and therapy.

Segregation of the ability-related brain areas in the neurometric ontology. After analyzing similarities of and differences between psychometric and neurometric ontologies, we investigated whether the entities of the neurometric ontology are built upon distinct neural networks. This approach was inspired by a study on cognitive control (i.e., executive functions) by Lenartowicz and colleagues (20). The authors applied a machine learning approach to classify data from more than a hundred neuroimaging studies, aiming to isolate component operations with similar and dissimilar brain-activation patterns across experiments (20). They found that ontological entities described in the psychometric literature of cognitive control were generally also differentiable on the basis of brain activation patterns. However, while shifting was consistently identified as a specific ontological entity in psychometrics, in brain-activity covariance structure analyses it could not be discriminated from response selection or response inhibition (3).

We identified the brain areas corresponding to the inferred cognitive entities in the neurometric ontology, and found that the areas corresponding to each entity had little overlap or showed complete exclusiveness with other entities. In more detailed observation, the overlaps mostly occurred between entities from the same (positive or negative) IOU matrix. Furthermore, entities derived from the two different IOU matrices tended to have few or sometimes no overlapping ability-related brain areas. This non-alignment of ability-related brain areas captured by the positive and negative IOU matrices emphasizes the important role of negative brain networks in the organization of cognitive ontologies (31, 32), complementing the positive brain networks more frequently featured in previous research.

The present study also attempted to validate the identified ability-related brain areas. Thus, we investigated the functional relevance of these brain areas by assigning them to different RSNs. First, regarding the ontological entities derived from the positive IOU matrix, we found that accuracy of cognitive effort involved the frontoparietal areas, in line with the parieto-frontal integration theory of intelligence (13). Next, EF was related to the FP network and the DMN,

15 specifically in the prefrontal and parietal areas. The present findings built upon anatomical properties of the brain complement those revealed by functional brain activation that occurs during executive control, involving the prefrontal, dorsal anterior cingulate, and parietal cortices (33). The Gs entity reflected in the positive IOU matrix only covered two brain areas located in the DMN and SM networks. Note that the functional involvement of the DMN and the motor cortex in mental speed has been reported previously (34, 35).

With respect to multiple ontological entities derived from the negative IOU matrix, we generally found large overlaps with the DMN. This finding supports the observation that the DMN is the brain’s task-negative network, as revealed by previous functional studies (36, 37). The present findings reveal that the DMN can also be considered a negative network from a structural point of view. In addition, the relevance of the DMN for Gf, as indicated by negative associations with anatomical properties of the brain, is consistent with a previous meta-analysis of functional and structural brain characteristics (13). Moreover, the overlapping of the Gf- and Gc-related brain areas with attention and visual networks is consistent with a previous study reporting a negative association of anatomical properties of attention- and visual processing-related brain areas with Gf- and Gc-related brain areas (38). Inhibition- and switching-related brain areas overlap with similar RSNs. We found no previous studies reporting the alignment of negative brain networks with EF revealed here. Finally, Gs-related brain areas derived from the negative IOU matrix overlapped with the DMN and motor network, emphasizing the involvement of those networks in mental speed, in both a positive and negative manner. Similar findings were previously reported in older adults (39).

In general, we observed that the associations between neurometric ontologies and the corresponding areas are, in many cases, in line with the literature on RSNs, which has focused on functional properties of the brain. This indicates that although the associations were identified from anatomical properties of the brain, they were functionally relevant to the cognitive ability reflected in a given ontological entity. However, as previous studies have reported mostly positive associations between cognitive tasks and brain properties, and not offered a comprehensive explanation of negative associations, our detailed analyses of positive and negative networks may stimulate further studies on how functional and anatomical properties of the brain assist or compete

16 with each other to shape cognitive abilities. Thus, the present findings provide new opportunities to study the structure–function relationships of the brain.

Motivated by our findings of the neurometric ontology—namely (i) its consistency with and interpretable dissimilarities to the psychometric ontology, in terms of inferred cognitive entities, and (ii) the exclusive and functionally relevant brain areas corresponding to the inferred entities (see previous sections)—we argue that the neurometric ontology is a crucial complement of the currently dominant psychometric entities of human cognition. There are at least two main reasons for this claim. First, convergence or divergence between psychometric and neurometric cognitive ontologies might pinpoint and help to resolve weaknesses reflected in psychological terminology and theory building (21, 23). Second, the juxtaposition of these ontologies is highly relevant from a clinical neuropsychological perspective, as in this context, the mapping of psychological functions and their corresponding brain systems is essential. However, psychological assessment continues to primarily rely on psychometric ontologies of cognition, whereas diagnoses in neurology and neuropsychology focus on brain structure and function. A unified ontological structure, which claims independent neural mechanisms for the entities, will provide a common base for both perspectives.

Dense connection between segregated ability-related brain areas in the neurometric ontology. After identifying the brain areas corresponding to neurometric ontological entities, we investigated the extent to which these segregated brain areas can reflect the positive manifold captured at stratum III of the CHC model. To that end, we analyzed the structural connection density between the core and extended areas within and between ontological entities. We found that the segregated core areas of different cognitive entities are densely connected, whereas the connection between the extended areas across entities is sparser than the average connection density of the whole brain structural connectome. In the analysis of modules or communities in the brain structural or functional networks, the inter-module connectivity is typically sparser than the intra-module connectivity (40, 41). Thus, the dense connections between the segregated core areas of different abilities are counterintuitive, and we have not seen similar reports in the literature. However, they reveal that the segregated ability-related brain areas are actually also integrated in terms of structural connections.

17 We thus emphasize two important but seemingly contradictory features of the inferred ability-related brain areas: They are exclusive (segregated) but more densely connected (integrated) than the averaged structural connections. We interpret the “segregation” feature to explain the partial independencies of stratum II entities in the psychometric structure of cognition. Furthermore, the dense connection of the ability-related brain areas across ontological entities, i.e., the “integration” feature, supports the positive manifold of the abilities that leads to the general intelligence entity of stratum III in the ontological structure provided in the CHC model. This interpretation offers a new perspective on how the structure of human intelligence can be understood in terms of underlying neural networks in the regional neuroanatomical properties and fiber network projections in the brain that support both segregation and integration. The segregation and integration configuration of brain networks have been studied to achieve a better understanding of cognitive abilities, including their relationships with general intelligence (42– 46). However, these previous studies focused on functional properties of the brain, thus prompting the question: do the anatomical properties of the brain display similar segregation and integration organizational features. Future studies will specifically investigate the association between the structural connections and the inter-individual variability between segregated ability-related brain areas and general intelligence.

Limitations

The present study is not without limitations. First, it only considered 15 cognitive tasks and four anatomical properties of the brain. Applying a larger number of cognitive tasks and measuring more brain properties, such as cytoarchitecture, connectivity, biochemistry, and gene expression, is a promising direction in this line of research. We derived the ability-related brain areas by overlapping task-related brain areas across corresponding tasks of a given cognitive entity. Therefore, employing a larger number of tasks will result in a more robust determination. Furthermore, a particular cognitive task may not be sufficiently isolated to measure a specific cognitive function (see (21)). For example, the Gs1 task challenges visual and semantic processing in addition to mental speed. Therefore, future work should rely on cognitive tasks that are as isolated as possible, to capture specific cognitive functions. Finally, task-related brain areas in this work were identified by linear associations. As suggested in the literature (47), a non-linear

18 approach using, for instance, artificial neural networks could be applied, to afford a more precise mapping of anatomical properties of the brain and cognitive behavior.

Conclusion

We used a novel approach to derive a cognitive ontology from anatomical properties of the brain, and compared this ontology with the psychometric ontology derived from task performance over many decades of research. The results revealed that the entities of the neurometric ontology partly reflect the current psychometric view. In important respects, the brain areas related to the neurometric ontologies correspond to findings from previous functional imaging studies of cognitive abilities. This is especially true for positive relationships, whereas negative relationships are less well investigated. However, negative networks are more sensitive than positive networks for identifying the psychometric ontology. We also found sparse (or even no) overlap between brain areas related to different neurometric ontological entities, supporting the existence of separable cognitive entities. Although the cognitive entities were segregated, the structural connections between their brain core areas were very dense, and thus their average connection density was greater than that of the whole brain connectome. These findings explain the moderate stratum II ability correlations (segregated ability-related brain areas), and that the positive manifold captured at stratum III represent general intelligence (denser connections than the average brain connectome).

Materials and Methods

Materials

Participants

This study was conducted using the publicly available data from the WU-Minn Human Connectome Project (HCP), covering several magnetic resonance imaging (MRI) modalities, including resting-state functional MRI, diffusion MRI, and structural MRI (48). The HCP database also provides demographic data and performance measures for several cognitive tasks that challenge different domain-specific abilities. Of the initial 1,206 participants whose data were available in the HCP database, those with incomplete data on brain imaging and/or cognitive tasks

19 were eliminated, giving a final sample of N = 838 (449 females, 760 right-handers, and three ambidextrous) individuals. Their ages ranged from 22 to 35 years. For more detailed information, including detailed data acquisition protocols of the HCP, please refer to the project’s website (https://www.humanconnectome.org/). The local ethics committee of Washington University approved the HCP study.

Anatomical properties of the brain

We considered four properties of the brain, derived from structural MRI: thickness, myelination, curvature, and sulcus depth. First, the T1-weighted and T2-weighted images were acquired (see (49) for the details of the scanning processes). The images were pre-processed to correct distortions and to align the images to the Montreal Neurological Institute space template (50). Next, segmentation of gray and white matter and reconstruction of the cortical surface were performed using the pre-processed images. All anatomical properties of the brain were estimated from the surface reconstruction. Thickness was measured as the distance between the pial surface and the gray–white matter border (51). Cortical thickness is known to correlate with the number of neurons (52). Myelination—an indicator of the myelin content—was determined as the ratio of T1 and T2 weights (T1/T2) (49), with a higher ratio indicating a thicker myelin sheath surrounding neuronal cells and fibers. Curvature indicates the bending of each vertex in the cortical surface, and a higher curvature indicates sharper bending, with positive values corresponding to upward curving (convex) (53). Lastly, sulcus depth was calculated as the distance between mid-surface gyri and sulci (54). Curvature and sulcus depth contribute to determining the sulcal patterns that predate the acquisition of cognitive skills (55). All voxel-wise data, including both individual and group averages, can be downloaded from the HCP website. We used the Multi-Modal Parcellation (MMP) atlas (24), which divides each hemisphere of the brain into 180 areas. We averaged the voxel-wise property measures within a given brain area to obtain an area-specific measure of the respective property. Thus, for each participant, four brain properties were featured in each brain area.

For the analysis of connections among brain areas, we measured structural connectivity based on white matter projections between brain areas in the MMP atlas. We applied probabilistic tractography to the diffusion MRI data to trace the white matter connections. Briefly, we set seed and target areas for a pair of brain areas. From each vertex of the seed area, we generated 5,000

20 streamlines and counted how many reached the target area. When the streamlines met with a voxel whose fractional anisotropy was less than 0.1, the propagation stopped. There were two directions of streamline, given that an area can serve as both a seed and a target. Thus, the final structural connectivity between two areas was the average of two directional connectivity probabilities (see (56) for details).

Cognitive tasks

Measures of performance in 15 cognitive tasks were entered in the present analyses. The tasks were adopted from the task-evoked fMRI measurement (in-scanner test), NIH Toolbox, and Penn Computerized Cognitive Battery (10, 57, 58), and were selected by the HCP as a representative set of tasks covering the most broadly investigated domain-specific abilities at stratum II, according to the CHC model (see above). Table 1 provides a summary of the tasks grouped into different stratum II abilities. We also included executive function (EF) as a domain- specific ability (59), because it plays a crucial role in human cognition and has pivotal diagnostic relevance in many mental conditions.

Table 1. Cognitive tasks and associated domain-specific abilities included in the present study

Domain-specific abilities Tasks Reasoning (Gf) Raven’s Progressive Matrices (Gf1) Spatial Orientation Processing (Gf2) List-Sorting Working Memory (Gf3) Comprehension Knowledge (Gc) Oral Reading Recognition Test (Gc1) Vocabulary Comprehension (Gc2) Memory (Gm) Verbal Episodic Memory (Gm1) Picture Sequence Memory (Gm2) Executive Function (EF) Dimensional Change Card Sort – Color (EF1) Dimensional Change Card Sort – Shape (EF1) Flanker Inhibitory Control and Attention Task – Congruent (EF3) Flanker Inhibitory Control and Attention Task – Incongruent (EF4) Mental Speed (Gs) Pattern Comparison Processing Speed (Gs1) Sustained Attention (Gs2) Relational Processing 1 (Gs3)* Relational Processing 2 (Gs4)*

21 Note. * means that the tasks were performed during the functional magnetic resonance imaging scanning (in-scanner tasks). A detailed description of these tasks can be found in Table S1 and in the Human Connectome Project manual (57).

The indicators Gf1, Gf2, Gf3, Gc1, Gc2, Gm1, and Gm2 were the accuracies of performance scores assessed by an examiner (60), whereas performances in the tasks EF1, EF2, EF3, EF4, Gs1, Gs2, Gs3, and Gs4 were evaluated using the inverted reaction times of correct responses, which indicate the number of trials correctly solved per second. All performance indicators were standardized prior to statistical analyses. In all tasks, higher values correspond to better performance.

Methods

Identifying task-related brain areas

We identified task-related brain areas for each of the 15 tasks by correlating anatomical properties of the 360 brain areas with task performance scores across individuals. The CORR function in MATLAB (https://www.mathworks.com/help/stats/corr.html) was applied to determine the Pearson’s correlation coefficients. This analysis resulted in one correlation value in each cortical area for a given brain property and task. Thus, for all tasks and the four brain properties, there were 15 × 4 correlation values in each cortical area. The CORR function additionally provides p-values, and a thresholding of p < .05 was applied to select relevant brain areas associated with a given task. Thus, brain areas that were significantly correlated with task performance were regarded as task-related brain areas. These were then split into positive and negative task-related brain networks according to the sign of the correlation.

As data mining was applied to four anatomical properties of the brain, four sets of task- related brain areas were obtained for each cognitive task, and these sets were split into positive and negative networks. For a multimodal representation, we determined the union of these sets of task-related brain areas across the four anatomical properties of the brain. Thus, to qualify as task- related, a given brain area had to be significantly correlated with the task score in at least one of the four properties. Note there are cases where certain brain areas were positively correlated with task performance in one anatomical property and negatively correlated with task performance in another anatomical property. These areas appeared in both positive and negative networks of task-

22 related brain areas. The obtained positive and negative brain networks for each of the 15 tasks were subjected to further analysis.

Quantifying the overlap of task-related brain areas

The task-related brain areas were not exclusive to single tasks, and therefore overlapped across some tasks. We thus aimed to quantify the overlap for every pair of tasks by using a well- known index termed Intersect Over Union (IOU) (61). The IOU index remains widely used for measuring the similarity between sample sets. In our case, the IOU index of two tasks was calculated as the ratio between the number of common brain areas related to both tasks and the total number of distinct brain areas in each of the two tasks, and simply expressed as follows:

퐼푂푈 = 푁푢푚푏푒푟 표푓 푐표푚푚표푛 푎푟푒푎푠 푏푒푡푤푒푒푛 푡푎푠푘푠 퐴 푎푛푑 퐵

푁푢푚푏푒푟 표푓 푎푟푒푎푠 푟푒푙푎푡푒푑 푡표 푡푎푠푘 퐴 + 푁푢푚푏푒푟 표푓 푎푟푒푎푠 푟푒푙푎푡푒푑 푡표 푡푎푠푘 퐵 − 푁푢푚푏푒푟 표푓 푐표푚푚표푛 푎푟푒푎푠 푏푒푡푤푒푒푛 푡푎푠푘푠 퐴 푎푛푑 퐵 .

Considering that 15 cognitive tasks were involved in the analyses, the computation of IOU indices of all task pairs resulted in a 15 × 15 IOU matrix. IOU calculation was applied for both positive and negative networks, and we thus obtained two 15 × 15 IOU matrices. As the task-related brain areas were based on the correlations between performance and brain properties, we emphasize that the IOU matrices reflect the covariance structure of task pairs across the participants in terms of neuroanatomical properties.

Exploring the structure of IOU matrices

We aimed to compare the cognitive ontologies derived from the structure of IOU matrices of task-related brain areas with the psychometric ontology established by covariance analyses of task performance scores. To this end, we used the following three 15 × 15 matrices indicating the association of all tasks or the overlap of task-related brain areas: (i) a correlation matrix of performance scores across all tasks, (ii) a positive IOU matrix of the task-related brain areas, and (iii) a negative IOU matrix of the task-related brain areas.

First, we performed a confirmatory factor analysis (CFA) of the correlation matrix of task performance scores to provide a baseline model of cognitive ontological entities for descriptive comparison with neurometric cognitive ontologies. We used the lavaan package

23 (https://lavaan.ugent.be) in R Software for Statistical Computing (https://www.r-project.org/) for this purpose. The model included the domain-specific cognitive ontological entities listed in Table 1. Factors were standardized for identification purposes, such that all factor loadings could be freely estimated.

Second, a CFA mimicking the domain-specific psychometric ontological entities was fitted to the positive and negative IOU matrices. By this analysis, we investigated whether the model fit, the factor-loading matrix, and the correlational structure of ontological entities derived from the IOU indices are comparable to the psychometric ontology established for performance score correlations.

Third, the factorial structure of the positive and negative IOU matrices was explored using exploratory factor analysis (EFA). To this end, we used the psych package (https://cran.r- project.org/web/packages/psych/index.html) in R. Unlike CFA, which requires prior assumptions regarding the factorial structure, EFA is a data-driven approach that allowed us to explore the number of factors needed to explain the structure of an association matrix, and the pattern of factor loadings. As different cognitive ontological entities indicated by factors in EFA are expected to be correlated, an oblique (promax) rotation was applied to achieve a simple structure and thus obtain interpretable factors. To determine the number of factors, we applied two criteria in the analyses 2 of both positive and negative IOU matrices, namely the scree plot and the 휒푑푖푓푓 difference test. Scree plots were created based on eigenvalues of a principal axis factor analysis aimed at finding the minimum residual solution. Then, by comparison with the course of random eigenvalues, the 2 number of factors in the best fitting model was determined. In parallel, the 휒푑푖푓푓 difference test was performed to compare different factor solutions (62). A series of competing models were estimated, with their number of factors increasing from one to the number suggested as the best solution by the scree plot. Comparisons were performed between each pair of neighboring models, e.g., one-factor versus two-factor models, and two-factor versus three-factor models, until the best 2 2 choice was identified. The 휒푑푖푓푓 and 푑푓푑푖푓푓 differences were computed. The 휒푑푖푓푓 value was distributed along 푑푓푑푖푓푓, the significance of which was relevant for determining the number of 2 factors. That is, if the 휒푑푖푓푓 value is significant, it can be concluded that a competing model with more freely estimated parameters fits the data better.

24 The two methods (CFA and EFA) rely on different assumptions, but may sometimes lead to consistent factorial structures when applied to the same data (63–65). The methodological choices above reflect the assumptions that can be made. There is vast knowledge on which tasks are loaded into which cognitive entity in the psychometric ontological structure. Furthermore, previous studies of the HCP data (e.g., (10, 11)) have confirmed the domain-specific cognitive entities considered in the current study. Thus, the factorial structure provided by the CFA on the covariance matrix of task performance scores is not specific for the present analyses; rather, it is a descriptive reference for interpreting the ontological entities derived from properties of the brain. Furthermore, there is no prior knowledge on how the IOU matrices of brain areas related to the 15 specific cognitive tasks are clustered. Thus, by applying a CFA to the IOU matrices mimicking the psychometric ontological structure, we first investigated whether task-related brain areas reveal exactly the same entities as performance scores do. To further explore the structure of the IOU matrices and identify potential differences between psychometric and neurometric ontological entities, an EFA approach is reasonable.

Model fit in the CFA was quantified by the 휒2 goodness-of-fit index (휒2), the comparative fit of index (CFI), the root-mean-squared error of approximation (RMSEA), and the standardized root-mean-squared residual (SRMR). For the EFA, the 휒2 test statistic and the RMSEA were evaluated. In large samples, the 휒2 test statistic is highly sensitive. Thus, alternative fit indices play an important role in model fit evaluation: acceptable values are > .95 for the CFI and < .08 for both the RMSEA and SRMR (66).

Data Availability. The datasets that support the findings of this study are available at http://www.humanconnectome.org/study/hcp-young-adult.

The codes used in this study will be available at https://github.com/kristantodan12/Mining-the- brain

Acknowledgments. This work was supported by the Hong Kong Research Grant Council (RGC) (HKBU12301019, HKBU12200620) under the Hong Kong Baptist University (HKBU) Research Committee Interdisciplinary Research Matching Scheme (IRMS/16-17/04, IRCMS/18-19/SCI01). This research was conducted using the resources of the High-Performance Computing Cluster

25 Centre, HKBU, which receives funding from the RGC, the University Grants Committee of the HKSAR and HKBU.

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31 Supporting Information

Supplementary Results

Task-related brain areas. We provide detailed information on task-related brain areas in the Fig. S1 supported by Table S2 (name of areas in MMP atlas) and Table S3 (identification number of task-related brain areas in MMP atlas). Here, we report the main findings on task-related brain areas (see Fig. S1A). From bottom to top, firstly, Gf1 was the task with the largest number of associated brain areas. These areas were dominated by the positive network and mostly located in the temporal and prefrontal cortex. Next, we found that for Gf2, the right hemisphere occupied a larger portion of task-related brain areas than the left hemisphere. Those areas were mostly located in the temporal and frontal cortex. Gf3 indicated hemispheric asymmetries as well, the right hemisphere being dominated by positive associations, but there was an evenly distributed positive and negative network observed for the left hemisphere. Gc1 had widely distributed positive and negative networks across different brain areas, dominated by the right hemisphere. The brain areas related to Gc2 were almost evenly distributed in the right and left hemisphere. Moreover, the visual cortex contributed to the positive network in case of both hemispheres. Gm1 was the task with the fewest task-related brain areas, which were mostly located in the right hemisphere. Gm2 covered brain areas similarly distributed across hemispheres and contributing similarly to the positive and negative networks. The areas for EF1 covered especially the parietal cortex. The three performance indicators EF2, EF3, and EF4, shared associated brain areas, especially characterized by positive correlations with the motor cortex in the left hemisphere. In Gs1, the number of areas in positive networks was more than two times the number of areas in negative networks, involving a broad range of brain areas from the visual, motor, and frontal cortex in both hemispheres. The related brain areas for Gs2 included the left visual cortex, bilateral motor, and left temporal cortex. Finally, Gs3 and Gs4 shared some areas in the frontal, temporal, and auditory cortex in negative networks.

Factor Analysis with threshold of p < .01. As written in the main text, the neurometric ontology was explored on IOU matrices based on identified task-related brain areas. Note that we used the threshold of p < .05 to determine the task-related brain areas. Here we confirm that the neurometric ontology also holds for stricter threshold p < .01.

As depicted in Table S9, we found relatively consistent structures on the p < .01 threshold compared to the one with p < .05. In positive IOU, both thresholds resulted in identical factors. On

32 the other side, the negative IOU on p < .01 thresholding suggested that four factors were the best fit of the IOU matrix. However, the tasks and the interpretability of the factors were mostly similar with the five factors from p < .05 threshold. Moreover, if we ran the exploratory factor analysis to find five factors on p < .01 threshold, the results were identical with the p < .05 threshold.

Ability-related brain areas. To support the brain plot for ability-related brain areas in Fig. 4A-B, we provide the lists of those areas in Table S10. For entities derived from the positive IOU matrix, accuracy of cognitive effort showed the largest number of ability-related areas (25 areas), followed by EF (9 areas), and Gs (2 areas). The ability-related areas of accuracy of cognitive effort covered some areas in: neighbouring visual areas (R (right hemisphere) – L (left hemisphere)), posterior cingulate cortex (R-L), mid cingulate cortex (R-L), superior parietal cortex (R), auditory cortex (R-L), frontal opercular cortex (R-L), medial temporal cortex (R), inferior parietal cortex (R-L), ventral stream visual cortex (R-L) and posterior opercular cortex (L), where R and L refers to the right and left hemispheres, respectively. The EF had the ability-related areas in POS1 in right posterior cingulate cortex, P24pr in right medial prefrontal cortex, STSvp in right and left auditory association cortex, Pol1 in right frontal opercular cortex, 4 in left motor cortex, 23d in left posterior cingulate cortex, 8C in left prefrontal cortex and PGi in inferior parietal cortex. Moreover, motor cortex and s6-8 in prefrontal cortex served as ability-related brain areas for Gs.

For the entities from negative IOU matrix, the brain areas relevant to Gf were dominated by the left hemisphere (60%). The areas covered: FFC in visual cortex (R), 10d in polar frontal cortex (R), EC in medial temporal cortex (R), A5, STSda, and STSvp in auditory association cortex (R- L), TGd and PHT in lateral temporal cortex (R-L), PGs and IP1 in inferior parietal cortex (R), 4 and 3a in motor cortex (L), V7 and VMV1 in visual cortex (L), SFL and 8av in prefrontal cortex (L), 10d in polar frontal cortex (L), a47r in inferior frontal cortex (L) and RI in early auditory cortex (L). Next, Gc was the factor with the highest number of corresponding brain areas: 69 areas, where 35 and 34 in the right and left hemisphere, respectively. The brain areas were distributed across different functional regions, with the biggest portions are: 11% in prefrontal cortex, 9% in mid cingulate cortex, and 7% in frontal opercular cortex. For Inhibition, 30% of the ability-related brain areas were in left posterior cingulate cortex, left inferior frontal cortex, and lateral temporal cortex. Switching was dominated (60%) by the areas from the left hemisphere, including MST and PH in neighboring visual areas, SFL, i6-8, A9-46v, and 8Av in prefrontal cortex, 5L and 34dv in

33 mid cingulate cortex, 23C, 7AL, 7PI, and 7PC in superior parietal cortex, P32pr and BBM in medial prefrontal cortex, 9M in medial prefrontal cortex, LIPd in superior parietal cortex, OP4 in posterior opercular cortex, RI in early auditory cortex, TE1p in lateral temporal cortex, and IP1 in inferior parietal cortex. Lastly, for Gs, there were only two areas, areas 3b in motor cortex (R) and TE1p in lateral temporal cortex.

Fig. S1. Distribution of task-related brain areas (A) and the detailed contribution of different structural brain properties in determining the task-related brain areas (B). All the brain maps in this paper were visualized using Connectome Workbench (https://www.humanconnectome.org/software/connectome-workbench).

Fig. S2. Scree plots of factor analyses, for (a) positive and (b) negative IOU matrices. The x-axis represents the number of factors, while the y-axis represents the eigenvalue of the principal factors from actual (blue line) and simulated data, expressed by random (reduced) correlation matrix (red dashed line). The suggested number of factors is determined by the number of eigenvalues above the points where two lines intersect, which are 3 and 5 factors for (a) and (b), respectively.

37 Table S1. Description of the cognitive tasks

Construct Task Description Reasoning (Gf) Raven’s Tests non-verbal reasoning using Raven’s Progressive Progressive Matrix Form A. Participants are presented with spatial Matrices (Gf1) arrangements of squares, with one square missing. The missing square has to be selected out of five alternatives. In total, there are 24 question and 3 bonus question. The tasks stops if participant incorrectly selects 3 answers in a row. Spatial Orientation It is measured using Variable Short Penn Line Orientation. Processing (Gf2) The participants need to rotate a line to be parallel with the reference line. To rotate, the participants need to click a button on the keyboard which rotate the line either clockwise or counterclockwise. There are 24 trials in this task. List Sorting The task requires participants to sequence presented stimuli. Working Memory The stimuli are the pictures of animals and foods, (Gf3) accompanied by sound clip and text that name the picture. In 1-list, the participants need to order the items (either animals or food) from smaller to bigger size. In 2-list, both animals and food are displayed. The participants need to sequence the food, from smaller to bigger size, followed by the animals with the same order. Comprehension Oral Reading The task tests the ability of the participants to read English Knowledge (Gc) Recognition Test as accurate as possible. The administrator scores them as (Gc1) correct or wrong. Vocabulary It measures the general knowledge of vocabulary. The Comprehension participants were asked to choose a picture, out of four (Gc2) pictures, which is closely related to the audio stimuli. Memory (Gm) Verbal Episodic It examines the verbal episodic memory where the Memory (Gm1) participants are presented with 20 words and required to remember them. Next, they are shown 40 words (20 new words in addition to the previously presented words) and need to decide whether they have seen the word previously.

38 Picture Sequence The task is done to assess the episodic memory. A sequence Memory (Gm2) of pictures (varies from 6 – 18 pictures depending on age) is presented to participant who is required to recall the sequence over two learning trails. A point is given for each adjacent pair of pictures. Therefore, the maximum point is the number of presented pictures minus one. Executive Dimensional In dimensional change card sort the participants are Function (EF) Change Card Sort - presented with target pictures which vary along features. A Color (EF1) series of pictures (which vary in intended feature) are then displayed to the participants who are required to match them to the target pictures according to the feature; in this task is color. After some trials, the feature is changed. “Switch” trials are also adopted in dimensional change card sort task (both color and shape features), which requires the cognitive flexibility of the participants. For example, 4 straight trials are to match the shape, then the next trial is color before moving back to the shape feature.

Dimensional Similar to (EF1), where instead of color, the feature Change Card Sort - considered on the pictures is shape. Shape (EF2) Note that “switch” trials are also applied.

Flanker Inhibitory This test measures inhibition. It requires participants to Control and decide the direction of the middle arrow from a group of Attention Task – arrows. The congruent means that the middle arrows point in Congruent (EF3) the same directions with the other arrows. Flanker Inhibitory Similar to EF3, it also measures inhibition. But for Control and incongruent, the middle arrows point in the opposite Attention Task – direction with the other arrows. Incongruent (EF4) Mental speed (Gs) Pattern Comparison The task measures the speed of the participants to decide Processing Speed whether a pair of pictures are the same. (Gs1)

39 Sustained Attention It measures the speed of the participants to press spacebar (Gs2) while presented with stimuli. Relational The participants are presented by pairs of objects and asked Processing 1 (Gs3) to decide whether those pairs differ in the same feature. This test was done during functional MRI scan. In this case, the scan is from right to left. Relational In this task, the scan is done from left to right. Processing 2 (Gs4) Note. In the HCP project manual following task abbreviations were used: Gf1 – PMAT24_A_CR; Gf2 - VSPLOT_TC; Gf3 - ListSort_AgeAdj; Gc1 - ReadEng_AgeAdj; Gc2 - PicVocab_AgeAdj; Gm1 - IWRD_TOT; Gm2 - PicSeq_AgeAdj; Ex1 - DCCS_C_s_mean_RT_s; Ex2 - DCCS_S_r_mean_RT_s; Ex3 - Flanker_c_mean_RT_s; Ex4 - Flanker_i_mean_RT_s; Gs1 - Processing_speed_mean_RT_s; Gs2 - Sustained_attention_median_RT_s; Gs3 - Relational_con_mean_RT_RL_s; Gs4 - Relational_con_mean_RT_LR_s.

40 Table S2. Brain areas in MMP atlas

(excel)

Table S3. The detailed information of task-related brain areas

(excel)

41 Table S4. Summary of CFA and EFA model fit estimated to identify neurometric ontological entities of human intelligence

Model 흌ퟐ CFI RMSEA SRMR CFA of performance correlation matrix 190.036 .978 .042 .035 CFA of positive IOU Matrix 510.256 .725 .072 .077 CFA of negative IOU Matrix 633.503 .638 .082 .081 EFA of positive IOU Matrix 62.180 - .000 - EFA of negative IOU Matrix 27.5 - .000 - Note. IOU – intersect over union; CFI – Comparative Fit Index; RMSEA – Root Mean Squared Error of Approximation; SRMR – Standardized Root Mean Squared Residual

42 Table S5. Standardized factor loadings and factor correlations of CFA applied in task scores correlation matrix

Tasks Gf Gc Gm EF Gs Raven’s Progressive Matrices (Gf1) .656 Spatial Orientation Processing (Gf2) .557 List Sorting Working Memory (Gf3) .473 Oral Reading Recognition Test (Gc1) .822 Vocabulary Comprehension (Gc2) .817 Verbal Episodic Memory (Gm1) .367 Picture Sequence Memory (Gm2) .542 Dimensional Change Card Sort - Color (EF1) .800 Dimensional Change Card Sort - Shape (EF1) .883 Flanker Inhibitory Control and Attention Task – .690 Congruent (EF3) Flanker Inhibitory Control and Attention Task – .669 Incongruent (EF4) Pattern Comparison Processing Speed (Gs1) .656 Sustained Attention (Gs2) .265 Relational Processing 1 (Gs3) .365 Relational Processing 2 (Gs4) .452 Factor Correlations Gf Gc Gm EF Gs Gf - Gc .790 - Gm .703 .391 - EF .302 .253 .348 - Gs .352 .341 .509 .790 - Note: All factor loadings and correlations are statistically significant (p < .05).

43 Table S6. The result of Chi-square difference test to determine the number of factors in EFA

(a) Positive IOU matrix

ퟐ 2 Structures 흌 풅풇 휒푑푖푓푓 푑푓푑푖푓푓 푝 1-factor 339.34 90 2-factor 111.19 76 228.15 14 0* 3-factor 62.18 63 49.01 13 0* 4-factor 36.32 51 25.86 12 .0112 5-factor 26.41 40 9.91 11 .5385

(b) Negative IOU matrix

ퟐ 2 Structures 흌 풅풇 휒푑푖푓푓 푑푓푑푖푓푓 푝 1-factor 415.38 90 2-factor 172.04 76 243.34 14 0* 3-factor 100.08 63 71.96 13 0* 4-factor 68.37 51 31.71 12 .0015* 5-factor 27.5 40 40.87 11 0* ퟐ 2 Note: 흌 = chi-square 풅풇 = degree of freedom, 휒푑푖푓푓 = chi-square difference, 푑푓푑푖푓푓 = difference of degree of freedom. The corrected p is .05/8 = .00625. *means that the p is lower than the corrected p. The bold row serves as the best model.

44 Table S7. Standardized factor loading and factor correlations estimated by EFA applied on the positive IOU matrix

Tasks Factor 1 Factor 2 Factor 3 (Accuracy) (EF) (Gs) Raven’s Progressive Matrices (Gf1) .71 -.01 -.08 Spatial Orientation Processing (Gf2) .74 -.08 -.07 List Sorting Working Memory (Gf3) .47 .02 .00 Oral Reading Recognition Test (Gc1) .61 .02 -.08 Vocabulary Comprehension (Gc2) .71 -.04 -.02 Verbal Episodic Memory (Gm1) .05 .12* .05 Picture Sequence Memory (Gm2) .25* .04 .06 Dimensional Change Card Sort - Color (EF1) .02 .40 .07 Dimensional Change Card Sort - Shape (EF2) -.03 .49 .04 Flanker Inhibitory Control and Attention Task – -.07 .67 -.10 Congruent (EF3) Flanker Inhibitory Control and Attention Task – .03 .63 -.13 Incongruent (EF4) Pattern Comparison Processing Speed (Gs1) .25 .04 .23** Sustained Attention (Gs2) .04 -.04 .28 Relational Processing 1 (Gs3) -.09 .04 .30 Relational Processing 2 (Gs4) -.03 -.08 .55 Factor Correlations Factor 1 (Accuracy) - Factor 2 (EF) .53 - Factor 3 (Gs) .49 .50 - Note: All factor loadings are statistically significant (p < .05). The highest loadings of the task are bold faced; these loadings are shown as solid lines in Fig. 3. * the task is included in the most interpretable factors. Note that these loadings on the factor are much smaller than those of the other tasks; hence, the task is not included in the factor. These loadings are shown as broken lines in Fig. 3.

45 Table S8. Standardized factor loading and factor correlations estimated by EFA applied on the negative IOU matrix

Tasks Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 (Gf) (Gc) (Inhibitory) (Switching) (Gs) Raven’s Progressive Matrices (Gf1) .56 .16 .01 -.10 -.01 Spatial Orientation Processing (Gf2) .62 .05 .07 -.05 -.03 List Sorting Working Memory (Gf3) .41 -.03 -.02 .04 .02 Oral Reading Recognition Test (Gc1) .06 .74 .07 -.03 -.03 Vocabulary Comprehension (Gc2) .30 .55 -.07 -.04 -.02 Verbal Episodic Memory (Gm1) -.03 .05 .06 .00 .16* Picture Sequence Memory (Gm2) .22* -.01 -.03 .05 .04 Dimensional Change Card Sort - Color -.03 -.05 -.09 .98 -.09 (EF1) Dimensional Change Card Sort - .16 -.02 .19 .36 -.02 Shape (EF2) Flanker Inhibitory Control and -.02 .02 .81 -.04 -.10 Attention Task – Congruent (EF3) Flanker Inhibitory Control and -.01 .01 .61 -.02 .04 Attention Task – Incongruent (EF4) Pattern Comparison Processing Speed .05 -.08 .10 -.03 .26 (Gs1) Sustained Attention (Gs2) -.04 .06 .00 .07 .14 Relational Processing 1 (Gs3) .05 -.05 -.06 -.05 .45 Relational Processing 2 (Gs4) .01 .02 -.08 -.02 .43 Factor Correlations Factor 1 (Gf) - Factor 2 (Gc) .56 - Factor 3 (Inhibitory) .44 .36 - Factor 4 (Switching) .46 .39 .57 - Factor 5 (Gs) .51 .47 .54 .47 - Note: All factor loadings are statistically significant (p < .05). Bold values assigned the highest loading of the task.

46 * the task is included in the most interpretable factors. these loadings on the factor are much smaller than those of the other tasks; hence, the task was not included in the factor. These loadings are shown as broken lines in Fig. 3

47 Table S9. The comparison of neurometric ontologies using p < .05 and p < .01 thresholds.

p < .05 p< .01 Positive structure Positive structure Best structure has three factors Best structure has three factors Factor 1 (Accuracy) → Gf1, Gf2, Gf3, Gc1, Gc2 Factor 1 (Accuracy) → Gf1, Gf2, Gc1, Gc2, Gc3 Factor 2 (EF) → EF1, EF2, EF3, EF4 Factor 2 (EF) → EF1, EF2, EF3, EF4 Factor 3 (Gs) → Gs1, Gs2, Gs3, Gs4 Factor 3 (Gs) → Gs1, Gs2, Gs3, Gs4 Negative structure Negative structure Best structure has five factors Best structure has four factors Factor 1 (Gf) → Gf1, Gf2, Gf3 Factor 1 (Gf) → Gf1, Gf2, Gf3 Factor 2 (Gc) → Gc1, Gc2 Factor 2 (Gc) → Gc1, Gc2 Factor 3 (Inhibitory) → EF3, Ef4 Factor 3 (Inhibitory and Gs) → EF3, Ef4, Gs1, Factor 4 (Switching) → EF1, EF2 Gs2, Gs3, Gs4 Factor 5 (Gs) → Gs1, Gs2, Gs3, Gs4 Factor 4 (Switching) → EF1, EF2

Five factorial structure Factor 1 (Gf) → Gf1, Gf2, Gf3 Factor 2 (Gc) → Gc1, Gc2 Factor 3 (Inhibitory) → EF3, Ef4 Factor 4 (Switching) → EF1, EF2 Factor 5 (Gs) → Gs1, Gs2, Gs3, Gs4

48 Table S10. The detailed information of ability-related brain areas (excel)