Abstract
Background
Various neuroimaging studies, both structural and functional, have provided support for the proposal that a distributed brain network is likely to be the neural basis of intelligence. The theory of Distributed Intelligent Processing Systems (DIPS), first developed in the field of Artificial Intelligence, was proposed to adequately model distributed neural intelligent processing. In addition, the neural efficiency hypothesis suggests that individuals with higher intelligence display more focused cortical activation during cognitive performance, resulting in lower total brain activation when compared with individuals who have lower intelligence. This may be understood as a property of the DIPS.
Methodology and Principal Findings
In our study, a new EEG brain mapping technique, based on the neural efficiency hypothesis and the notion of the brain as a Distributed Intelligence Processing System, was used to investigate the correlations between IQ evaluated with WAIS (Whechsler Adult Intelligence Scale) and WISC (Wechsler Intelligence Scale for Children), and the brain activity associated with visual and verbal processing, in order to test the validity of a distributed neural basis for intelligence.
Conclusion
The present results support these claims and the neural efficiency hypothesis.
Introduction
Jung and Haier [1] reviewed studies from functional (i.e., functional magnetic resonance imaging and positron emission tomography) and structural (i.e., magnetic resonance spectroscopy, diffusion tensor imaging and voxel-based morphometry) neuroimaging paradigms and reported a striking consensus, suggesting that variations within a distributed network predict individual differences found in intelligence and reasoning tasks. They described this network in the Parieto-Frontal Integration Theory (P-FIT). The P-FIT model includes the dorsolateral prefrontal cortex (BAs 6, 9, 10, 45, 46, 47), the inferior (BAs 39, 40) and superior (BA 7) parietal lobule, the anterior cingulate (BA 32), and regions within the temporal (BAs 21, 37) and occipital (BAs 18, 19) lobes. White matter regions (the arcuate fasciculus) were also implicated. Various neuroimaging studies demonstrated that both frontal and posterior brain regions are associated with intelligence. As a result, it is now widely believed that a brain network characterized by interactions between multiple brain regions is likely to be the neural basis of intelligence [2].
The theory of Distributed Intelligent Processing Systems (DIPS) was first developed in the field of Artificial Intelligence to formalize systems comprised of multiple agents that have individual expertise in solving defined problems but gain the ability to solve tasks of greater complexity through cooperation. DIPS intelligence is, therefore, a function of the types of tools used by its agents, as well as how and for what purpose these tools are used [3]–[10]. Intelligence is both a function of agent diversity and the extent of versatility and plasticity of the relationships shared by these agents. Rocha et al have discussed at length the brain as DIPS [8], [11], [12].
DIPS reasoning is the cooperative activity among a collection of agents coupled, as much as possible, in a decentralized and loose manner that eventually provides a solution to a given problem. By loose, we mean that the relationship between the agents can easily be modified and can therefore account for a solution to a task. By decentralized, we mean that both control and data are logically and geographically distributed; neither global control nor global data storage exist. The control structure is not dependent on the knowledge and properties of specific agents (neurons). Instead, it is embedded in the rules that govern messaging among agents, or can be found in the chemical transactions at the synaptic level. Messages are exchanged by mail systems because each agent (neuron) knows how to address communication to, or has specific connections with, other specific agents (neurons) that may contribute to the task solution. Messages can also be exchanged by blackboard systems (e.g., working memory), where agents post information to be shared with or accessed by any other agents (neurons) that may contribute to a specific DIPS reasoning process (brain processing).
DIPS knowledge is distributed among its agents (neurons) according to their specialization, and is primarily encoded by the relationships (connections) shared by these neurons. In the case of memory, for instance, some agents (e.g., sensory neurons) are responsible for storing data (e.g., sensory information) while others (e.g., hippocampal neurons) keep track of the relationships between these pieces of data by storing information about the associations between these agents (e.g., connecting the different sensory neurons). In the case of procedural knowledge, some agents relate data (e.g., sensory or memorized information) to their processing tools (e.g., motor actions). The complexity of DIPS knowledge depends on the number of specialized agents (neurons) and the complexity of their relationships.
Task distribution is an interactive process between an agent with a task to be executed and a group of agents that may be contributing to task execution. Many of these agents may propose similar but not identical solutions to a given task, either because they may share information from different sources or because they use different tools to handle the same piece of information. This redundancy supports the robust degradation properties of DIPS because agents may be lost without greatly affecting the system's performance. However, this same redundancy may also cause conflict, which, in turn, requires task solutions to be carried out under the guidance of special rules implemented by specialized agents (for examples, see [4], [6], [11], [12]).
EEG mapping studies of the physiological correlates of human intelligence have focused on the level and topographical distribution of cortical activation. The experiments clearly showed that EEG recordings correlate with intellectual abilities [13]–[20]. In fact, strong empirical evidence suggests that individuals with higher intelligence display more focused cortical activation during cognitive performance, resulting in lower total brain activation compared with individuals who have lower intelligence. Such data support the neural efficiency hypothesis [19], [21]. Additionally, a high level of expertise was beneficial for good task performance, but exerted a topographically distributed influence on cortical activation patterns. These findings suggest that higher cognitive performance and the underlying cortical activation are not simply a function of knowledge and competency in a specific domain. They are also a function of the efficiency of information processing by widely distributed systems [16].
Rocha et al [9], [12] proposed that the brain is a DIPS formed by collections of loosely interacting neurons (agents) specialized for data collection (sensors), problem solving (associative neurons), data communication (interneuronal systems), acting upon the surrounding environment (motorneurons), etc. Based on the neural efficiency and DIPS hypothesis, the authors developed a new technique for EEG brain mapping, and applied it to the study of arithmetic cognition in children and adults. The rationality of such approach is presented in the Appendix S1. Principal component analysis showed three distinct patterns of neuronal recruitment for arithmetic calculations in all experimental groups, varying with the type of calculation, age and sex (figure 8).
Figure 8. The message exchange entropies 
for agent
(A) and
the entropy 
of the
recruitment of the agent 
in the
solution of a task 
(B).
See text for further explanation.
The purpose of the present paper is a) to introduce a formal model of DIPS intelligence that may be useful for understanding human intelligence and its neuropsychological substrates; b) to use the above EEG mapping technology in order to investigate the correlations between IQ (evaluated with WAIS [Wechsler Adult Intelligence Scale] or WISC [Wechsler Intelligence Scale for Children]) and brain activity associated with visual (puzzle solving and mental rotation) and verbal processing (charade comprehension and text understanding); and c) test the validity of the proposed theoretical construct.
Results
The mean adult IQ value was 103 and the mean child IQ value was 99, thus, intelligence was equivalent in the two experimental groups. There was no difference in IQ according to abilities of visual and verbal reasoning (Table 1). No statistical IQ or RT differences were observed between genders. RT was smaller for adults compared with the children, and the correlation coefficient for RT×A was −0.51 (R2 = 0.26).
Table 1. RT Factor analysis.
| Factor Loadings (Unrotated) | |
| Factor 1 | |
| Mr | 0.862152 |
| Pz | 0.900775 |
| Ch | 0.738045 |
| St | 0.743899 |
| Expl.Var | 2.652798 |
| Prp.Totl | 0.6632 |
| Eigen value | 2.652798 |
Mr – Mental Rotation RT; Pz – Puzzle RT; Ch – Charade RT; St – story understanding RT, Expl. Var – explained variance; Prp.Totl – probability.
The Z-scores results for the comparison between the Hypothetical Brain and the Real brains of the studied population are shown in figure 1 and they clearly demonstrate that entropy values associated with the different types of brain are significantly different, since the minimum Z-score obtained was 2.46. Therefore, our null hypothesis was rejected. These differences persisted throughout all other comparisons between the hypothetical brain and the brains differentiated by gender (figure 2), age (figure 3) and tasks (figure 4). For these comparisons, the Z-score obtained for some electrodes did not reached the 0.05 significance cutoff (shown as white areas in the figures). However, the number of such electrodes were always smaller than the electrodes that attained statistical significance.
Figure 1. Comparison between a “Hypothetical” (H) and the Real (R) Brains.
The Hypothetical brain was obtained by randomizing the calculated entropies (see text for further details. The actual calculated entropies were used to obtain the Real brain. The mappings H and R depict the averaging of these entropies. The comparison between averaging mappings H and R was quantified by the Z-scores shown by the mapping Z. Noted that the minimum Z-score was 2.48 and the maximum was 11.
Figure 2. The EEG mappings for the calculated linear regression.
calculated for females (F) and males (M) Legends as
in Figure 1. The
Pearson's correlation coefficient between the regression mappings F and
M was −0.27. The Z mappings Zf and Zm mappings
show the differences between the averaging mappings <F> and <M>
and the Hypothetical brain H in figure 4. The areas for which the Z-score is smaller than 1.96
are shown in white, and the areas for the Z-score is greater than 1.96 are
collored according to the magnitude of the Z-score.
Figure 3. The EEG mappings for the calculated linear regression.
calculated for adults and children Legends as in
Figure 1. The
Pearson's correlation coefficient calculated for these mappings was
−0.16. The Z mappings Zc and Za mappings show
the differences between the averaging mappings <C> and <A> and
the Hypothetical brain H in figure 4. The areas for which the Z-score is smaller than 1.96
are shown in white, and the areas for the Z-score is greater than 1.96 are
collored according to the magnitude of the Z-score.
Figure 4. The EEG mappings for the calculated linear regression.
calculated for visual (V) and verbal (L) games
Legends as in Figure 1.
The Pearson's correlation coefficient calculated for these mappings was
0.22. The Z mappings Zv and ZL mappings show the
differences between the averaging mappings <v> and <z> and the
Hypothetical brain H in figure
4. The areas for which the Z-score is smaller than 1.96 are shown
in white, and the areas for the Z-score is greater than 1.96 are collored
according to the magnitude of the Z-score.
Table 2 shows the calculated
values for 
, 
,
and 
for each game. Mental
Rotation (Mr) was associated with the smallest and Story Understanding
(St) with the highest 
. The value of
was almost the same for all games. The values of
ranged from 0.27 in the case of the verbal games to 0.48 in
the case of the puzzle. The value of 
was around 0.7 for all
games.
Table 2. The efficiency values.
|
|
|
|
|
|
|
| Mr | 68 | 11 | 24 | 8 | .35 | .72 |
| Pz | 76 | 11 | 37 | 8.5 | .48 | .77 |
| Ch | 76 | 11 | 22 | 7.5 | .27 | .78 |
| St | 79 | 12 | 22 | 7.5 | .27 | .73 |
Mr - Mental rotation; Pz – Puzzle; Ch – Charade comprehension; St – Story understanding.
, 
,
the
entropy for random decision and 
the
entropy for heuristic decision.
The multiple regression analysis revealed two statistical models correlating IQ with
age (A), RT, 
and 
and with
. Model 1 positively correlated IQ with age (A) and
, and negatively correlated IQ with RT and
. The regression coefficient R for this model was 0.54 and
explained 0.29 of data variance. Model 2 positively correlated IQ with age (A) and
, and negatively correlated IQ with RT. The regression
coefficient R for this model was 0.48 and explained 0.24 of data variance.
The multiple regression 
was used to generate
the 
mapping in figure 5. 
decreased as
increased for the anterior (mainly central and right)
electrodes and increased for the posterior (mainly central and right)
electrodes.
Figure 5. The EEG mappings for the calculated linear regressions.
and 
Light to dark
blue areas are those for which 
and pink to
dark red areas are those for which 
. Max and Min
– maximum and minimum values for 
,
respectively. The Pearson's correlation coefficient between IQ and RT
mappings was −0.16.
The multiple regression 
was used to generate
the 
mapping in figure 5. The 
values calculated for
FP1, FZ, CZ and OZ were directly related to IQ, implying that IQ increased as
for these electrodes increased. In contrast,
values obtained for C3, F4 and O2 were inversely related to
IQ; thus, IQ decreased as 
for these electrodes
increased.
The multiple regression 
, calculated separately
for women and men, was used to obtain the brain mappings shown in figure 2. The Pearson's
correlation coefficient for these two mappings was −0.27. In women, high
is mostly associated with high
for the left brain and with low
for the right hemisphere electrodes. In men, an opposite
pattern was observed, with high 
mostly associated with
high 
for the right brain and low 
for the left
hemisphere electrodes.
The multiple regression 
, calculated separately
for adults and children, was used to obtain the brain mappings shown in figure 3. The Pearson's
correlation coefficient for these two mappings was −0.16. The inverse
correlation between 
and
calculated for the right anterior frontal and right
posterior electrodes, was similar in both groups. The main difference between the
two mappings was the opposite relationship between 
and
calculated for the left anterior electrodes. For these
electrodes 
was inversely correlated with
in adults and directly correlated with
in children. Finally, a positive correlation between
and 
generally dominated in
children compared with adults.
The multiple regression 
, calculated for the
visual and verbal games, was used to obtain the corresponding brain mappings shown
in figure 5. The Pearson's
correlation coefficient for these two mappings was 0.22. The direct correlation
between 
and 
calculated for the
central (FZ, CZ and OZ) and right posterior (P3 and O1) electrodes, was similar in
both groups. An inverse correlation of 
with
was observed for the F4, F7, C3 and O2 electrodes in verbal
games. In contrast, the opposite relationship was seen for the FP1, T3 and T5
electrodes when verbal and visual games were compared.
Discussion
In the field of physiological study of human intelligence, there is strong evidence of a more efficient operation (i.e., less activation) of the brain in brighter individuals (the neural efficiency hypothesis). Haier et al. [22] observed a negative correlation between intelligence and the extent of energy consumption (glucose metabolism) in the brain during cognitive task performance. These initial findings led the authors to formulate the neural efficiency hypothesis of intelligence, claiming that “subjects performing a complex task may well use a limited number of brain circuits and/or fewer neurons, thus requiring minimal glucose use, while poor performers use more circuits and/or neurons, some of which are inessential or detrimental to task performance, and this is reflected in higher overall brain glucose metabolism”.
Here, because our null hypothesis was rejected (see figure 1), the correlation coefficient
ri,j between the EEG activity recorded by the electrodes
, 
was used to calculate
(equations 1 to 4) the entropy 
, quantifying the
commitment of the neurons recorded by the electrode 
to solving a task
. The recruitment 
of the brain in
solving the game 
(equation 5) was set depending on the number
and 
of neurons
for which 
and
for which 
, respectively (see
figure 2 and equation 4).
Finally, the brain efficiency in handling the task 
was defined as
(equation 6), where 
is the entropy of
.
In this context, the neural efficiency hypothesis implies
and 
, in order to make
and 
. In other words, the
neural efficiency hypothesis requires the number
of neurons recruited for the task solution, and the number
of neurons forbidden from participating in the task
solution, to be as small as possible. Here, 
was statistically
similar for the visual (40 bits) and verbal (43 bits) games (43 bits). Therefore,
(
= number of recording
electrodes = 20). In other words, the brain recruitment as
measured by 
is equal to only 10% of the maximum entropy that
could be measured by the 20 recording electrodes.
In addition, the calculated 
was smaller than 0.5
and 
was greater than 0.7 for all games. The neural efficiency
has to be greater than 
if random strategies
were used to solve the games, and greater than 
when heuristics were
used to solve the tasks because 
. It may be proposed,
therefore, that subjects solved the games with a neural efficiency
that was at least greater than
, and thus greater than 0.5. It may also be hypothesized that
and 
, and therefore
, when individual knowledge increases and allows the subjects
to create heuristics for efficient task solutions. In any of these cases,
because 
cannot be greater than
1. Recall, however, that 
was inversely related
to 
. Therefore, heuristic solutions must predominate for high
, in order to decrease 
and keep
. Similarly, a random solution may be used in the case of low
because 
for all games. As a
consequence, it may be concluded that 
for high
and, at least 
for low
.
Although the present results seem to confirm the neural efficiency
hypothesis, caution is necessary because, as discussed above (see
methods), the expected values of 
were obtained under
the assumption that subjects used some optimizing strategies. In the case of the
puzzle, the analysis of the sequences of piece placements showed that they used the
proposed strategy of organizing the puzzle pieces into meaningful items in order to
solve the game. However, there is no available information about the kind of
possible heuristic used to solve the other games. In order to validate the present
findings, future studies require specially designed games that allow the analysis of
strategies used for their Solutions.
Graph theory allows the definition of what should be considered an optimal network.
The notion of an optimal network is closely associated with the small-world
phenomenon [23], [24]. The so-called small-world network architecture is
distinguished from either ordered or random networks. On average, a sparsely
connected graph is expected to have a lower clustering coefficient and longer path
length compared with a densely connected graph with the same topology. Networks with
small-world architecture are characterized by a combination of strong local
clustering and a short characteristic path length (an index of global integration).
This means that, although most of the connectivity is local, the network remains
highly integrated due to a small number of long distance connections. Networks with
scale-free architecture [25] are characterized by the presence of nodes with a very
large number of long distance connections (the hub nodes). The likelihood
of a node having 
connections is given
by 
, 
. Broad-scale networks
are characterized by a degree distribution that has a power law regime followed by a
sharp cutoff that restricts the increase of 
. The cutoff function
constrains the maximum number of nodes that may connect to hub nodes [26]. For
example, 
is a “broad-scale” network, where
is the limiting degree. From equation 4, broad-range and
scale-free networks have clusters of well-connected nodes
and 
for which
because the characteristic pathway length
tends to 2 and a small number of hub nodes
for which 
if
.
Micheloyannis et al [27] recorded EEG signals to study neuronal interactions during working memory tests in individuals who had few years of formal education (LE) compared with individuals who had university degrees (UE). They quantified the synchronization between EEG channels in several frequency bands, and then converted EEG signal correlations into graphs to estimate the clustering and distance characteristics of the underlying processing networks. According to the authors, findings supported the neural efficiency hypothesis and suggested that the connections between brain areas of well-educated subjects engaged in working memory tasks have less small-world characteristics than those of less-educated volunteers. Iturria et al. [26] used diffusion-weighted Magnetic Resonance Imaging (DW-MRI) to estimated the anatomical connection probabilities (ACP) between 90 cortical and subcortical brain gray matter areas. They concluded that all the studied networks have small-world and broad-scale characteristics. Van den Heuvel et al [28] used a voxel-wise approach for a model-free examination of both inter-regional as well as intra-regional connectivity in the human brain. Resting-state 3 Tesla fMRI scans of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs. This result, together with a short average path length, indicated a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Their findings suggested a combined small-world and scale-free organization of the functionally connected human brain. The results were interpreted as evidence for a highly efficient organization of the functionally connected brain, in which voxels are mostly connected with their direct neighbors, forming clustered sub-networks that are held together by a small number of highly connected hub-voxels that ensure a high level of overall connectivity.
The correlation coefficients 
calculated for the EEG
activity recorded by the electrode entropy 
and
were assumed here to be surrogates for the connectivity
between the neurons recorded by these electrodes. In this context,
calculated for the recording electrode
may be assumed to represent the connectivity
of the neurons recorded by 
. In other words, the
number of instances 
, when the calculated
is equal to 
, is a measure of
in the studied population. The regression analysis showed
that 
, 
and
, 
, leading to the
conclusion that the solution of our games was supported by broad-scale or scale-free
networks.
In addition, the present results showed that 
was inversely related
to 
and directly related to 
. This means that
high-
individuals tended to recruit fewer (smaller
) highly correlated (larger 
) neurons, compared
with low-
volunteers, to solve the games. Therefore, it may be
proposed here that IQ is correlated with the dynamics of broad-scale (or scale-free)
networks organized in the brain for different purposes (e.g., [29]–[31]). The information flow in
this type of network is very efficient because it depends on a small number of
connections (axons) with the hub nodes, instead of relying on a large number of
randomly distributed connections, as is the case in random networks (e.g., [23], [26]).
The 
mapping in figure 5 shows that 
increased as
, calculated for FP1 and the central electrodes (FZ, CZ and
OZ), increased, and decreased as 
, calculated for C3,
F4, PZ and O2, increased. Lee et al [32] showed that high g-loaded tasks specifically increased
regional activity in the bilateral fronto-parietal network that included the lateral
prefrontal, anterior cingulate and posterior parietal cortices. In addition, the
regional activations of the superior-g group were significantly stronger than those
of the control group, especially in the posterior parietal cortex. Finally,
regression analysis revealed that activity of the superior and intraparietal
cortices (BA 7/40) strongly covaried with individual differences in g. Although EEG
recorded activity cannot be easily mapped to spatial location, there is an almost
perfect match between the 
mapping in figure 5 and the map shown in
figure 2 of Lee et al [32].
Haier et al [33]
showed that more gray matter in a number of Brodmann areas (BA) was associated with
higher 
, and suggested a distributed neural basis of intelligence
similar to that disclosed by our data. Recently, Jung and Haier [1] reported a
striking consensus among different papers suggesting that variations in a
distributed network predict individual differences found in intelligence and
reasoning tasks. They described this network as the Parieto-Frontal Integration
Theory (P-FIT). The P-FIT model includes the dorsolateral prefrontal cortex (BAs 6,
9, 10, 45, 46, 47), the inferior (BAs 39, 40) and superior (BA 7) parietal lobule,
the anterior cingulate (BA 32), and regions within the temporal (BAs 21, 37) and
occipital (BAs 18, 19) lobes. The P-FIT model includes, therefore, many of the
components presently identified by the 
mapping in figure 5.
Another experimental approach to elucidating basic cognitive mechanisms that underlie
general intelligence (psychometric g) is based on the attempt to relate psychometric
g to the speed of information processing [34]. Within this conceptual
framework, a large number of studies provided evidence for a relationship between
levels of psychometric g and certain parameters of reaction time
(
) derived from Hick's law (e.g., [35]). In the present study,
and 
were also inversely
related.
The 
mapping in figure 5 shows that RT increased as 
, calculated for the
posterior right hemisphere, increased, whereas 
obtained from the
right anterior electrodes decreased. There is some overlap between the
and 
mappings (see figure 5); however, the activity
recorded by FZ, P4 and O2 was related to 
and
in opposite ways. The Pearson's correlation coefficient
for the 
and 
mappings was
−0.16. These findings show that 
and
may share some common neural substrates but are two
different neural constructs.
The consensus view states that there are no sex differences in intelligence. However, Lynn [36] has formulated a developmental theory of sex differences in intelligence that challenges this view. The theory states that boys and girls mature at different rates, such that the growth of girls accelerates at the age of about 9 years and remains in advance of boys until 14–15 years. At 15–16 years the growth of girls decelerates relative to boys. From this age on, boys continue to grow and increase their mean IQ relative to that of girls. Colom and Lynn [37] presented new evidence for the theory from the Spanish standardization sample of the fifth edition of the Differential Aptitude Test (DAT). Their results showed that sex differences for 18 year olds in the DAT performance as a whole is a 4.3 IQ point advantage for boys, a value that is very close to the advantage that can be predicted from their larger brain size (4.4 IQ points). Jackson and Rushton [38] found that 17- to 18-year old males averaged 3.63 IQ points higher than did their female counterparts on the 1991 Scholastic Assessment Test (SAT). Here, no IQ sex difference was observed, although it must be noted that the experimental group was small and involved both children and adults. Because of the small number of individuals in each experimental subgroup (n = 20) no gender statistics was separately analyzed for each of these subgroups.
Despite the fact that no 
statistical difference
was observed here between male and females, the 
mappings calculated
for male and females separately (see figure 6) showed interesting differences. The Pearson's correlation
coefficient for the gender mappings is −0.27, the highest discrimination
between all the mappings in figures
2, 3, 4, and 5. The right hemisphere and the anterior pole of
the left frontal lobe are associated with high 
in males, whereas
almost the entire left hemisphere correlated positively with the female
(green and blue areas in figure 2). In contrast, the left hemisphere
(except O2) was negatively related with male 
, whereas female
decreased as 
increased for the
right electrodes F4, F8, P4 and O2 (red and pink areas in figure 2). Njemanze [39] evaluated cerebral
lateralization during Raven Progressive Matrices in female and male subjects.
Bilateral simultaneous transcranial Doppler (TCD) ultrasound was used to measure
mean blood flow velocities (MBFV) in the right and left middle cerebral arteries
(MCAs) in 24 (15 females and 9 males) right-handed normal subjects. The authors
found that female subjects used a left hemisphere strategy, whereas males used a
right hemisphere strategy to successfully solve Raven Progressive Matrices.
According to the author, these results imply that intelligence is associated with
neural systems within one hemisphere that are gender-accessible to a variety of
cognitive functions. Neubauer et al. [19] found that in males, the
highest correlations were observed for spatial 
, and in females for
verbal 
. Furthermore, the sexes displayed topographical differences
in neural efficiency patterns. Jaušovec and Jaušovec [18] described
gender EEG differences concerning both general and emotional intelligence. Rocha et
al. [9] used the
presently discussed EEG brain mapping technology to study arithmetic cognition in
children and adults. Factor analysis showed three distinct patterns of neuronal
recruitment for arithmetic calculations in all experimental groups, which varied
according to the type of calculation, age and sex. Males were faster in arithmetic
calculation than females, irrespective of age. However, individuals of both sexes
were equally accurate in their calculations. It is plausible to conclude that males
and females have different cognitive styles that nevertheless result in no or
minimal 
or cognitive differences.
Figure 6. The games.
The game rules are: a) Mental rotation (Mr): an object in a given spatial orientation is provided as a model to be matched to one out of four possible spatial orientations of the same object. Each game session involved 10 decision-making trials designed to explore visual reasoning; b) Puzzle solving (Pz): nine pieces of a scene, animal or object must be assembled over a nine-cell rectangle. The entire game includes three different pictures to be assembled. A warning signal indicates any piece misplacement. In this case, the subject had to remove the misplaced piece before trying another piece. Each game session involves at least 27 trials of decision-making designed to explore visual planning and reasoning; c) Charade solving (Ch): a three to four phrase description of a fruit or animal (e.g.; “My juice is delicious, my colour is my name; …”) is provided 500 ms before different pictures are displayed for decision making. Mean soundtrack duration for all charades is around 4 seconds. Each game session involved 10 trials of decision-making designed to explore speech comprehension and semantic memory; d) Story understanding (St): a verbal description of scenes of a Christmas story is provided 500 ms before five Christmas scenes are visually displayed for decision-making. Mean soundtrack duration for all scene descriptions is 5 seconds. Each game session involved 10 trials of decision making designed to explore speech comprehension and episodic memory.
Event-related brain potential (ERP) components showed typical gradual decrements in
latency and amplitude with increasing age [40]. Regression analyses between
Raven's intelligence scores and latency of the ERP components showed negative
correlations for the late endogenous components at age 9. At ages 10 and 11, the
earlier components showed positive correlations while the later components continued
to show negative correlations. The amplitude measures showed only positive
correlations, which shifted from the exogenous P1 component at age 9 toward the
later endogenous components at ages 10 and 11. Here, the Pearson's correlation
coefficient for the 
mappings calculated
separately for children and adults (figure 3) was −0.16. The general picture revealed by these
mappings seems to be that the children's networks involved in game solutions
were broader than those used by adults. Fair et al. [41], [42] analyzed the connectivity of
control networks and showed that adults, compared with children, used control
networks with fewer short-range connections and more long-range connections. The
authors concluded, as we did, that adult networks are more cohesive and
interconnected than the corresponding children's networks.
In conclusion, we proposed a general prediction model that assumes IQ to be linearly
correlated with 
, age (A), response time (RT),
or 
. This model relates IQ
to: the adequacy 
of the recruitment of neurons for solving a given task
of complexity 
; the extent
of this recruitment andits neural efficiency measured as
, showing that these relationships are influenced by age and
correlated with RT. The IQ and RT correlations with 
indicate that IQ and
RT are better understood as different but correlated neural constructs.
Considering 
to be a measure of the connectivity
of the neural networks involved in our game solution, it was
shown that these networks have broad-scale and scale-free properties. Broad-scale
and scale-free properties are assumed to belong to efficient networks from the point
of view of information flow. Consequently, we proposed that IQ is associated with
the broad-scale and scale-free qualities of the neural networks that support
reasoning and cognition.
The network-based understanding of brain function is a very recent paradigm that is being tested by neuroscientists as a formal tool to model cerebral function. Here, we used such an approach to study the relationship between IQ and the brain. The results are promising; however, much more work remains to account for some of the weak points of the present investigation and to research complex issues such as IQ, sex and age.
Materials and Methods
The experiment
Volunteers of two experimental groups
Children (C): 20 children of both sexes (10 female and 10 male), age ranging from 7 to 11 years (mean = 9.15; sd = 1.38), who were attending an elementary school program, and
Adults (A): 20 adults of both sexes (10 female and 10 male), age ranging from 23 to 45 years (mean = 29.2; sd = 5.85), all having finished college
played four different types of computer games (figure 2) while their EEG was recorded (20 electrodes placed according to the 10/20 system; impedance smaller than 10 Kohm; notch filter 50 Hz; sampling rate of 256 Hz and 10 bit resolution). The subjects' IQ was evaluated by the Wechsler Intelligence Scale for Children (WISC), or the Wechsler Adults Intelligence Scale for Children (WAIS) in a different session.
The games
Four different types of games were used (figure 6):
Puzzle solving (Pz): nine pieces of a scene must be assembled over a nine-cell rectangle to match the template figure.
Mental rotation (Mr): the task is to mach the actual spatial orientation of a target object to one out of four different spatial orientations.
Charade solving (Ch): a verbal description of four attributes of a fruit or animal is provided 500 ms before five different pictures of fruits or animals are displayed. The task is to match the verbal description to one out of five of these pictures.
Story understanding (St): a verbal description of four attributes of Christmas story scenes is provided 500 ms before Christmas scenes are visually displayed 500 ms before five different pictures of the story are displayed. The task is to match the verbal description to one out of these five scenes.
Factorial analysis showed that RT for all games heavily dependent on one general factor (Table 3).
Table 3. The mean response time for each game.
| RT | SD | |
| Mr | 4.07 | 1.01 |
| Pz | 7.63 | 2.34 |
| Ch | 5.36 | 1.51 |
| St | 10.49 | 3.32 |
Mr - Mental rotation; Pz – Puzzle; Ch – Charade comprehension; St – Story understanding.
The calculation of the efficiency 
in solving each
game requires the estimation of its 
(see equation 6).
The game solution implies at least three main steps:
identification: recognizing the objects, scenes and puzzle pieces as well as the meaning of each phrase that describes their attributes;
decision-making: selecting the assumed game solution, and
mouse control: reporting the game solution
These steps require specific computational capabilities estimated as
, 
and
, respectively. Therefore:
 |
(1) |
The
estimation of 
and 
is difficult, but
the possible range of 
variation may be
estimated as proposed below and provides some information about the lower limit
of 
because 
. Also,
if 
because both
visual and/or verbal decoding, as well as motor control, are well learned.
The actual value of 
depends on the
strategy used to solve the game. For example, the puzzle solution implies nine
decisions about the relation of each puzzle piece and its location in the
puzzle. If errors are made the number of decisions increases. A brute-force or
random puzzle solution implies that the uncertainty
of this random decision is
 |
because:
first decision implies that each piece location has the same probability of
;second decision implies the same probability of
because if
no error occurred in a), one piece of the puzzle was already
located,and so on …
An alternative strategy to reduce the task entropy
for puzzle solution, is to identify and organize the
puzzle pieces into meaningful items. In the case of the puzzle in figure 6, these meaningful
items are: the house composed of seven pieces; the wolf composed of three
pieces; the tree composed of two pieces; the girl composed of two pieces; the
sun represented by one piece and the flowers represented by one piece. If a
subject decides first to locate the wolf pieces and then the house pieces, the
uncertainty 
of this heuristic decision is:
wolf:
because the probability of its pieces location
are respectively 
,
and
(as in a,
b and c above) andhouse:
because the probabilities of the location of its
pieces are respectively 
, ,
,
,
and
because
two of the wolf's pieces are also house's pieces, and
.
In the case of the rotation game, the total of all object orientations to be
discriminated is eight. A brute-force solution implies
because the volunteer has to match
(
) the orientation of the target and the orientation of
the four possible solutions. Again, heuristics may be used to select meaningful
general orientations like left, right, up, down, etc. in order to reduce the
task entropy 
. For instance, in the example in figure 2, a decision can be achieved in two
steps: 1) the up/down (u/d) decision that implies
and 
, and then 2) the
left/right (l/r) decision that implies 
and
, such that 
.
In the cases of the charade and story games, each of the four verbal descriptions
has to be matched to each of their visual counterparts in five different
pictures; that is, each description has to be matched against 20 visual
alternatives. A brute-force solution implies 
because the
volunteer has four decision steps represented by the probabilities
, 
,
and 
. However, because
the number of attributes necessary to solve many of the tests is smaller than
four, the volunteer may use different strategies to reduce
. The reduction to three discriminating factors decreases
to 14 bits, whereas the reduction to two discriminating
factors decreases 
to 7.5 bits.
The EEG recording and processing
Two networked personal computers were used (figure 7): one to record the EEG and the
other to display the game. Times for each test display
(
) and decision (
) were recorded and
synchronized with the EEG recording. Table 3 shows the mean
and 
calculated for
each game. After the experiment, EEG was visually inspected for artifacts that
could compromise the analysis, and such records were discarded. Two EEG epochs
of two seconds (from 
to
, and from 
to
) preceding the decision were selected to calculate the
entropy 
for each recording electrode
according to equations 1 to 4. We assumed the linear
regression coefficient ri,j calculated for the EEG activity recorded
by the electrodes 
,
as the measure of the pi,j of message
exchange between the neurons recorded by these electrodes. Equation 6 was used
to calculate 
.
Figure 7. The experiment.
Two networked microcomputers were used to record the EEG activity (10/20 system) while the individual is solving a specific cognitive task. The beginning of each task and the moment a decision is made are saved in the database together with the type of decision-making (D) and time required (response time ST) to achieve such decision. The linear correlation coefficients ri,j for the recorded activity at each recording electrode ei, with reference to the recorded activity for each other 19 recording sites ej, were calculated for each game (COG) performed by a given subject. These ri,j were used to calculate the correlation entropy h(ei) for each recording electrode ei. In this way, h(ei) was calculated for all 20 recoding electrodes. The corresponding values of h(ei) constitute the Entropy Data Base. Regression analysis between RT and h(ei) was used to build the cognitive mapping. Each mapping shows the contribution βi hm(ei) of each electrode ei to ST. hm(ei) is the average of h(ei) calculated for all subjects. IQs values of each subject were added to each corresponding data base record.
Here, we assumed that the null hypothesis states that the entropy calculated as above is equal to the brain activity of a hypothetical brain obtained by 1) randomly reordering the recorded EEG activity by the 20 channels and then 2) computing the entropy of a “hypothetical” brain using the randomized EEG activity. Any difference between this “hypothetical” and the real brains of the studied sample is quantified by calculating the Z scores between the hypothetical and these real brains.
The following efficiency coefficients were calculated:
 |
(2) |
Since 
and
then:
 |
(3) |
Multiple regression analysis was used to calculate:
 |
(4) |
as well as the significance
-level 
of each angular
coefficient 
. In addition, the number 
of negative
angular coefficients with 
and the number
of positive angular coefficients with
were obtained for a given significance level
. Finally, the values of 
,
and 
were obtained.
The normalized values of 
were used to build
the brain mappings to display the results of the regression analysis (figures 2, 3, 4, and 5). The mapping color-encoding routine was
obtained with commercial software (Icelera Inc.). Statistically positive
values (
) are encoded from
red (
) to yellow (
); statistically
negative 
values (
) are displayed
from blue (
) to green (
), and
statistically non-significant 
values
(
) are shown in orange. Brain contours are used as
references for spatial location of the 10/20 system electrodes. The
Pearson's correlation coefficient was used to measure the similarity
between regression mappings.
Multiple regression analysis was also used to study the correlations between IQ,
RT, Sex, Group and Game, as well as to investigate a linear model of IQ
depending on 
, RT, Group and Game, and 
= Max(
)−Min(
). Statisca®
was used for all statistical analysis.
Ethical Aspects
This work was reviewed and approved by the Institutional Review Board of APAE-Jundiai (Associação de Pais e Amigos dos Excepcionais de Jundiai) and written consent was obtained from all participants in case of adults and from parents/guardians in the case of children.
Supporting Information
Loosely connected DIPS.
(DOC)
Acknowledgments
The authors thank Dr. F.A.B. Coutinho for his helpful comments on the manuscript.
Footnotes
Competing Interests: The authors have declared that no competing interests exist.
Funding: The funders from LIM HCFMUSP (Laboratórios de Investigação Médica) and CNPq (Conselho Nacional de Pesquisas) had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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Loosely connected DIPS.
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