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1
Normal and Low IQ children
Fábio Theoto Rocha
1
, Armando Freitas da Rocha
1
and Suely Angelotti
2
1 - RANI – Research on Natural and Artificial Intelligence
2 – APAE Jundiai
http://papers.ssrn.com/abstract=2340549
2
Abstract: The neural efficiency hypothesis (NEH) of intelligence claims that
subjects performing a complex task may well use a limited number of brain circuits
and/or fewer neurons while poor performers use more circuits and/or neurons,
some of which are inessential or detrimental to task performance. The present
paper studies the EEG activity associated with reading and arithmetic calculation
by normal and mental retarded children. Correlation analysis of the electrical
activity recorded by 10/20 electrode system was used to calculate the amount of
information allocated by individuals to solve these tasks. Multiple regression
analyses showed that IQ linearly correlates with the amount of information
provided by each electrode about task solution. This analysis also shows that
normal children allocate an amount of computational resources
N
BH )( greater
than that allocated by mental retarded children
L
BH )( to solve both reading and
calculation task. Most important, it is shown that
NL
BHTHBH )()()( << what
means that mental retarded children allocate less and normal children allocate
more computational resources than the task uncertainty
)(TH
. This shows that
neural efficiency is bound by task uncertainty, such that intelligence increases as
)(
)(
BH
TH approaches 1 and decreases otherwise. Although the different genders
were shown to use different neural circuits to solve the same task, these
differences are equally effective and did not resulted in IQ differences.
Keywords: EEG; neural efficiency; distributed intelligence; g intelligence; IQ,
gender differences
3
Introduction
The theory of Distributed Intelligent Processing Systems (DIPS) was first
developed in the field of Artificial Intelligence to formalize systems composed by
multiple agents that have individual expertise in solving defined problems but gain
the ability to solve tasks of greater complexity through cooperation (Rocha, 1992;
Rocha, 1997; Rocha et al, 2004; 2005 2011). According to this theory, intelligence is
both a function of agent diversity and the extent of versatility and plasticity of the
relationships shared by these agents. According to Jung and Haier (2007) and their
Parieto-Frontal Integration Theory (P-FIT ), variations within this network of widely
distributed neurons predict individual differences found in intelligence and reasoning
tasks. 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 (Iturria-
Medina et al. 2008; Rocha et al, 2011; Song et al, 2008).
EEG mapping studies of human intelligence have clearly showed that EEG
recordings correlate with intellectual abilities (e.g., Doppelmayr et al, 2002, 2005;
Fink and Neubauer 2006; Freudentalher et al, 2000; Grabner, Neubauer and Stern,
2006; Jaušovec, 2000; Jaušovec and Jaušovec, 2005; Micheloyannis et al, 2006;
Neubauer and Fink, 2003, 2005; Schmid, Tirsch and Scherb, 2002; Stauder et al,
2003) and suggest 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. Haier et al.
(1988) observed a negative correlation between intelligence and the extent of
4
energy consumption (glucose metabolism) in the brain during cognitive task
performance. These initial findings led the authors to formulate the neural
efficiency hypothesis (NEH) 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”. fMRI studies on brain
networks (e.g., Dozembach et al, 2006, 2007; Grecius et al, 2003) suggest that IQ
is correlated with the dynamics of broad-scale (or scale-free) networks (Iturria-
Medina et al, 2008; Reijneveld et al, 2007, van den Heuvel et al, 2008; Wats, 1999)
organized in the brain for different purposes 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 (Micheloyanis et al,
2006; Reijneveld et al, 2007; Yturria-Medina et al, 2008).
Both DIPS and NEH were used by Rocha et al (2011) to develop a new
EEG brain mapping technology to study brain correlates of intelligence. In this
approach, the information
)(
i
eH
provided by electrode
i
e
about the brain activity
associated with cognitive task is a function of the correlation coefficient
ji
r
,
between the electrical activities recorded by
i
e
and by all other recoding electrodes
j
e
(See methods for details). Principal Component Analyses (PCA) of
)(
i
eH
calculated for each step of task solution discloses patterns of EEG activity that are
5
assumed to be associated with activity of distinct neural circuits enrolled to solve
the task. PCA is a statistical tool for investigating patterns of covariation in a large
number of variables (Hair et al, 1998), for example
)(
i
eH
calculated for each
electrode and each decision making, and for determining if this information may be
condensed into small sets of these variables called principal components. The
principal components calculated for
)(
i
eH
associated with the solution of a given
task are assumed to correlate with the activity of the different neural circuits involve
in the solution of this task (Rocha et al, 2004, 2005). Regression analysis between
IQ and
)(
i
eH
may be used to study neural correlates of intelligence associated
with task solution.
Rocha et al. (2011) used this experimental approach to study IQ neural
correlates in a population of 20 children and 20 adults of both sexes and showed
that
)(
i
eH
calculated for the studied cognitive tasks attained values around of
10% of their maximum possible values. This result was interpreted as supportive of
NEH because it means that only a small number of neural circuits were enrolled in
task solution. In addition, they showed that high-
IQ
individuals tended to recruit
fewer (smaller )(
i
eH ) highly correlated neurons, compared with low-
IQ
volunteers,
to solve the games. This is the expected dynamics of neural efficient broad-scale
(or scale-free) networks organized in the brain for different purposes (e.g.,
Dozembach et al, 2007).
6
Volunteers IQs in Rocha et al. (2011) were within normal range. So, it is
important to expand their study to people that are assumed to have cognitive
impairment. This is the purpose of the present paper. In order to accomplish it we
studied a group of 20 children (both sexes) presenting important cognitive
difficulties and enrolled in a special education school because their IQ are below
70 in Wechsler Intelligence Scale for Children (WISC), and another group of 20
children (both sexes) enrolled having their IQ above 80, enrolled in a regular
elementary school and presenting a normal cognitive development. Both groups
solved reading and arithmetic tasks while their EEG was recorded.
Material and Methods
Volunteers of two experimental groups:
a) Normal IQ (N): 40 children of both sexes (20 female and 20 male), age ranging
from 7 to 9 years (mean=8; sd=0.83), IQ = 102.4 ± 13.5 (no gender difference),
who were attending a regular elementary school, and
b) Low IQ (L): 40 children of both sexes (20 female and 20 male), age ranging
from 7 to 12 years (mean=9.82; sd=1.69), IQ = 56.9 ± 11.3 (no gender
difference), who were attending a special elementary school (APAE – Jundiaí).
solved reading and arithmetic tasks like those illustrate in figure 1 while their EEG
was recorded (20 electrodes placed according to the 10/20 system; impedance
7
smaller than 10 Kohm; notch filter 50Hz; sampling rate of 256 Hz and 10 bit
resolution, ear lobe reference). The subjects’ IQ was evaluated by the Wechsler
Intelligence Scale for Children (WISC) in a different session. We preferred to
control our experiments taking cognitive development instead of age into
consideration. Both N and L groups were learning to read phrases and to do
simple arithmetic calculations, because of this L were older than N children.
The exact moments (
o
t
) each game screen was presented and exact
moments (
f
t
) the volunteers chose an answer to the reading or arithmetic task
were registered in the experimental data base together with information about the
type of answer (right or wrong). Response time was calculated as
of tt −
for all
activities and volunteers. EEG epochs of two seconds of recorded electrical activity
preceding the moment
f
t
were selected for analysis. Reading activities involved
both reading words and phrases (10 activities) and/or phrases (10 activities) and
arithmetic tasks involved addition, subtraction and/or multiplication (10 activities
each). A total of 20 EEG epochs associated with each reading task (words or
phrases) and a total of 30 EEG epochs associated with arithmetic tasks were,
therefore, selected for each individual. In this context a total of 800 decisions on
reading and of 1200 decisions on arithmetic tasks were selected for analysis in
case of each experimental group N or L. EEG was carefully inspected for artifacts
and bad records were discarded. This reduced the studied EEG epochs to 3480,
with a rejecting rate around 13%.
8
Figure 1 – Examples of reading and arithmetic tasks
Signals from a multi-channel EEG are unavoidably correlated due to the fact
that the recording from each electrode are generated by local field potentials or
source signals (
i
s) from several distinct cortical areas. The source signals
i
s can
be summed up and projected to the electrodes. In this context, EEG data )(te
i
recorded at a single electrode
i
e are a simple weighted
i
w sum of underlying (
k
)
cortical source signals )(ts
l
generated by
i
s at time t, that is:
)()(
1
tswte
l
k
l
i
li
∑
=
=
(1)
The number
k
of active sources is determined by the task being currently
processed by the brain.
9
Each electrode may record signals from sources
l
s that have different
spatial and temporal distributions, and different electrodes may record signals from
the same source
l
s. Therefore, EEG data )(td
i
recorded by each single electrode
i
e may provide different or redundant information about the sources
l
sactivated by
the task being currently processed. In this context, a key datum that may be
obtained from the EEG about how the task is being processed is the amount of
information ( )(
i
eH ) each electrode may provide about the sources
l
s(Rocha et al,
2010; 2011). Because EEG data are assumed to be a weighted sum of the
electrical activity of different sources, correlation analysis of the EEG activity
)(td
i
recorded by the different electrodes
i
e may be used to calculate )(
i
eH in
order to summarize information provided by each electrode
i
e about all involved
sources
i
sinto a single variable as proposed by Rocha et al (2011). The rationality
is the following.
The Pearson correlation R is +1 in the case of a perfect positive (increasing)
linear relationship (correlation), −1 in the case of a perfect decreasing (negative)
linear relationship (anticorrelation),and some value between −1 and +1 in all other
cases, indicating the degree of linear dependence between the variables. As it
approaches zero there is less of a relationship (closer to uncorrelated). The closer
the coefficient is to either −1 or +1, the stronger the correlation between the
variables. In this context, the correlation strength
r
is equal to
R
. If
data )(
td
i
,)(td
j
furnished by two electrodes
i
e,
j
e provide equivalent information
10
about sources
i
sthen Pearson correlation coefficient
ji
R
,
calculated for
)(td
i
,)(td
j
will approach
1
±
, otherwise it will approach 0. The highest uncertainty
about the information equivalence provided by
i
e,
j
e occurs when the correlation
strength
ji
r
,
approaches 0.5. Therefore, in the same line of reasoning used by
Shannon (1948) to define the amount of information provided by a random
variable, it is proposed that the informational equivalence,
)(
,ji
rH
of )(td
i
,)(td
j
furnished by
i
e,
j
e is the expected value ))((
,ji
rIE of the information
)(
,ji
rI provided by
ji
r
,
. Therefore:
[
]
)1(log)1()(log))(()(
,2,,2,,, jijijijijiji
rrrrrIErH −−+−==
(2)
such that if 5.0
,
=
ji
r then 1)(
,
=
ji
rH and if 1
,
=
ji
ror 0
,
=
ji
rthen 0)(
,
=
ji
rH .
Now, given
19
19
1,
∑
=
=
jji
i
r
r (3)
the entropy of
i
r is
[
]
)1(log)1(log)(
22 iiii
i
rrrrKrH −−+−=
(4)
11
and it quantifies the mean informational equivalence from )(td
i
concerning that
provided by all other
)(td
j
, because the different electrodes (information channels)
provide different, but correlated, information about
i
s.
In this context, we propose that
19
])()([
)(
19
1,
∑
=
−
=
jjii
i
rhrh
eH
(5)
quantifies the information provided by )(td
i
about the sources
i
s involved in a
cognitive task solving, because
a) if
kr
ji
=
,
for all all
j
e
then kr
i
=, )()(
,iji
rHrH = for all
j
e
, and consequently
0)( =
i
eH . This indicates that )(td
i i
edoes not provide any additional
information about the sources
i
s;
b) for all other conditions 1)(0 <<
i
eH and quantifies the information provided by
)(td
i
about the sources
i
s.
While Event Related Activity and Spectral Band Analysis may provide
information about specific and localized sources
l
sinvolved in a task solving, )(
i
eH
provides information about the spatial and temporal distribution of these sources,
therefore, provides information about how different sets of neuron enroll
12
themselves in a widely distributed network to solve a given task (Rocha et al,
2011). Another interesting )(
i
eH property is that it summarizes information about
all sources
l
s into a single variable, simplifying many analysis (e.g., regression
analysis, principal component analysis, etc.) involving behavioral and neural
variables (Rocha et al, 2011). Here, this summarizing )(
i
eH property allowed us to
study the relation between IQ and EEG activity.
)(
i
eH was calculated for each reading and arithmetic task and each
volunteer, that is it was calculated for 3480 EEG epochs. Multiple regression
analysis was used to study the relation between IQ and )(
i
eH according to the
model proposed by Rocha et al (2011):
)()(...)(
23
2
2221202011
SMaxSeHeHaIQ
βββββ
++∆++++= (6)
where
))(min())(max(
minmax ii
eHeH −=∆
−
,
2
20
1
2
20
)(
=
∑
=ii
eH
Sand ))(max()max(
i
eHS =
(7)
To study possible gender influences upon the relation between IQ and
)(
i
eH , gender was assumed as a dummy variable in another statistical model
(Hayashi, 2000)
13
)max()()()(
25
2
242323
2
2221
SGGSGeGHSMaxSeHaIQ
iiii
χδδδδββββ
++∆++++∆++=
(8)
where
G
is the dummy having value 1 for female and 0 for male. In this context, the
coefficients
i
δ
provide a measure of female impact on IQ calculated by equation 8.
i
δ
helps to determine whether there is a discrimination in IQ between men and
women. If 0<
i
δ
(negative coefficient), then for the same )(
i
eH , women have lower
IQ than men. On the other hand, if δ
0
>0 (positive coefficient), then for the same
)(
i
eH , women have higher IQ than men.. Note that the coefficients
i
δ
attached to
the dummy variable
G
are differential intercept coefficients. Here, regression
calculated by equation 6 is called model M1 and that calculated by equation 8 is
called mode M2.
Results
Normal IQ (N) children solved all reading and arithmetic tasks with a low
mean rate of errors of 1.8±1.2. Around 40% of Low IQ (L) were able to solve most
of phrase reasoning activities and 20% of them experienced great difficulties with
multiplication. Their error mean rate was 3.2±1.2. N children took 13.1± 5.1
seconds to solve reading activities and 13.8±5.3 seconds to solve arithmetic tasks,
whereas L children took 15.8± 10.2 seconds to solve reading activities and
11.4±8.36 seconds to solve arithmetic tasks.
14
Calculated )(
i
eH was smaller for L children than for N children for all
electrodes except O2 and OZ (see table I). In the same way, both
minmax −
∆ and
2
S
were smaller for L children than for N children. Finally, max( )(
i
eH
) was small
for L children than for N children whereas min( )(
i
eH
) did not differed for both
groups. Calculated )(
i
eH
statistically differed between male (M) and female (F)
volunteers for half of the electrodes (table I) and
minmax −
∆ and
2
S
were smaller
for R in comparison to C. Figure 4 shows the )(
i
eH
mappings for L, N, M and F, as
well as for the )(
i
eH
differences between these groups.
Table I - )(
i
eH
calculated for all (A), low IQ (L), normal IQ (N), male (M) and
female (F) volunteers. p statistical significance for L-N and M-F differences.
A L N p F M p
C3 2.77 1.81 3.59 0.00 2.71 2.85 0.05
C4 2.30 1.95 2.59 0.00 2.72 1.75 0.00
CZ 2.49 2.15 2.78 0.00 2.27 2.78 0.00
F3 2.77 2.19 3.26 0.00 2.50 3.11 0.00
F4 3.21 2.46 3.85 0.00 3.19 3.24 0.47
F7 2.45 2.02 2.82 0.00 2.40 2.52 0.09
F8 2.73 2.07 3.29 0.00 2.68 2.79 0.07
FP1 2.65 2.12 3.11 0.00 2.62 2.69 0.22
FP2 2.92 2.20 3.53 0.00 2.82 3.04 0.00
FZ 2.84 2.40 3.21 0.00 2.85 2.82 0.74
O1 2.62 2.10 3.07 0.00 2.56 2.69 0.05
O2 2.39 2.36 2.42 0.25 2.25 2.58 0.00
OZ 2.31 2.33 2.30 0.58 2.15 2.53 0.00
P3 2.60 1.84 3.25 0.00 2.48 2.75 0.00
P4 2.41 1.85 2.88 0.00 2.36 2.46 0.11
PZ 2.20 1.84 2.50 0.00 1.73 2.81 0.00
T3 2.36 1.75 2.89 0.00 2.41 2.30 0.09
T4 2.38 1.74 2.93 0.00 2.28 2.50 0.00
T5 2.27 1.82 2.65 0.00 2.23 2.32 0.11
T6 2.42 1.95 2.83 0.00 2.17 2.75 0.00
S
2
1138.92 2022.52
4354.27 0.00 3097.73
3528.55
0.00
∆ 4.01 3.35 4.59 0.00 3.90 4.16 0.00
max 3.17 2.49 3.76 0.00 3.12 3.24 0.07
15
Figure 4 - )(
i
eH mappings for normal (N), low (L), male (M) and female (F)
volunteers, and also for the differences between N and L (N-F) groups and male
and female (M-F) volunteers. Mappings were generated with data from table I.
Figure 4 clearly shows that )(
i
eH is smaller for N in comparison to L children.
Low )(
i
eH values were observed for N children mostly in case of temporal-parietal
16
electrodes. High )(
i
eH values were observed for L children mostly in case of right
frontal electrodes and for F3, C3 and P3. High values of )(
i
eH were obtaine for
electrodes C3, F3, FZ, CZ and PZ and T6 in case of females, and for electrodes F$ and
FZ in case of males. The lowest )(
i
eH was obtained for electrode PZ in case of males
and for electrode C4 in case of females. )(
i
eH differences between males and females
were high for middle-line and left electrodes.
The results for M1 multiple regression analysis are shown in Table II. Model
M1 accounts for 42% of data covariance when both N and L children are studied
together (A in table II and Figure 5); for 60% of data covariance when only N
children are considered (N in table II and Figure 5); and for 14% of data covariance
when only L children are studied (L in table II and Figure 5). The majority of
i
β
are
highly statistically significant (p < 0.01) for both A and N and many of them are
statistically significant (p < 0.05) in the case of L children.
In Model M1, IQ positively correlated with )(
i
eH calculated for the
electrodes C3, CZ, F3, F4, F8, O1, P3, P4,T3 and T6 it is inversely correlated with
)(
i
eH calculated for the electrodes F7, FZ, O2 and OZ when all children were
considered (A in table II and Figure 4). IQ positively correlated with )(
i
eH
calculated for the electrodes CZ, O1 and P4,
and it is inversely correlated with
)(
i
eH calculated for the electrodes C3, C4, F7, FP1, O2, OZ, P3, T3 and T4 when
N children were considered (N in table II and Figure 4). In the case of L children,
IQ positively correlated with )(
i
eH calculated for the electrodes F7, FZ and P3,
and it is inversely correlated with )(
i
eH calculated for the electrodes FP1, P4 and
17
T5. IQ was negatively correlated with
2
S
for both N and L children, whereas it was
negatively correlated with
∆
in case of A children and positively correlated with
∆
in case of N and L children. IQ was positively correlated with ))(max(
i
eH in case of
A children and negatively in case of N children.
Table II - Model M1 regression analyses for all volunteers (A), normal IQ (N) and
low IQ (L) volunteers.
A N L
i
β
p
i
β
p
i
β
p
C3 0.27
0.00
-0.31
0.00
-0.27
0.00
C4 -0.01
0.67
-0.25
0.00
-0.17
0.00
CZ 0.07
0.02
0.65
0.00
0.72
0.00
F3 0.24
0.00
-0.02
0.73
0.05
0.22
F4 0.20
0.00
-0.04
0.56
0.04
0.56
F7 -0.20
0.00
-0.29
0.00
-0.38
0.00
F8 0.09
0.01
0.04
0.37
-0.07
0.12
FP1 -0.03
0.42
0.10
0.01
0.02
0.59
FP2 0.05
0.25
0.09
0.11
0.17
0.00
FZ -0.32
0.00
0.02
0.71
-0.01
0.80
O1 0.16
0.00
0.28
0.00
0.26
0.00
O2 -0.24
0.00
0.08
0.01
0.04
0.14
OZ -0.21
0.00
-0.18
0.00
-0.24
0.00
P3 0.13
0.00
-0.19
0.00
-0.09
0.02
P4 -0.03
0.43
0.17
0.00
0.23
0.00
PZ -0.05
0.07
0.04
0.23
0.09
0.02
T3 0.07
0.01
-0.38
0.00
-0.38
0.00
T4 0.05
0.10
-0.22
0.00
-0.28
0.00
T5 -0.01
0.71
-0.01
0.78
0.00
1.00
T6 0.12
0.00
0.22
0.00
0.26
0.00
S
2
0.01
0.91
-0.49
0.00
-0.28
0.00
∆ -0.67
0.00
0.88
0.00
0.39
0.01
max 0.58
0.00
-0.26
0.01
-0.06
0.52
R
2
0.42 0.60 0.14
18
Figure 4 – IQ M1 regression mappings calculated for all volunteers (A),
normal IQ (N) and low IQ (L) volunteers. Values of linear ( i
β
) for those
statistically significant inferences (p<0.01) are displayed in rose to dark red if
0<
i
β
and in green to blue if
0>
i
β
. Non significant inferences (
0=
i
β
) are
displayed in white. Data used to construct these mappings are shown in
Table II.
The results for M1 multiple regression analysis are shown in Table III. Model
M2 accounts for 42% of data covariance when both N and L children are studied
together (A in table II and Figure 5); for 60% of data covariance when N children
are considered (N in table III and Figure 5), and for 14% of data covariance when L
children are studied (L in table III and Figure 5). Data in table II were used to build
19
the M1 Regression Mappings shown in Figure 4. Model M2 accounts for 64% of
data covariance when both N and L children are studied together (A in table II and
Figure III); for 71% of data covariance when N children are considered and for 69%
of data covariance when L children are studied.
Table III - Model M2 regression analyses for all volunteers (A), normal IQ (N) and
low IQ (L) volunteers.
regression coefficients differential intercept coefficients
A
N L A N L
i
β
p
i
β
p
i
β
p
i
δ
p
i
δ
p
i
δ
p
C3 4.95 0.00
-0.23 0.00
-0.63
0.38
-6.52 0.00
-2.47
0.00
-5.14 0.00
C4 0.19 0.81
-0.09 0.00
0.50 0.53
0.41 0.69
1.25 0.11
-2.47 0.05
CZ 0.24 0.74
0.71 0.00
-2.07
0.00
1.34 0.16
4.32 0.00
7.14 0.00
F3 0.89 0.29
0.08 0.04
-0.61
0.42
-1.84 0.06
-2.25
0.01
0.83 0.45
F4 -0.49
0.60
0.05 0.44
-0.39
0.64
2.05 0.09
-0.97
0.30
0.55 0.67
F7 1.19 0.08
-0.42 0.00
1.13 0.04
-1.57 0.05
2.62 0.00
1.33 0.17
F8 -0.95
0.18
-0.09 0.04
-0.52
0.41
5.16 0.00
-0.15
0.80
2.38 0.01
FP1 1.96 0.00
0.02 0.59
0.35 0.62
-1.51 0.11
-0.28
0.59
-6.17 0.00
FP2 1.69 0.03
0.18 0.00
-0.90
0.16
-3.37 0.00
-1.86
0.03
1.84 0.05
FZ 1.41 0.01
-0.01 0.85
1.66 0.03
-4.11 0.00
-0.08
0.86
-1.47 0.24
O1 2.96 0.00
0.27 0.00
0.13 0.86
-1.43 0.07
0.83 0.04
-0.9 0.41
O2 -1.55
0.01
0.04 0.12
0.41 0.61
2.12 0.01
1.15 0.02
-2.22 0.05
OZ -0.89
0.18
-0.24 0.00
-0.98
0.18
-1.78 0.04
-0.97
0.04
3.14 0.01
P3 5.33 0.00
-0.10 0.01
0.40 0.59
-7.74 0.00
-3.73
0.00
-0.08 0.95
P4 2.02 0.00
0.21 0.00
-1.05
0.17
-1.12 0.19
-0.33
0.47
1.75 0.15
PZ -1.90
0.00
0.14 0.00
1.95 0.01
2.31 0.01
2.28 0.00
-4.47 0.00
T3 -5.66
0.00
-0.40 0.00
-0.89
0.16
11.08
0.00
4.44 0.00
4.82 0.00
T4 2.31 0.00
-0.31 0.00
-0.28
0.71
-3.80 0.00
-3.16
0.00
2.09 0.05
T5 -0.37
0.53
0.00 0.89
0.35 0.60
-1.83 0.02
-1.42
0.00
-6.19 0.00
T6 -0.25
0.70
0.27 0.00
-0.71
0.32
0.86 0.30
0.72 0.16
0 0.99
S
2
-0.01
0.00
0.14 0.00
-0.01
0.84
0.01 0.00
0.00 0.16
0 0.32
∆ -0.24
0.91
-0.16 0.00
-1.26
0.38
6.29 0.02
3.52 0.03
10.38
0.00
max -0.23
0.88
-0.11 0.24
2.80 0.53
-4.21 0.04
0.28 0.82
-13.34
0.00
Gender 26.40
0.00
-21.22
0.00
-5.14
0.00
R
2
0.64
0.71
0.69
20
Figure 5 – IQ M2 regression mappings calculated for all volunteers (A),
normal IQ (N) and low IQ (L) volunteers. Mappings H display the correlation
between IQ and )(
i
eH while mappings G display the impact of female gender
(femaleness) on IQ. Data used to construct these mappings are shown in
Table III.
In Model M2, IQ positively correlated with )(
i
eH calculated for the
electrodes C3, CZ, FP1, FP2, FZ, O1, P3 and T4 it is inversely correlated with
21
)(
i
eH calculated for the electrodes O2, PZ, and O2 when all children were
considered (regression coefficients in table IIIA and H mappings in Figure 5). IQ
positively correlated with )(
i
eH calculated for the electrodes F8, OZ, P3, P4 and
PZ it is inversely correlated with )(
i
eH calculated for the electrodes F7 and T3
when N children were considered (N in table III and Figure 5). In the case of L
children, IQ positively correlated with )(
i
eH calculated for the electrodes F7, FZ,
and PZ, and it is inversely correlated with )(
i
eH calculated for electrodes CZ (L in
table III and Figure 5). Gender was positively correlated with IQ for A children and
negatively correlated with IQ in case of the other experimental groups (N and L).
IQ was negatively correlated with
2
S
for A children and positively correlated with
2
S
in N group. IQ was not correlated with ))(max(
i
eH
. Finally, IQ was negatively
correlated with
∆
in case of N children.
Differential intercept coefficient analysis showed (table III and G graphs in
Figure 5) that for the same value of )(
i
eH
in group A, femaleness increased
influence of electrodes F8, O2, PZ and T3 upon IQ determination; whereas it
decreased it in case of electrodes FP2, FZ, C3, OZ, P3, T4 and T5. In group N,
femaleness increased influence of electrodes CZ, F7, O1, O2, PZ and T3 upon IQ
determination; whereas it decreased it in case of electrodes F3, FP2, C3, OZ, P3,
T4 and T5. Finally, in group L, femaleness increased influence of electrodes CZ,
F8, OZ, T3 and T4 upon IQ determination; whereas it decreased it in case of
electrodes FP1, C3, C4, O2, PZ and T5. IQ was positively correlated with
2
S
for A
22
children. IQ was positively correlated with
∆
in all experimental groups. Finally, IQ
was negatively correlated with ))(max(
i
eH for A and L children and positively
correlated with ))(max(
i
eH in case o N children.
The results for multiple regression analysis in case of reading and arithmetic
activities are shown in Tables IV and V. Model M1 accounts for 38% of data
covariance when R is taken into consideration and it accounts for 54% of data
covariance when C is studied. Model M2 accounts for 61% of data covariance
when reading R is taken into consideration and it accounts for 69% of data
covariance when C is studied.
In case of reading (R in table IV and Figure 6) and model M1, IQ positively
correlated with )(
i
eH calculated for the electrodes C3, CZ, F3, F4, O1, T3, T4 and
T6,
and it is inversely correlated with )(
i
eH calculated for the electrodes F7, FZ,
O2 and OZ. In the case of calculating (C in table V and Figure 7), IQ positively
correlated with )(
i
eH calculated for the electrodes C3, F3, F4, O1, P3 and T3
,
and
it is inversely correlated with )(
i
eH calculated for the electrodes F7, FP1, FZ, O2,
OZ, PZ and T4. IQ was positively correlated with
2
S
in case of R and negatively
correlated in case of C. IQ was negatively correlated with
∆
for both R and C.
Finally, IQ was positively correlated with ))(max(
i
eH
for both R and C.
23
Table IV Model 1 Regression analyses for Reading and Calculating activities
R
C
C3 0.20
0.00
0.29
0.00
C4 -0.01
0.79
0.04
0.23
CZ 0.19
0.00
-0.02
0.50
F3 0.12
0.04
0.24
0.00
F4 0.14
0.04
0.28
0.00
F7 -0.13
0.00
-0.21
0.00
F8 0.10
0.07
0.03
0.58
FP1 0.07
0.17
-0.20
0.00
FP2 0.07
0.29
0.00
1.00
FZ -0.31
0.00
-0.32
0.00
O1 0.09
0.04
0.11
0.01
O2 -0.19
0.00
-0.36
0.00
OZ -0.28
0.00
-0.10
0.00
P3 0.02
0.76
0.08
0.04
P4 0.03
0.47
-0.08
0.08
PZ 0.01
0.76
-0.09
0.02
T3 0.11
0.03
0.09
0.03
T4 0.23
0.00
-0.14
0.00
T5 -0.08
0.09
-0.05
0.11
T6 0.13
0.01
0.06
0.17
S
2
-0.17
0.06
0.39
0.00
∆ -0.48
0.00
-0.57
0.00
max 0.39
0.00
0.83
0.00
R
2
0.38
0.54
Figure 6 – IQ M1 regression mappings calculated for Reading (R) and
Calculating (C) activities for all volunteers. Data used to construct these
mappings are shown in Table IV.
24
In case of reading (R in table V and Figure 7) and model M2, IQ positively
correlated with )(
i
eH calculated for the electrodes C3, CZ, F3, F4, O1, T3, T4 and
T6,
and it is inversely correlated with )(
i
eH calculated for the electrodes F7, FZ,
O2 and OZ. In the case of calculating (C in table V and Figure 7), IQ positively
correlated with )(
i
eH calculated for the electrodes C3, F3, F7, FP2, FZ and P3 and
it is inversely correlated with )(
i
eH calculated for the electrodes F7, FP1, FZ, O2,
OZ and T4. Gender was negatively correlated with IQ for both R and C activities.
IQ was negatively correlated with
2
S
and
∆
for both R and C activities. Finally, IQ
was positively correlated with ))(max(
i
eH
for both R and C activities.
Differential intercept coefficient analysis showed (table V and G graphs in
Figure 7) that for the same value of )(
i
eH
in case of R, femaleness increased
influence of electrodes C3, FZ, O1,O2, P4 and T4 upon IQ determination; whereas
it decreased it in case of electrodes CZ,OZ,PZ, T3 and T5. In case of C,
femaleness increased influence of electrodes CZ, F4, F8, O2 and T3 upon IQ
determination; whereas it decreased it in case of C3, F7, FP1, FP2, FZ and P3. IQ
was positively correlated with
2
S
and
∆
for both R and C activities. Finally, IQ was
negatively correlated with ))(max(
i
eH
for both R and C activities.
25
Table V - Model 2 Regression analyses for Reading and Calculating activities
regression
coefficients
differential intercept
coefficients
R C R C
i
β
p
i
β
p
i
δ
p
i
δ
p
C3 7.21 0.00
4.90 0.00
-11.48
0,00
-6,33
0,00
C4 -0.02 0.99
-1.24 0.24
6.86 0,00
0,38 0,77
CZ -2.87 0.05
-0.70 0.39
5.38 0,00
2,69 0,01
F3 -2.15 0.21
1.65 0.09
-2.46 0,23
-0,41
0,72
F4 1.57 0.34
-0.02 0.99
-3.47 0,13
2,26 0,10
F7 0.43 0.72
1.79 0.03
1.15 0,46
-1,95
0,05
F8 -0.43 0.72
-1.66 0.05
5.03 0,00
5,12 0,00
FP1 1.64 0.19
1.04 0.18
2.37 0,16
-2,46
0,02
FP2 0.03 0.98
1.75 0.05
0.98 0,61
-3,31
0,00
FZ 1.96 0.04
1.57 0.02
-8.43 0,00
-2,96
0,00
O1 7.23 0.00
0.89 0.23
-6.07 0,00
-0,08
0,94
O2 2.30 0.06
-4.37 0.00
-1.30 0,39
2,98 0,00
OZ -3.08 0.02
0.19 0.81
0.37 0,83
-1,03
0,30
P3 0.87 0.59
3.36 0.00
-3.21 0,13
-4,15
0,00
P4 6.44 0.00
0.47 0.52
-2.44 0,16
-0,97
0,32
PZ -2.85 0.01
0.82 0.29
0.75 0,64
-0,58
0,56
T3 -2.47 0.04
-4.10 0.00
9.00 0,00
8,34 0,00
T4 5.80 0.00
1.38 0.12
-9.59 0,00
-1,29
0,25
T5 -1.91 0.08
-0.96 0.17
-3.60 0,02
-0,01
0,99
T6 -1.46 0.33
-0.11 0.88
3.41 0,05
-0,13
0,89
S
2
-0.01 0.00
-0.01 0.00
0.01 0,00
0,01 0,08
∆ -0.93 0.80
-1.35 0.58
3.65 0,45
9,64 0,00
max 1.31 0.58
2.22 0.28
-3.87 0,24
-7,31
0,01
Gender
42.34 0.00
9.85
0.00
R
2
0.61
0.69
26
Figure 7 – IQ M2 regression mappings calculated for reading (R) and
calculating (C) activities. Mappings H display the correlation between IQ and
)(
i
eH while mappings G display the impact of female gender (femaleness) on
IQ.
27
Discussion
Here, it is proposed that )(
i
eH measures the amount of information
provided by
i
e
about the neural sources
i
s
involved with a task solution. )(
i
eH is
expected to increase as the number of sources
i
s
involved in cognitive task
solution increases and/or as the strength of association between these sources
enhances. By the one hand, there is a rich literature correlating intelligence and
EEG, showing that IQ is correlated with various EEG-band powers (e.g.,
Doppelmayr et al, 2002; 2005, 2006; Fink and. Neubauer, 2006, Jaušovec, 2000;
Jaušovec and Jaušovec, 2005, Schmid et al, 2002, Tzur. and Berger; 2007); with
Event Related Desynchronization (Neubauer et al, 2005) and with various ERP
components (e.g.; Jaušovec and Jaušovec, 2000; Stauder et al, 2011). By the
other hand, different studies (Cohen et al, 2008; Esposito et al, 2009; Jacobs et al,
2006; Karch et al, 2010, Polezzi et al, 2010 and Tzovara et al, 2012) using different
techniques correlated specific ERP components or EEG spectral bands (SB) to
specific electrical sources locations
i
s
. These studies have been shown that
i
s
varies for each ERP and SB components and that different sources
i
s
may be
linked to the same ERP or SB. Therefore, )(
i
eH is to be correlated with IQ as it
was found in the present study and previously reported by Rocha et al (2011).
The calculated amount of information )(
i
eH provided by each electrode
i
e
was smaller for L children compared to N children for all electrodes, except O2 and
28
OZ. In addition,
minmax −
∆, max( )(
i
eH ) and
2
S
were also smaller in case of L
children compared to N children. The differences are explained assuming that L
children were less successful than N children in solving the same reading and
arithmetic activities because they were less efficient in enrolling the different types
of neurons required for these tasks solution.
Rocha et al. (2006) studied 176 children having IQ < 70 and found that
51.4% of them exhibit structural lesions identified by MRI such as, focal thinning of
the corpus callosum at the isthmus level; asymmetry of the lateral ventricles;
periventricular leukomalacia; atrophy or dysgenesis of the corpus callosum;
congenital malformations; and round hyperintense lesions in the white matter.
Children in the present L group are among those studied by Rocha et al. (2006)
and include equal number of children having or not MRI signals of structural lesion.
Lesions in some of these children were large enough to compromise almost an
entire lobe and important connecting fiber systems as arcuate fasciculus. These
children experienced important delays in language acquisition and their language
abilities became dependent on action of areas other than those classic areas
supporting language neural processing (Foz et al, 2002). All these types of brain
damage may reduce the number of circuits L children would try to recruit to solve
cognitive tasks as well as may reduce any functional interaction between the
neural sources they are able to activate. Haier et al (1988; 1995) studied brain size
and cerebral glucose metabolic rate (GMR) in individuals with mild mental
retardation (MR), individuals with Down syndrome (DS) and showed that the MR
29
and the DS groups both had brain volumes of about 80% of controls; variance was
greatest within the MR group. For all subjects combined, the correlation between
brain size and IQ was .65 (p < ,005). In this line of reasoning, they help to
understand why the values of )(
i
eH ,
minmax −
∆
, max( )(
i
eH ) and
2
S
found for L
children were small than those calculated for N children.
The neural efficiency hypothesis of intelligence (Haier et al., 1988) proposes
that people shall use a limited number of neurons or neural circuits to solve any
cognitive task. Rocha et al. (2011) defined the efficiency
)(B
ξ
of a brain in solving
a given task to be determined by the ratio )(
)(
BH
TH , where
)(TH
is the entropy of the
task T being solved and )(BH is the entropy used by the brain B to solve T and is
calculated as
20
)(
)(
20
1
∑
=
=
ii
eH
BH
. The amount of noise in any informational device
increases as the ratio )(
)(
BH
TH increases (Shannon, 1948), therefore correct solution
of any task demands
)(BH
to be greater than
)(TH
, that is
1)(
<
B
ξ
, to eliminate
error. Here, reading and calculating tasks required subject to choose one among
five possible solutions, therefore, 32.2)
5
1
(log)(
2
==TH (Rocha et al, 2011). It
follows from values on table I that the entropy used by L children to solve reading
and calculating tasks was 05.2)( =
L
BH and that used by N children
was 99.2)( =
N
BH . It is interesting to note that
NL
BHTHBH )()()( << or, in other
30
words, 13.1)( =B
L
ξ
in the case of L children and 78.0)( =B
N
ξ
in the case of N
children. Therefore, reasoning was noisier in case of L children than in case of N
children, what may explain why L children erred more.
The task solving time (RT) coefficient of variation ( )(
)(
RTMean
RTSD ) was larger
for L children in comparison to N children, and no RT statistical was observed
between groups. The large SD for L children implies that some subjects were very
quick in selecting a task solution (e.g. in case of arithmetic tasks) whereas some
others took very long time to decide about task solution (e.g., in case of reading
tasks). These results and the fact that 1)( >B
L
ξ
, seem to support the claim that at
least some of the L children did not fully understood the tasks they have to solve.
From the above, we have to propose that neural efficiency does not have to
merely imply less neuron, but a minimum adequate set of neurons to solve a given
task that guarantees
1)(0
<
<
B
ξ
. By the one hand, neural efficiency requires
)(BH
being lowered as possible to reduce computational costs, but by the other hand
)(BH
has to be greater than
)(TH
to reduce noise and the associated
computational errors. In this line of reasoning, a possible L children low
computational capacity does not allow them to adequately increase
)(BH
as
)(TH
increases with task difficulty, making them to err more and to be either slower (e.g.,
reading) or faster (e.g., calculating) than N children in solving our reading and
calculating tasks.
31
Regression analysis showed that IQ correlates with )(
i
eH as previously
reported by Rocha et al. 2011. The regression mappings in Figure 3 detail this
relation for the entire studied population (A) and separately for N and L children.
Two distinct groups of electrodes can be distinguished in these mappings, one
subgroup (PE) is composed by the set of electrodes for which )(
i
eH positively
correlate with IQ (color encoded from green to dark blue in the figures) and the
other subgroup (NE) is composed by the set of electrodes for which )(
i
eH
negatively correlate with IQ (color encoded from rose to dark red in the figures).
Therefore, high IQ people are supposed to have high )(
i
eH for PE electrodes and
low )(
i
eH for NE electrodes, the reverse being true for low IQ people. Both PE and
NE sets are composed by electrodes distributed over both hemisphere showing
that IQ is correlated with neuronal activity widely distributed over the brain, as
assumed if the brain is considered a Distributed Intelligent System as in the
Parieto-Frontal Integration Theory (Jung and Haier, 2007) and in Rocha et al,
2011.
Jung and Haier (2007) reviewed studies from functional and structural
magnetic resonance imaging, diffusion tensor imaging and voxel-based
morphometry, 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) and it includes the dorsolateral prefrontal cortex (BAs 6, 9, 10, 45,
32
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 (e.g., the arcuate fasciculus) were also
implicated. Here, for almost all analysis, NE is mostly composed by FP1, F7, FZ,
OZ and O2 and PE is mostly composed by C3, CZ, F3, F4, P3, T3 and T4 (Figures
4 and 6) showing that IQ is associated with the activation of different sources
widely distributed over the brain as proposed by P-FIT.
Measurement of the brain’s glucose metabolism rate using positron
emission tomography was used by Haier et al (1988) propose NEH. However,
evidence in favor NEH comes also from EEG measurement methods (e.g., Event-
Related Desynchronization or ERD as in Neubauer and Fink, 2003). These EEG
studies have being shown gender differences for the correlation between IQ and
brain activity (e.g., Freudenthaler et al, 2000; Jaušovec and Jaušovec, 2005;
Neubauer and Fink, 2003, 2006; Neubauer et al, 2005). Here, we used sex as a
dummy variable to study the possible correlations between IQ, )(
i
eH and gender.
Being female added around 26 points to IQ/ )(
i
eH linear coefficient in group
A (Tables III) which implies that for the same IQ, the calculated )(
i
eH for females
has to be in general smaller than that calculated for males as observed here (see
table I). Femaleness increased the differential intercept coefficient associated with
electrodes F8, O2, PZ and T3 and decreased the coefficients associated with
electrodes C3, FP2, FZ, OZ, P3, T4 and T5 (see table III, and Figure 5). If )(
i
eH is
33
smaller for females in comparison to males, then )(
i
eH calculated for all these
electrodes shall not result into significant gender IQ differences. This is the case in
the present study, since male (65) is not statistically (p=0,25) different from female
(75) IQ. Similar results were observed when reading and arithmetic activities were
considered (see table IV and Figure 7).
Being female decreased IQ/ )(
i
eH linear coefficient by 21 and 5 points in
case of N and L groups. Also, femaleness was associated with positive CZ, F7,
O1, O2, PZ and T3 differential intercept coefficients in case of N and only CZ, F8,
OZ and T3 case of L children. Negative differential intercept coefficients were
associated with electrodes C3, F3, FP2, OZ, P3, T4 and T5 in case of N and with
electrodes C3, FP1, PZ and T5. However, )(
i
eH was smaller for females in
comparison to males in both groups and no gender IQ difference were observed in
either of these groups. Therefore, we have to conclude that gender influence on
brain activity did not resulted in statistical IQ difference even if normal and low IQ
children were considered separately.
From the above discussion, we have to conclude that gender differences
detected by M2 model (show in tables III and IV and Figures 5 and 7) support the
hypothesis that man and woman enroll different neural circuits to solve the same
(reading or calculating) task, but they do this with equal efficiency because those
gender differences did not result in statistical gender IQ differences.
34
We conclude, here, that our results seems to support and expand the theory
of neural efficiency and to expand our previous findings showing that IQ correlates
with the amount of information )(
i
eH provided by each electrode
i
e
and supports
the hypothesis that intelligence is a property of a neural distributed processing
system.
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 children’s parents/guardians
.
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