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Va r k
i = 1 Y i
k
i = 1 Va r [ Y i ]= k
1
λ
Va r
[
X
]=
=
2 .
(9.6)
These mathematical results can be used to predict the skill learning phenomena,
together with the prediction described below that entities may learn to skip certain
server(s). First, because E
,if k <
X ] <
.
This may be one of the reasons that the skipping of server(s) can explain a reduc-
tion in interkey time in typing normal text (the first skill learning phenomenon in
this chapter) and repetitive letters (the third skill learning phenomenon). Second,
skipping some of the servers will decrease the variance of the Erlang distribution
because if k <
[
X
]=
k
(
1
/ λ )
k , then it follows that E
[
E
[
X
]
X ] <
. This is one possible reason why skipping
over server(s) can account for the reduction in the variability of interkey time in the
learning process (the second skill learning phenomenon).
k , then Var
[
Va r
[
X
]
9.2.4.2 Predictions of the First Brain Imaging Phenomenon
At the Pho server during the initial stages of learning, entities can go through the
CE server for eye movement control to locate the specific position of a target key on
the keyboard ( [12], see Fig. 9.1) and for response selection and inhibition. Entities
can also traverse the route from Pho to BG, but it takes longer than going through
the CE because the BG may not work effectively in retrieving the motor program
from LTPM [2] and its Q value of time-saving reward is smaller than that of CE.
Entities can also choose the route from Pho
M1 directly. However, the occurrence
of typing errors will decrease the Q value of error-saving reward from 18 Pho
M1.
As the number of practice trials increases, the route Pho
BG is selected by the
majority of the entities because the functions of CE are gradually replaced by the
BG with less process time based on parallel cortico-basal ganglia mechanisms [33].
Second, at the CE server, entities can traverse one of the routes from CE to BG,
SMA, or M1. If entities select the first route, the correct motor program will be re-
trieved without decreasing the Q t + 1
E
(
i
,
j ) value. If the second or the third route is cho-
sen, its Q t + 1
E
value will decrease because no correct motor program is retrieved.
The third prediction involves the BG server. Since stimuli keep changing in
typing multidigit sentences, entities can go from the BG directly to M1 skipping
SMA whose function is motor program assembling [36]. However, ensuring move-
ment accuracy for error detection [17] will decrease Q t + 1
E
(
i
,
j
)
(
,
)
...
M1.
In sum, at the beginning of the learning process, entities will go through Pho
i
j
in route BG
CE
BG
SMA
M1. After learning, the majority of entity will travel Pho
BG
SMA
M1.
9.2.4.3 Predictions of the Second Brain Imaging Phenomenon
If stimuli change from repetitive letters to regular words in the same task, the enti-
ties will change routes from Pho
M1 to Pho
BG
SMA
M1 because the error-
saving reward decreases in route Pho
...
M1 without the motor program functions of
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