Figure 1
From: Using GeneReg to construct time delay gene regulatory networks
The forward selection of regulators in time delay linear regression model. The selected regulator set with m regulators is defined as 
the S indexes of regulators in Ωs are 
The to-be-selected regulator set with n regulators is defined as 
and the S indexes of regulators in Ω
t
are 
In the forward selection procedure, each regulator in Ω
t
will be successively tested whether it can be added into Ω
s
. During each test process, the time delays of Ω
s
are held the same. All possible time delays of the regulator in Ω
t
with smallest S index that is 
are traversed, and the time delay of which achieves the smallest AIC of 
is considered as the optimal time delay of . This smallest AIC of is then compared with the AIC of original . If 
wil be moved from Ω
t
to Ω
s
. Otherwise, will be eliminated from Ω
t
. In next round, the new regulator in Ω
t
with smallest S index will be tested until Ω
t
is empty.