Information Technology Reference
In-Depth Information
network configuration and a measure
U
of the overall change from the original net-
work configuration.
The various interactions involving node
i
are mediated by interaction coefficients
whose role is to quantify the strength of the interaction. The diffusive interaction
between primary nodes
i
and
j
is mediated by the interaction coefficient
v
ij
∈
[
0
,
1
]
f
((
2
v
ij
=
x
i
−
x
j
)
)
.
(21.1)
The interaction coefficient
v
i
∈
[
of this aggregated consensual interaction con-
trols the extent to which expert
e
i
is influenced by the remaining experts in the
group.
0
,
1
]
v
i
=
j
=
i
v
ij
/
(
n
−
1
)
.
(21.2)
The inertial interaction between primary node
i
and the associated secondary node is
mediated by the interaction coefficient
u
i
∈
[
which controls the extent to which
the expert
e
i
resists to opinion changes due to the collective consensual trend
0
,
1
]
f
((
2
u
i
=
x
i
−
s
i
)
)
.
(21.3)
The values of these interaction coefficients are given by the first derivative of the
scaling function
1
β
e
−
β
(
x
−
α
)
)
f
(
x
)=
−
ln
(
1
+
(21.4)
where
α
∈
(
0
,
1
)
is a threshold parameter and
β
∈
(
0
,
∞
)
is a free parameter. The
graph of the scaling function
f
is shown in Fig. 2.
Fig. 21.2
The graph of the
scaling function
f
The sigmoid function
f
(
, plays a crucial role in the network dynamics and
is obtained as the derivative of the scaling function
f
x
)
which, in turn, enters the
construction of the soft consensus cost function from which the network dynamics
derives
(
x
)
1
f
(
x
)=
e
β
(
x
−
α
)
.
(21.5)
+
1
