When you press the **OK** button in this window, the computer checks that

- the focus node has precisely one parent,
- the names of the states of the parent node are sufficiently long for the steps described below to be doable.

If these conditions are satisfied, the above window closes. Furthermore, the states and amplitudes stored in memory for the focus node are changed. If the conditions are not satisfied, the above window remains open, the states and amplitudes are not changed, and a warning message appears on the screen.

Let m[P_{1}, L] be an operator which acts on any string STR, and
yields the substring consisting of the elements of STR at positions from
P_{1} to P_{1}+L-1. (We assume that the length of STR is
>= P_{1}+L-1). For example, if P_{1}=2, L=3, and STR =
*apple*, then m[2,3]*apple* = *ppl* .

Let P_{1} be your entry to the first field of the above window, and
let L be your entry to the second. P_{1} and L must both be positive
integers. Quantum Fog defines the set of states of the marginalizer
to be { m[P_{1},L]STR : for all STR such that STR is the name
of a state of the parent node}. For example, suppose that the set of states
of the parent node is { *apple, banana, mango, fig* }. Furthermore,
suppose that P_{1}=2, L=2. Since m[2,2]*apple = pp* ,
m[2,2]*banana = an* , m[2,2]*mango = an* , m[2,2] *fig
= ig* , Quantum Fog will define { *pp , an , ig* } to
be the set of states of the marginalizer. As another example, suppose that
the states of the parent node are the 32 binary numbers 00000, 00001, ...,
11111. Furthermore, suppose that P_{1}=2, L=1. Then Quantum Fog will
define the states of the marginalizer to be 0 and 1.

When the state of the parent node is STR, Quantum Fog assigns unit amplitude
to state m[P_{1}, L]STR of the marginalizer, and it assigns zero
amplitude to all other states of the marginalizer. In the fruit example presented
above, when the state of the parent node is *apple* , Quantum
Fog assigns unit amplitude to state *pp* , and zero amplitude to states
*an* and *ig* . In the binary numbers example presented
above, when the state of the parent node is 01011, Quantum Fog assigns unit
amplitude to state 1, and zero amplitude to state 0.

More information about Marginalizers can be found in the document entitled "Quantum Fog Library Of Essays" that accompanies this manual.