T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 108

Table 4.6 Negative Intersection of NDB 1 and NDB 2

∩

NDB 1 NDB 2 NDB NDB NDB

3 1 2

10** 0*10 10**

011* 1*01 011*

000* *010 000*

0*10
1*01
*010

Table 4.7 Negative Union of NDB 1 and NDB 2

NDB 1 NDB 2 NDB NDB NDB ∪

3 1 2

10** 0*10 0110

011* 1*01 1001

000* *010

Table 4.8 Negative Join ( ) of NDB 1 and NDB 2

NDB 1 NDB 2 NDB 3 = NDB 1

NDB 2

10** 0*100 10***

011* 1*011 011**

000* *0100 000**

0*100
1*011
*0100

input NDBs are placed in the resultant NDB, and can be defi ned as
follows:

NDB NDB ∪ NDB { zz x y , x M y , ( x ∈ NDB ∧ y ∈ NDB )}

3 1 2 1 2

where

=

Coalesce xy Two strings x and y of length n coalesce into string

z iff x matches y and for all 1

≤
Match x M y : Two strings, x and y , match iff for all i (( x [ i ]

≤

i

= ∨

y [ i ])

= ∨ =

( x [ i ] *) ( y [ i ] *))

h erefore, when the two strings in both databases are exactly the same (compar-
ing each bit of the string, i.e., x M y ), then this string is appended into the NDB 3 ,
for example (Table 4.7).
Negative join. h is operation results in the NDB, which contains all the strings
except those that are in the join of two PDBs: DB 1 , DB 2 . An example of nega-
tive join is given in Table 4.8.