Diversified Insulin-Associated Beta-Behavioral and Endogenously Triggered Exposed Symptoms (DIABETES) Model of Diabetes in India - Computational Intelligence Techniques for Comparative Genomics - page 8

Corollary The dot product of B i , biological DOI and S m , sociological DOI yields
again the dot product of B p and S q

B i : S m 7! B p : S q

where p = (n i), q = (j m) where n, m are the total number of variables in

− −

respective DOI and

B i þ S m 7! B p 0 þ S q 0

That is the (.) association between any two entities may lead to association of
some other entities in the same DOI and the (+) association between any two
entities may lead to association of some other entities in the same DOI but not the
same as the dot product variable p and q.

Lemma 3 The association between two entities may be additive or multiplicative in
the sense that the sequence of operations are not important. With the timing per-
spective, the integration of two different activities like update and composition can
also be introduced in the process model. They are like precedence and succession
operators used in high level programming languages.

(iv) Precede:

Corollary The value of social and biological events are rst updated and then

composed with the biological system. The sequence of operations bear the priority
of individual entities illustrating the recent events and entities are to be considered.

þþ S m : B i

þþ B I : S m

Lemma 4 This refers that the person might have been affected by oral cancer in
the past but there are very many chances of he getting affected by the same in
future.

(v) Succeed:

Corollary The socio events and the biological events are composed together and
then, the result is updated and these operations can be represented as

S m B i þþ B i S m þþ

Lemma 5 This refers that presently if the person is suffering from oral cancer but
there is no assurance that he might not be affected by the same in future.