of cognitive cellular mutation control. We wish to analyze the way structured
stress affects the interaction between cognitive mutation control (CMC) and
an adaptive mutator, the principal line of defense against the CMC for a
growing tumor. To do this we extend the theory to three interacting infor-
mation sources.
The Rate Distortion and Joint Asymptotic Equipartition Theorems are
generalizations of the Shannon-McMillan Theorem which examine the inter-
action of two information sources, with and without the constraint of a fixed
average distortion. We conduct one more iteration, and require a generaliza-
tion of the SMT in terms of the splitting criterion for triplets as opposed to
single or double stranded patterns. The tool for this is at the core of what
is termed network information theory [14, Theorem 14.2.3]. Suppose we
have three (piecewise adiabatically memoryless) ergodic information sources,
Y1 , Y2 and Y3 . We assume Y3 constitutes a critical embedding context for
Y1 and Y2 so that, given three sequences of length n, the probability of a
particular triplet of sequences is determined by conditional probabilities with
respect to Y3 :
P(Y1=y1,Y2=y2,Y3=y3)=
πn=ιP (Ун | Узі )P(y2i | Узі )Р(Узі).
(8)
That is, Y1 and Y2 are, in some measure, driven by their interaction with
Y3
Then, as per our previous analyses, triplets of sequences can be divided
by a splitting criterion into two sets, having high and low probabilities re-
spectively. For large n the number of triplet sequences in the high probability
set will be determined by the relation [14, p. 387]
N(n) ∖ exp[nI(Yι; Y2∣Y3)],
21