TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER



B1 bk+1, ..., bm.

Thus we permit a graded response, supposing that if

h(x) B0

the pattern is not recognized, and if

h(x) B1

the pattern is recognized and some action bj , k + 1 j m takes place.

We are interested in paths x which trigger pattern recognition-and-response
exactly once. That is, given a fixed initial state
a0 , such that h(a0) B0 ,
we examine all possible subsequent paths
x beginning with a0 and leading
exactly once to the event
h(x) B1. Thus h(a0, ..., aj) B0 for all j < m,
but
h(a0, ..., am) B1.

For each positive integer n let N (n) be the number of paths of length
n which begin with some particular a0 having h(a0) B0 and lead to the
condition
h(x) B1. We shall call such paths ‘meaningful’ and assume N(n)
to be considerably less than the number of all possible paths of length
n -
pattern recognition-and-response is comparatively rare. We further assume
that the finite limit

H lim log[N(n)
n→∞   n

both exists and is independent of the path x. We will - not surprisingly
- call such a pattern recognition-and-response cognitive process
ergodic.

We may thus define an ergodic information source X associated with
stochastic variates
Xj having joint and conditional probabilities P (a0, ..., an)
and
P (an|a0, ..., an-1) such that appropriate joint and conditional Shannon
uncertainties may be defined which satisfy the relations

H[χ] = lim logN(n) =
n→∞   n

lim H(Xn|X0,...,Xn-1)=
n→∞



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