TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

For a given generalized language of interest with a well defined ergodic
source uncertainty H we write

H[K,J,X]

Imposition of invariance of H under a renormalization transform in the
implicit parameter r leads to expectation of both a critical point in K , which
we call K_C , reflecting a phase transition to or from collective behavior across
the entire array, and of power laws for system behavior near K_C . The addition
of other parameters to the system, e.g. some V , results in a ‘critical line’ or
surface KC(V ).

Let κ = (K_C - K)/K_C and take χ as the ‘correlation length’ defining
the average domain in r-space for which the information source is primarily
dominated by ‘strong’ ties. We begin by averaging across r-space in terms of
‘clumps’ of length R. Then, taking Wilson’s [60] physical analog as a starting
point, we choose the renormalization relations as

H[KR,JR,X] = f(R)H[K,J,X]
χ(KR, Jr) = ' KJ

R

(3)

with f(1) = 1 and J₁ = J, K₁ = K. The first of these equations states
that ‘processing capacity,’ as indexed by the source uncertainty of the sys-
tem, the ‘richness’ of the generalized language, grows monotonically as f (R).
The second just states that the correlation length simply scales as R. The
first equation significantly generalizes Wilson’s approach. First, since both
H[K_R, J_R] and H[K, J] are dimensionless, f(R) must itself be dimensionless.
This is most easily done by assuming that we replace R with R/R₀ , where
R₀ is some ‘characteristic length’ of the system for which renormalization is
a reasonable procedure. We then set R0 ≡ 1, thus measuring in units of R0.
Wilson’s equation (4) states that free energy density remains constant dur-
ing renormalization: If F [K_R, J_R] is the free energy of the clumped system,

13

<<   10   11   12   13   14   15   16   >>

More intriguing information