By A. I. Markushevich
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Extra resources for Curvas Maravillosas, Numeros Complejos y Representaciones Conformes, Funciones Maravillosas
Let K, = (Kc — K)/Kc and take \ a s the 'correlation length' defining the average domain in r-space for which the information source is primarily dominated by 'strong' ties. The first step is to average across r-space in terms of 'clumps' of length R=
We will return to this point repeatedly. 2. 'Biological' phase transitions Now the mathematical detail concealed by the invocation of the asymptotic limit theorems emerges with a vengeance. 1) states that the information source and the correlation length, the degree of coherence on the underlying network, scale under renormalization clustering in chunks of size R as H[KR,JR]/f(R) = with / ( I ) = 1, K\ = K^J\ — J, where we have slightly rearranged terms. 4) The Ui, Vi, i — 1, 2 are functions of KR, JR, but not explicitly of R itself.
They can be tuned continuously... Suppose that a structured external environment, itself an appropriately regular information source Y, 'engages' a modifiable cognitive system. The environment begins to write an image of itself on the cognitive system in a distorted manner permitting definition of a mutual information I[K] splitting criterion according to the Rate Distortion or Joint Asymptotic Equipartition Theorems. K is an inverse coupling parameter between system and environment (Wallace, 2002a, b).
Curvas Maravillosas, Numeros Complejos y Representaciones Conformes, Funciones Maravillosas by A. I. Markushevich