Executable Figure 10 of Chaos paper
Foreword
The simple model we describe below illustrates a technique for the extraction of so-called "information carriers" of a given rule set. It corresponds to Fig.10 of the following paper (submitted to a special issue of Chaos).
The idea is this. The user specifies an observable F of interest to her, and a procedure generates a set of patterns Fi such that:
- the user observable F is one of the Fi's
- the average dynamics of the Fi's is given by a self-contained differential system
By "self-contained" we mean that the (multilinear) differential equations mention only the Fi's. In other words, the Fi's are all one needs to know in order to describe the average dynamics of F - the rest of the system can be safely ignored. In this specific sense, the Fi's carry all the information relative to the dynamics of F. We call them "information carriers" for that reason - or sometime also "fragments".
(Note that the method does not assume anything on the rate constants and results in an exact "compression" of the original differential semantics of the rule set.)
Below, we construct the stochastic version of the Fig.10 model, so that we can superimpose the obtained stochastic trajectories to that of the differential system and, in so doing, illustrate the soundness of the fragmentation method. That is to say the "large number" behaviour of the Fi's in the original stochastic system is well described by the differential system obtained by fragmentation.
A scalable implementation of fragmentation together with many examples, some of them rather large models of biological networks, is explained in an earlier 2009 paper (published in special issue of PNAS).
Created
June 30th by Vincent Danos
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