X-Message-Number: 25983
From:
Date: Tue, 5 Apr 2005 15:31:41 EDT

In 2.ii.0 I have said that very nonlinear systems could be simulated at 3
levels: Boolean, differential an stochastic. The best prospect being something
between differential and stochastic, namely the omega Taylor serie from van

Kampen. A first project would cut the taylor expansion at the first order. There
are similarly a number of intermediate state between boolean and differential.

The first "post-boolean" model is the kinetic logic formalism, put forward by
Thomas and D'Ari (1). In a boolean system, a variable is either On or Off, 0
or 1. In the kinetic logic, here are more states: 0, 1, 2, 3,... It is best
for study purpose but falls short of what is requested in uploading.

The next step is the Continuous logical network of Mestl et al. (2) The basic
elements are molecular concentrations and interactions are modeled by linear
differential equations: d(concentration of A)/dt = Cte1 - Cte2(concentration
of a). Cte1 and Cte2 are functions of the concentration jumping from one

constant value in a range to another. These values are precomputed and storred
in a
memory.

The third intermediate formalism uses differential equations broken in

chunks. There in a grammar telling how and when to use such or such fragment in
this
or that case (3).

Why bother about that ? The next step in complexity is the full differential
model and it is insufficient. So anything simpler seems without interest. In

fact, some element may be computed one time and the result storred in a memory.
In this case a very precise model will be used, if something is computed very
often, the model must be simpler. May be after a long chain, there will be a
precise computation on a sample of reactions so that a corrective term will be

On FPGA, the full differential model is very costly, if here is a solution to
reduce its computing request, it is welcome. That is why the grammar -
differential solution is interesting.

(1) Thomas, R., and D'Ari R., (1990). in : Biological Feedback. CRC Press,
Boca Raton, Fla.
(2) Mestl et al. (1996) Choas in high-dimensional neural and gene networks.
Physica D. vol. 98: p. 33.
(3) Fleischer, K., (1995). A Multiple-Mechanism Developmental Model for

Defining Self-Organizing Geometric Structure. Ph.D. thesis, California Institute
of