Re: Formalization of the Artificial Life Systems

[Vladimir Jojic]

On Tue, 20 May 1997, David Sumpter wrote:

> Hi people,
> 
> I've been trying to do some work on this sort of stuff, for simple agents in 
> a 
> simple environment. My model is specific to my problem whioch is Honey Bee 
> ThermoRegulation.
> 
> BI defined bee agents b \in B, the set of all bee agents, to be pairs 
> b(t)=(x,y) 
> defining their co-ordinates at a point in time. In this way the bees have no 
> memory so are very simple. The bees move in a `thermo-environment' which is a 
> lattice T_{xy}(t). (Think about the HeatBugs demo).

Hi David,

The heat bugs, were supposed to be presented in the abstract I sent to
modeling, but I changed my minde, since I would have to send proofs that
those are actually vector spaces and the rest of the math stuff ... 

> I have defined the movement 
> of bees as operations on sets of possible points to which they can move 
> dependent on values in T. Since these rules contain a random element the set 
> B and lattice T are a stochastic dynamical system. 
 
Now, let me just comment on this, you could have created a vector space
(with 5 or more dimensions), and base vectors for that space, that would
take care of those constraints for that movement, and that way having the
behavior easily defined ... with one vector or addition (or some other
operator, you define) of several vectors ....

> I've managed to prove a few simple things about one dimensional thermospaces 
> with simple bees. I'm trying to prove some more interesting things in two 
> dimensions. It gets a lot harder. It does however help do things like set 
> parameters sensibly, proving they do not contradict assumptions made in your 
> model.

Could you tell me, what did you prove, maybe I can help you with
suggestions to make those proofs look as they should ... if you are not
using vector spaces ... You could interesting stuff, once you define base
vectors *and* some unusual operators over thos vectors (you could just get
some interesting stuff).

As for defining operators, simplest approach would be to define the Cayley
tables ... take a look at some intro. to linear algebra text book ...

> I'd love hear from anyone doing similar stuff.....I haven't seen anything 
> like 
> it. One mathematician here at UMIST said to me "Oh they do stuff like this 
> for 
> Cellular Automata but generally its a bit namby pamby, you may as well have a 
> go. One advantage is you don't have to have a real mathematics background to 
> do 
> this sort of thing." Hmmm.

This mathematician says:
"You need a real mathematical background for this, at least
introduction to linear algebra (and hopefully more)."

Your mathematician probably refers to Von Neumann and Turing machine, and
you really don't need more than some knowledge about the induction method
and sets to understand it and play with it... 
 
Now similar papers:

1) Luc Steels, published a paper called:
Mathematical Analysis of Behavior Systems. 

Steels is more on the engineering and robotics side... 

2) Behavior Analysis and Training - A Methodology for Behavior Engineering 
(IEEE Transactions on Systems, Man and Cybernetics, Vol. 26, No. 6, 1996.)
Marco Colombeti, Marco Dorigo, Member IEEE, Giuseppe Borghi

(unfortunately I have only a fragement of this paper, but it is giving
a description of what could be done, and again has the pragmatic approach,
(this is expected from the IEEE), still it is interesting)

This all I managed to find, but there is more probably. I will ask Luc
Steels for some pointers ... and notify you by the swarm mailing list (if
no one objects)

Regards,
Vladimir




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