[seqfan] Presentation

[Wouter Meeussen]

dear members,

I'm a chemist by formation and profession, working in (soon to be closed?)
R&D lab of a Oils&Fats company located in Belgium (Flanders).

I have been playing with bits of math as a hobby. After getting Mathematica
at work, that literally exploded my possibilities, but also my awareness of
my ignorence.

So, consider me an amateur (<Lat. "amare")

My playing field is planted trivalent binary trees, (bits of) combinatorics,
and the joys of symbolic algebra in general. I'll give an example of such a
hybrid at the end of this mail.

Apart from Seqfan, I read the "math-fun" mailing list and of course "mathgroup".


Oh yes, I'm old enough to have used a slide rule at university.


wouter.




****************************************************************
Example of stuff that I sent to math-fun, combining a system of coupled
differential equations and trees :
****************************************************************
hi,

I just finished a Mathematica 3.0 notebooklet on the "railway station"
graph, obtained by setting two planted binary trees end to end:

                        |
                       / \
                      /\  \
                     / /\  \
                     . . . .
                     \/   \/
                      \   /
                       \ /
                        |

the above example has trees {1,1,0,1,0,0} on top and {1,1,0,0,1,0} below it.

Each tree node can be considered as a cell with one input and two outputs
(in the top half), or two inputs and one output (in the bottom half), the
shared leaves passively passing the flux downward.

The downward flux in the top half can be set as:
y'[t]= -y[t]/2 (*left*) -y[t]/2 (*right*) + f[t]  (*influx from top*)

The downward flux in the bottom half as:

y'[t]= -y[t] (*outflux down*) + u[t] (*infux top left*) + g[t] (*influx top
right*)

                
Depending on the function fed in at the top, the function at the bottom
takes different forms.
When fed with E^-t at the top, the bottom comes out as :

 
    3      4    5
40 t  + 5 t  + t
- -----------------
          t
     480 E

For different "railway stations" or graphs of the above type, with E^-t as
input,
a polynomial with integer coefficients in t divided by E^t n! 2^(n-1) will
come out at the bottom ( n being the number of leaves plus one).

For an input at the top of E^(-I k t) the computer grinds a little longer on
the successive symbolic integrations, and a dampend oscillation comes out.
Its amplitude "soon" settles to a steady state value that depends on the
setting for k and on the network topology (choice of trees to make up the
"railway station"). 

In case anyone feels a sudden urge to relive his childhood thrills with
model trains and railway stations (weren't the stations always more
interesting than the straight tracks?), I got some mean Mathematica
"implicit integrations" ready for the asking,
*************************************************************

NV Vandemoortele Coordination Center
Oils & Fats Applied Research
Prins Albertlaan 79
Postbus 40
B-8870 Izegem (Belgium)
Tel: +/32/51/33 21 11
Fax: +/32/51/33 21 75
vdmcc at vandemoortele.be