       help!! Clueless on how to proceed...

• To: mathgroup at smc.vnet.net
• Subject: [mg33414] help!! Clueless on how to proceed...
• From: heimantj at celera.com (theiman)
• Date: Wed, 20 Mar 2002 01:53:31 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I am a Mathematica newbie and I have no clue as to how to proceed.
The system I have is as follows:

Abundance of a transcript at i at time t  i.e. A(t)=S i (t)
-ln(2)/halflife*A(t)
S i (t) = S i if T1<t<t2
S i (t) = 0 otherwise

The formal solution for a non cyclic event is:

eq1 A i (t) = 0       if t<=t1
eq2 A i (t) =(S i/ln(2)/halflife)*(1-e^-((ln(2)/halflife)*(t-t1)))
if t1<t<=t2
eq3 A i (t) =(((S i/ln(2)/halflife)*(1-e^-((ln(2)/halflife)*(2-t1)))*(e^-((ln(2)/halflife)*(t-t2))))
if t2<t

I am interested in applying this to a cyclic situation.  According to
the author, I need to use the Laplace transform of equations 1-3 and
find the periodic solution.  How would one do that in Mathematica?

The next question is I would like to fit the actual abundance levels E
for each gene with the equations 1-3 (that were transformed using the
Laplacian transform) by minimizing the sum of squares   Sum(for all t)
[A i (t) -E i t]^2 in the space of parameters t1, t2, Si, and
ln(2)/halflife.  Is there a simple way to do this in Mathematica?