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? Any suggestions or thoughts about this would be greatly appreciated!!! Sincerely, Tom