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Finding the amount of steps in each state
So before i get into what i've been doing. I think i found my mistake that is throwing off my numbers yesterday by .004. I didn't take into account the fact that ATP can bind to the head if the unbound head is in front or in back. Since that constant is for Empty bound with anything unbound. So I am trying to fix it right now.
OK that didn't fix the problem. In fact it made it worse. Now the Markov has a <t> = .0093 while the sim has .0081. Fuck this is fucking annoying
This blows. So I think i have the generating matrix more correct now that i realized that i was missing a state before, but when i put it in the k effective is way off from the 1000 sim. Da Fuck?! This is frustrating as hell
So i deleted some steps and started over, and it turns out i had a number in the wrong column. So now everything looks good again. From the Markov method I got .0082 and from 1000 sim I got .0081. So that is looking good. Seems like i solved the problem from yesterday.
Now on to solving the problem from today and that is the numbers of times in each state from the 1000 sim dont' match the Markov theory. let's get cracking
From the 1000 sims i get 13.33 steps on average before completing the cycle. From the Markov method i get 12.76. And the number of times in each steps are different as well. I am not sure what to look at for the problem. Since Markov gives the correct expected time, I don't think my matrix is wrong. There might be something wrong in the way i am creating the fundamental matrix but i don't think so. I checked it a couple of times. Well something has to be wrong, I'll have to look for it.
Q matrix is correct. The rest is extremely basic algebra which Labview is doing so there is nothing wrong in there. I don't know what is wrong here. I guess I can move on knowing that the probabilities Markov gives me is a bit off from the simulation.
None of the probabilities are off by that much. most are off by .004 so i don't think it'll kill me using these numbers, but i am curious what is wrong. If there error isn't in my calculation of the fundamental matrix maybe it's in how i calculate times in the state in the 1000 sims.
Nothing wrong with the way i take expectation value. ok let's see what's next. alright i give up i can't find the mistake. i am just gonna have to go with it and remember that the probabilities are .004 off from what i get from sim. hopefully down the line i can find the error like i did today from yesterdays.
I'm not happy because this is taking a long time to get right. But i have to keep reminding myself that in the end I'll have the rate constants right and then chocolate shakes will flow from the water fountains. or something like that