Davidson Missouri W/Mathematical Modeling
Markov Chain Model For Flipping
One of the first projects we worked on was to develop a mathematical model of graphs for the pancake problem. These graphs were used to find the percent of plasmids that solved problem based on the number of flips. We also developed graphs with biases to see if the length of the flips effect the probability of making the flip. In some of the graphs we saw bouncing because from a starting point you can only get to a solution by an odd number of flips or an even number of flips. If you get to a point on an even number of flips you can never get to an odd number. When the graph shows convergence, regardless whether the number of flips is even or odd you will have a chance to get to one of the solutions. The convergence occurs at .25 because there are 2/8 chances of getting to the solution after a high number of flips which reduces to ¼. We also did graphs using bias wieghts where it takes more flips for the graph to have the bouncing behavior. The biologist suspect that the length of the flips effects the probability of making the flips. Then you would compare mathematical graph to the biologist graph to see the bias.
MATLAB programs that we developed using Markov Chains
True Positives / False Positives
MATLAB programs used to find the false positives:
1. Adelman's False Positives with 12 nodes
2. Adelman's False Positives with 14 nodes
3. Counter Program for Adelman's False Positives
Possion Model For the Number of Plasmids
Using this statistical method we used to make a chart of the probability of finding true positives based on the number of plasmids.
