BME 143 PSet 2 Pset 2 is due at 10pm on 10/18. Upload your written solutions with labeled figures plus matlab code to canvas. You may use hand drawn tables and diagrams if they are scanned and placed into your write up. Do not zip or compress your files to be uploaded. Submission Instructions: Submit all .m files necessary to run your script and use one script to recreate the scripts for grading. Additionally, write-ups must be submitted: you can optionally publish your script (publish is an option in the MATLAB editor), and submit as a PDF, with discussion for each problem included in the script as green text. Alternatively, submit a word or pdf document with your discussion and any MATLAB outputs (graphs, images, etc). 1. (20 pts) SVD for image analysis: convert jumbo.gif to a matrix of type double. Perform an SVD on the image matrix. Represent the image with only the first singular vector and column. Represent the image with the first 5 singular vectors. Then try the first 50. Plot the singular values. At what point does adding more dimensions stop drastically increasing the image? Please explain what information you used to make this decision. Repeat a similar exercise for two of your own images. Aim for an image with a regular pattern and one with less order. Explain how the differences in pattern/frequency/noise are reflected by the SVD analysis. (functions you might want to use are: imtool, imshow, im2double) 2. (20 pts) PCA: There is example data (myData in pset2.mat) of five signaling entities (A, B, C, D, E; columns in the matrix). Use pca analysis (or a series of pca analyses) to hypothesize relationships between A, B, C, D, and E. Justify your hypothesis with the pca results. 3. (20 pts) Bayesian and logic networks - Refer to figure 3.13 of Voit (below). What is the probability that G, C, and S are on while R is off? Create a conditional probability table of the probability of C knowing the state of R and S. Draw a logic diagram of this network and produce the input/output table of the network. In one short paragraph, compare and contrast two situations in cell signaling where you would use a logic network or a Bayesian network. 4. (40 pts) PLSR: Use the "nipals" function found here with an example (PLSRDemo.m) to perform PLSR analysis on the data found in plsrdata.xls. The steps required to perform the PLSR analysis are outlined below. The data describes the percent death at three different time points (output "Y") for cells under four conditions ("samples"). Four proteins were measured at ten time points (input "X"). A fifth sample is provided as a test case. Do not include it in generating the PLSR model. This question was inspired by http://stke.sciencemag.org/cgi/reprint/sigtrans;6/271/tr7.pdf, though you should not need to read it to complete this question. Generate the PLSR model: -Create X and Y matrices and scale them using unit variance scaling (divide each variable (protein measurement at one time point) in each sample by the square root of the variance of that variable across all four samples.) -Use the scaled X and Y matrices to generate a 2-component PLSR model (hint! lines 97-100 of the demo code may be helpful to you...they were to me!) -Plot the predicted (model) output (unscaled) compared to the original output. How do they compare? Evaluate the X and Y loadings (hint, see lines 111-132 of the demo code): -Plot the X loadings. -Plot the Y loadings. -Discuss your observations. Test the PLSR model: -Using the fifth sample that was not included in the PLSR model above, use the model to predict the death time course in this sample based on the protein values. Plot your results and use your plot to discuss how the model prediction compares to the measured results.