NOTES, SLIDES, AND PAPERS

Date: 01-08-2026

• Introduction

Date: 01-15-2024

Quote of the Day

"The only way to do great work is to love what you do" ― Steve Jobs 

• The Extraordinary SVD: During the lecture, Dr. Cleve Moler will join the class virtually 

  1. How SVD Saved the Universe

  2. SVD Measures Partisanship in the U. S. Senate

  3. 1976 Matrix Singular Value Decomposition Film

  4. Direct link to YouTube:  https://www.youtube.com/watch?v=R9UoFyqJca8

Date: 01-20-2024

Quote of the Day

"One never notices what has been done; one can only see what remains to be done" ― Marie Curie 

• Singular Value Decomposition (SVD) 

• Example 1

Papers

1. Lieberman-Aiden, Erez, ..., Groudine Mark, ..., Lander Eric. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." Science 326.5950 (2009): 289-293. 

2. Turk, Matthew, and Alex Pentland. "Eigenfaces for recognition." Journal of cognitive neuroscience 3.1 (1991): 71-86. (Classic! just browse)

Date: 01-22-2024

Quote of the Day

"If you want to be the best, you have to do things that other people aren’t willing to do ― Michael Phelps 

Papers

1. Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998). 

2. Udell, Madeleine, and Alex Townsend. "Why are big data matrices approximately low rank?." SIAM Journal on Mathematics of Data Science 1.1 (2019): 144-160. 

PatentsUS6285999B1

1. US6285999B1 Method for node ranking in a linked database. Lawrence Page: 1998-01-09

2. 115-008219-US-PS1 Network approach to navigating the human genome. Indika Rajapakse: submitted November 2020.

Date: 01-27-2026

Quote of the Day

"Nature has a great simplicity and therefore a great beauty" ― Richard Feynman 

• Poincare Diagram: Stability diagram classifying Poincaré maps as stable or unstable according to their features

• Inverse and Pseudoinverse of a Matrix: This comes up all the time when you are dealing with real data 

• Dynamic Mode Decomposition (DMD) and DMD Demo Codes

Book

• Kutz, J. Nathan, et al. Dynamic mode decomposition: data-driven modeling of complex systems. Society for Industrial and Applied Mathematics, 2016. 

Chapter 1: Dynamic Mode Decomposition: An Introduction

Additional Reading

1. Schmid, Peter J. "Dynamic mode decomposition of numerical and experimental data." Journal of fluid mechanics 656 (2010): 5-28. 

2. Schmid, Peter J. "Dynamic mode decomposition and its variants." Annual Review of Fluid Mechanics 54 (2022): 225-254. 

3. Tu, Jonathan H. "Dynamic mode decomposition: Theory and applications." PhD diss., Princeton University, 2013.

Date: 01-29-2025

"If you don’t believe in yourself why is anyone else going to believe in you?" ― Tom Brady

• Problem Set 1: Discussion and Grading 

• DMD again...

• Eckhart-Young Theorem

Papers

1. Joshua Pickard, Cooper Stansbury, Amit Surana, Anthony Bloch, and Indika Rajapakse. "Biomarker Selection for Adaptive Systems." Proceedings of the National Academy of Sciences, (2025)

Date: 2-03-2026

Quote of the Day

"I think one of the things about creativity is not to be afraid of saying the wrong thing " ― Sydney Brenner 

• Data and Laplacian Matrix

• Edify Image

Papers: I am sharing these references for completeness; you do not need to read them. I personally think it is helpful to know where these methods were originally introduced. 

1. Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416.  (Excellent Review!)

2. Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." Advances in neural information processing systems. 2002. 

3. Ng, Andrew Y., Michael I. Jordan, and Yair Weiss. "On spectral clustering: Analysis and an algorithm." Advances in neural information processing systems 2 (2002): 849-856.

4. Eliasof, Moshe, Eldad Haber, and Eran Treister. "Graph neural reaction diffusion models." SIAM Journal on Scientific Computing 46, no. 4 (2024): C399-C420.