Embedded Files
Instructor: Prof. INDIKA Rajapakse (indikar@umich.edu)
Teaching Assistant: RAM Prakash (nuvi@umich.edu)
Location: 1200 Chemistry Building, Class Time: Tuesday and Thursday, 8:30 AM - 10:00 AM
Office Hours:
Indika R - Tuesday and Thursday , 4:00 PM - 5:00 PM: https://meet.google.com/dnm-zipr-tsb or in person after class
Ram P - Wednesday 3:00 - 4:00 PM Zoom and Friday 3:00 PM - 4:00 PM in person Room 3370, NCRC B520
James Simons: My Guiding Principles
Links
Canvas, Piazza, and Comments/feedback
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
A service course on linear algebra regularly taught by Gil Strang. Here is the course webpage.
Recommended Reading Material
Dr. Cleve Book: Numerical Computing with MATLAB
Jon Kleinberg's Book: Networks, Crowds, and Markets
Francesco Bullo's Book: Lectures on Network Systems
Albert-László Barabási's Book: Network Science
References of Interest
Great Blogs! I visit these from time to time, and they have many great articles: Cleve Moler's Blog and Bits of DNA
PROBLEM SETS
PROBLEM SETS
PS1: Due September 9, 2025
Computing the Normalized Laplacian Matrix
PS2: Due September 30, 2025
Data: PS2_data.mat
MATLAB Starter Code: PS2_code.mlx
PS3 (Part 1): Due October 9, 2025
PS3 (Part 2): Due Friday, October 24, 2025
FINAL Project: Due December 17, 2025 (no extensions!)
PROBLEM OF THE DAY
PROBLEM OF THE DAY
NOTES, SLIDES, AND PAPERS
NOTES, SLIDES, AND PAPERS
Date: 08-26-2025
Date: 08-26-2025
Introduction: Slides
Papers
Turing, Alan Mathison. "The chemical basis of morphogenesis." Philosophical Transactions of the Royal Society B: Biological Sciences, 370(1666), p.20140218. (Classic!)
Rajapakse I. "Conversation with Dr. Steve Smale and Dr. Lee Hartwell." NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 68 (9).
Date: 8-28-2025
Date: 8-28-2025
Quote of the Day
"Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence" ― Helen Keller
Notes
Papers
Small World: Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.
Small World: Milgram, Stanley. "The small world problem." Psychology today 2, no. 1 (1967): 60-67.
Scale-free: Barabási, Albert-László, and Réka Albert. "Emergence of scaling in random networks." Science 286, no. 5439 (1999): 509-512.
FUN readings.....
Alon, Uri. "Biological networks: the tinkerer as an engineer." Science 301.5641 (2003): 1866-1867.
Date: 09- 02-2025
Date: 09- 02-2025
Quote of the Day
"If you don’t believe in yourself why is anyone else going to believe in you?" ― Tom Brady
Notes
Singular Value Decomposition (SVD)
Date: 09-04-2024
Date: 09-04-2024
Quote of the Day
"No great discovery was ever made without a bold guess" ― Isaac Newton
Notes
Singular Value Decomposition (SVD)
Papers
Turk, Matthew, and Alex Pentland. "Eigenfaces for recognition." Journal of cognitive neuroscience 3.1 (1991): 71-86. (Classic! just browse)
Sweeney P, Chen C, Rajapakse I, Cone R. "Network Dynamics of Hypothalamic Feeding Neurons." Proceedings of the National Academy of Sciences, 118.14 (2021).
Date: 09-09-2025
Date: 09-09-2025
Quote of the Day
"Things won't go perfect. It's all about how you adapt from those things and learn from mistakes" ― Michael Phelps
Notes
Inverse and Pseudoinverse of a Matrix
Papers
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.
Chen H, Chen J, Muir LA, Ronquist S, Meixner W, Ljungman M, Ried T, Smale S, Rajapakse I. "Functional Organization of the Human 4D Nucleome. " Proceedings of the National Academy of Sciences 112.26 (2015): 8002-8007. Supporting Information
Date: 09-11-2025
Date: 09-11-2025
Quote of the Day
"You never lose a dream, it just incubates as a hobby" ― Larry Page
Notes
Date: 09-16-2025
Date: 09-16-2025
Quote of the Day
"Young man, in mathematics you don't understand things. You just get used to them" ― John von Neumann
Guest Lecture: Dr. Cleve Moler
MathWorks Co-Founder and Chief Mathematician Cleve B. Moler
Date: 09-23-2025
Date: 09-23-2025
Quote of the Day
"Everyone's dream can come true if you just stick to it and work hard" ― Serena Williams
Notes
Network Centrality Measures
Papers
Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998).
PatentsUS6285999B1
US6285999B1 Method for node ranking in a linked database. Lawrence Page: 1998-01-09
115-008219-US-PS1 Network approach to navigating the human genome. Indika Rajapakse: submitted November 2020.
Date: 09-25-2025
Date: 09-25-2025
Quote of the Day
"Study hard what interests you the most in the most undisciplined, irreverent and original manner possible" ― Richard Feynman
Notes
Date: 09-30-2025
Date: 09-30-2025
Quote of the Day
"Innovation distinguishes between a leader and a follower" ― Steve Jobs
Notes
Dynamic Mode Decomposition (DMD)
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
Please get familiar with these two papers. They will give you some idea of Network Controllability
Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173. Slides: Courtesy of Yang Liu
Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha MS, Bloch A, Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7. Data-guided Control (DGC)
Papers: An excellent reference on low-rank matrices for those who would like to learn more.
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.
Date: 10-02-2025
Date: 10-02-2025
Quote of the Day
“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” ―William Paul Thurston
Network Controllability: Slides Courtesy of Yang Liu
Date: 10-07-2025
Date: 10-07-2025
"Science and everyday life cannot and should not be separated" ― Rosalind Franklin
PS3: Due October 9, 2025
Controllability Gramian: Quantitative measure of how "easy" it is to steer the system in different directions of its state space!
Network Controllability and Applications: Slides from Scott Ronquist
Papers: Please check this slide deck. I’ll update it from time to time when I find a good paper on network control. Thanks.
Date: 10-09-2024
Date: 10-09-2024
"Anytime you get technical development that’s two to threefold or more efficient, accurate, cheaper, a whole range of experiments opens up" ― Frederick Sanger
Data-guided Control (DGC): Slides from Scott Ronquist
Network Observability: Slides: Courtesy of Yang Liu
Papers
Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Observability of complex systems." Proceedings of the National Academy of Sciences 110, no. 7 (2013): 2460-2465.
Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha MS, Bloch A, Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7. Data-guided Control (DGC) Supporting Information and Slides from Scott Ronquist
Pickard, J., Stansbury, C., Surana, A., Muir, L., Bloch, A., & Rajapakse, I. (2025). Dynamic sensor selection for biomarker discovery. Proceedings of the National Academy of Sciences (online).
Date: 10-16-2025
Date: 10-16-2025
Quote of the Day
"Ideas only realize their power when people understand them" ― Duncan Watts's book Six Degrees: The Science of a Connected Age
Recap and Missed Sections
Optimal Hard Threshold (OHT): 1. Slides from Matan Gavish 2. OHT and Clustering
Data-guided Control (DGC): Slides from Scott Ronquist
Additional Reading
Gavish, Matan, and David L. Donoho. "The optimal hard threshold for singular values is 4/sqrt(3)." IEEE Transactions on Information Theory 60.8 (2014): 5040-5053. (Amazing Paper!)
Excellent book chapter (Please read pages 31 - 32): https://databookuw.com/
GENERAL READING
GENERAL READING
I will add to this list throughout the semester
Strogatz SH. "Exploring complex networks." Nature. 2001 Mar;410(6825):268-76.
Rajapakse I. "Conversation with Dr. Steve Smale and Dr. Lee Hartwell." NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 68 (9).
Hartwell, Leland H., et al. "From molecular to modular cell biology." Nature 402.6761 (1999): C47-C52.
Strogatz, Steven H. "Love affairs and differential equations." Mathematics Magazine 61, no. 1 (1988): 35-35. (FUN read!)
Stephen Hoge:
https://www.youtube.com/watch?v=Rn9sRkkqGT4
https://www.youtube.com/watch?v=1-kHTzt7EVs
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