Instructor: Prof. INDIKA Rajapakse (indikar@umich.edu)

Teaching Assistants: COOPER Stansbury (cstansbu@umich.edu) and EVAN Urban (urbaneva@umich.edu)

Location: 1200 Chemistry Building

Class Time: Tuesday and Thursday, 8:30 AM - 10:00 AM

Office Hours: 

• Tuesday and Thursday (Indika R), 4:00 PM - 5:00 PM:  https://meet.google.com/dnm-zipr-tsb  or in person after class

• Monday (Cooper S), 11:00 AM - 12:00 PM: https://meet.google.com/qic-ybqf-nio

• Friday (Evan U), 2:00 - 3:00 PM: https://meet.google.com/djt-uwnt-upg 

Challenge Problem!

Links

• Syllabus and Topics and Timeline

• Canvas, Piazza, and Comments/feedback 

• MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference 

• Basic Notation

• Simplicity, Rigor, and Magic

• James Simons: My Guiding Principles 

Recommended Reading Material

• Dr. Cleve Moler's Book: Numerical Computing with MatLab

• Jon Kleinberg's Book: Networks, Crowds, and Markets 

References of Interest

• Digital Library

• Generative AI Resources

• Great Blogs!  I visit these from time to time, and they have many great articles

  • Cleve Moler's Blog and Bits of DNA

• The Advanced Research Projects Agency for Health (ARPA-H) 

PROBLEM OF THE DAY

POD1: Class Expectations

POD2: Eigenvalues of A and L

• • • Hint 

PROBLEM SETS

PS1: Due September 14

• • MATLAB Starter Code:  MATLAB starter code 

  • Python Example: Python Code

  • Data: D.csv

  • Solutions; MATLAB File

  • Networks of Interest

PS2: Due September 28 

• Computing the Normalized Laplacian Matrix

• MATLAB

PS3: Due October 10 

• Data: PS3_data.mat

• MATLAB Starter Code: PS3_code.mlx

PS4: Due October 26

• Data

• MATLAB Starter Code

• Cutting a Graph (Example)

• Part I Solutions

PS5: Due November 6

• Data

• Helper Code

• Solutions

PS6: Due November 17

• Data

• Helper Code

Final Project: Due December 14 (no extensions!)

• Data and Visualization Resources

• LaTex Template

• Slide Template

• Final Presentation: 12/13/2023 at 1:30 - 3:30 PM

NOTES, SLIDES, AND PAPERS

Date: 08-31-2023

Introduction: Slides

Papers

1. Turing, Alan Mathison. "The chemical basis of morphogenesis." Philosophical Transactions of the Royal Society B: Biological Sciences, 370(1666), p.20140218. (Classic!)

Date: 09-05-2023

Quote of the Day

"Ideas only realize their power when people understand them" ― Small Worlds: The Dynamics of Networks between Order and Randomness (Book) 

Notes

• Matrix Operations

• Basic Graphs and Adjacency Matrices 

• Networks: (1) Random, (2)  Small-world, (3) Scale-free, (4) Ramanujan 

Papers

1. Small World: Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.

2. Small World: Milgram, Stanley. "The small world problem." Psychology today 2, no. 1 (1967): 60-67. 

3. Scale-free: Barabási, Albert-László, and Réka Albert. "Emergence of scaling in random networks." Science 286, no. 5439 (1999): 509-512. 

FUN readings.....

1. Alon,  Uri. "Biological networks: the tinkerer as an engineer." Science 301.5641 (2003): 1866-1867. 

2. Too much Coupling

Date: 09-07-2023

Quote of the Day

"Think mathematically, act computationally" ― Arthur Krener 

Notes

• Singular Value Decomposition (SVD)

• Important Eigenvalue: Example 1, Example 2

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. 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: 09-12-2023

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)

Papers

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

2. Sweeney P, Chen C, Rajapakse I, Cone R.  "Network Dynamics of Hypothalamic Feeding Neurons." Proceedings of the National Academy of Sciences, 118.14 (2021). 

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: 09-14-2023

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 Receives ICIAM Industry Prize 2023

• 1. How SVD Saved the Universe

  2. 1976 Matrix Singular Value Decomposition Film

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

Date: 09-19-2023

Quote of the Day

"Science and everyday life cannot and should not be separated" ― Rosalind Franklin

SVD and Network Compression 

Notes

• The Eckhart-Young Theorem

Papers

1. Tero, Atsushi, Seiji Takagi, Tetsu Saigusa, Kentaro Ito, Dan P. Bebber, Mark D. Fricker, Kenji Yumiki, Ryo Kobayashi, and Toshiyuki Nakagaki. "Rules for biologically inspired adaptive network design." Science 327, no. 5964 (2010): 439-442. 

FUN readings.....

Nurse, Paul, and Jacqueline Hayles. "The cell in an era of systems biology." Cell 144.6 (2011): 850-854. 

Date: 09-21-2023

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 

Notes

• Vector and Matrix Norms 

Papers: Turing System

1. Turing, Alan Mathison. "The chemical basis of morphogenesis." Philos Trans R Soc Lond B BiolSci 237(1952):37–72.

2. Smale, Steve. "A mathematical model of two cells via Turing’s equation." The Hopf bifurcation and its applications. Springer, New York, NY, 1976. 354-367.

3. Rajapakse I, and Smale S. "Emergence of Function from Coordinated Cells in a Tissue." Proceedings of the National Academy of Sciences 114.7 (2017): 1462-1467. 

4. Stansbury, Cooper M., Gabrielle A. Dotson, Harrison Pugh, Alnawaz Rehemtulla, Indika Rajapakse, and Lindsey A. Muir. "A lipid-associated macrophage lineage rewires the spatial landscape of adipose tissue in early obesity." JCI Insight. 2023 .  

Date: 09-26-2023

Quote of the Day

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

Notes

• Dynamic Mode Decomposition (DMD)

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

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

Date: 09-28-2023

Quote of the Day

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

The human genome is made up of 3 billion base pairs, on 23 chromosome pairs that contain over 20,000 genes

Notes

• Inverse and Pseudoinverse of a Matrix 

• Network Centrality

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. 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: 10-03-2023

Quote of the Day

“The secret of getting ahead is getting started.” ― Mark Twain  

Notes

• Network Centrality

• Optimal hard threshold

Papers

1. 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. 

2. Excellent book chapter (Please read pages 31 - 32)

Date: 10-05-2023

Quote of the Day

"The best way to have a good idea is to have lots of idea" ― Linus Pauling

• Data-Guided Controllability 

• Network Controllability: Slides and Jamboard

• Examples

Papers

1. 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

2. 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)

3. Gilbert, Elmer G. "Controllability and observability in multivariable control systems." Journal of the Society for Industrial and Applied Mathematics, Series A: Control 1, no. 2 (1963): 128-151.

4. Lin, Ching-Tai. "Structural controllability." IEEE Transactions on Automatic Control 19, no. 3 (1974): 201-208.  (Beautiful paper!)

Date: 10-10-2023

Quote of the Day

"Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things" ― Sir Isaac Newton

Guest Lecture: Prof. Lee Hartwell

Notes

• • The Laplacian

  • Spectral Clustering and K-means

  • A Tutorial on Spectral Clustering (Excellent Review!)

Papers

1. Ng AY, Jordan MI, Weiss Y. "On spectral clustering: Analysis and an algorithm." In Advances in neural information processing systems (2002) (pp. 849-856).

Date: 10-12-2023

Quote of the Day

"Do one thing every day that scares you" ― Eleanor Roosevelt 

Notes

• Spectral Clustering

• Jamboard

• TURING System! Mathematics of morphogenesis, the processes by which order is created in the developing organism 

Papers

1. Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158. 

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

Date: 10-19-2023

Quote of the Day

"If I have seen further, it is by standing on the shoulders of giants" ― Isaac Newton 

Notes

• Bifurcations and Genetic Networks

Papers

1. Timothy Gardner, Charles Cantor, and James Collins. "Construction of a genetic toggle switch in escherichiacoli." Nature, 403(6767): 339, 2000.

2. Michael Elowitz and Stanislas Leibler. "A synthetic oscillatory network of transcriptional regulators." Nature, 403(6767): 335, 2000.

3. Spencer, Sabrina L., et al. "The proliferation-quiescence decision is controlled by a bifurcation in CDK2 activity at mitotic exit." Cell 155.2 (2013): 369-383. 

4. Rajapakse I, and Smale S. "Mathematics of the Genome." Foundations of Computational Mathematics 17.5 (2017): 1195-1217. 

Date: 10-24-2023

Quote of the Day

"You never lose a dream, it just incubates as a hobby" ― Larry Page

Recap and Missed Section 

• Optimal hard threshold: Excellent book chapter (Please read pages 31 - 32) 

• PageRank (PR)

  • From Cleve Moler: 1: The World’s Largest Matrix Computation 2. Google PageRank 

• Agreement in a Network and Fiedler number

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. 

3. Olfati-Saber, Reza, J. Alex Fax, and Richard M. Murray. "Consensus and cooperation in networked multi-agent systems." Proceedings of the IEEE 95.1 (2007): 215-233.  

Date: 10-26-2023

Quote of the Day

"New ideas pass through three periods: 1) It can't be done. 2) It probably can be done, but it's not worth doing. 3) I knew it was a good idea all along! " ― Arthur C. Clarke

Jamboard

• Entropy

  • Slides from ICML 2019

• Network Robustness: Network robustness is the ability of a network to survive from random failures or deliberate attacks (e.g., removal of nodes or edges). It is intimately related to the underlying network structure/topology.

Papers

• 1. Kitano, Hiroaki. "Biological robustness." Nature Reviews Genetics 5.11 (2004): 826-837.

  2. Chen P, Wu L, Liu S, Rajapakse I. "Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications." 2019 International Conference on Machine Learning  (2019).

  3. Sweeney P, Chen C, Rajapakse I, Cone R.  "Network Dynamics of Hypothalamic Feeding Neurons." Proceedings of the National Academy of Sciences, 118.14 (2021). 

Book Chapter

Network Science:  Network Robustness 

Date: 10-31-2023

Network Controllability  again...

Please read the following papers carefully! 

1. 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

2. 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

Date: 11-02-2023

Network Controllability

Date: 11-07-2023

"Anytime you get technical development that’s two to threefold or more efficient, accurate, cheaper, a whole range of experiments opens up" ― Frederick Sanger

Network Controllability and Applications

Slides from Scott Ronquist 

Papers

1. Gu, Shi, Fabio Pasqualetti, Matthew Cieslak, Qawi K. Telesford, Alfred B. Yu, Ari E. Kahn, John D. Medaglia et al. "Controllability of structural brain networks." Nature communications 6, no. 1 (2015): 1-10. 

2. Bassett, Danielle S., and Olaf Sporns. "Network neuroscience." Nature neuroscience 20, no. 3 (2017): 353-364. 

Date: 11-09-2023

Lecture summary Jamboard

• Why Hypergraphs?

• Notes: 

  • Tensors

  • Multi-correlations

  • Hypergraphs and Tensors

  • CVX: Matlab-based modeling system for convex optimization 

Papers

1. Benson, Austin R., David F. Gleich, and Jure Leskovec. "Higher-order organization of complex networks." Science 353.6295 (2016): 163-166. 

URL: https://snap.stanford.edu/higher-order/

2. Levine, Jonathan M., Jordi Bascompte, Peter B. Adler, and Stefano Allesina. "Beyond pairwise mechanisms of species coexistence in complex communities." Nature 546, no. 7656 (2017): 56-64. 

3. Chen C, Surana A, Bloch A, Rajapakse I. "Controllability of Hypergraphs." IEEE Transactions on Network Science and Engineering, 2021.

Date: 11-14-2023

Lecture summary Jamboard

• Homework 6

• Notes: 

  • Hypergraphs and Tensors

  • CVX: Matlab-based modeling system for convex optimization 

Papers

1. Pasqualetti, Fabio, Sandro Zampieri, and Francesco Bullo. "Controllability metrics, limitations and algorithms for complex networks." IEEE Transactions on Control of Network Systems 1, no. 1 (2014): 40-52. 

2. Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15, no. 1 (2016): 142-161. 

Date: 11-16-2023

HAT: Hypergraph Analysis Toolbox

Date: 11-21-2023

Hypergraphs: STEPHEN WOLFRAM 

Wolfram Physics Project Launch

Papers

1. Feng, S., Heath, E., Jefferson, B., Joslyn, C., Kvinge, H., Mitchell, H. D., ... & Purvine, E. (2021). Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC bioinformatics, 22(1), 1-21. 

2. Dotson, Gabrielle A., Can Chen, Stephen Lindsly, Anthony Cicalo, Sam Dilworth, Charles Ryan, Sivakumar Jeyarajan et al. "Deciphering Multi-way Interactions in the Human Genome." Nature Communications 13, no. 1 (2022): 5498. 

3. Donnat, Claire, and Susan Holmes. "Tracking network dynamics: A survey using graph distances." The Annals of Applied Statistics 12.2 (2018): 971-1012 

4. Surana A, Chen C, Rajapakse I. "Hypergraph Similarity Measures."  IEEE Transactions on Network Science and Engineering,  2022

Date: 11-21-2023

"Things won't go perfect. It's all about how you adapt from those things and learn from mistakes" ― Michael Phelps 

Network Visualization

• Simple Network Data Set

Observability of Complex Biological Systems: Slides: Courtesy of Yang Liu

Lecture summary Jamboard 1 and Jamboard 2

Papers

1. 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.  

2. Pickard J,  Surana A, Bloch A, Rajapakse I. Observability of Hypergraphs, arXiv:2304.04883, Accepted (2023 62nd IEEE Conference on Decision and Control (CDC) 

3. Yuan, Zhengzhong, Chen Zhao, Zengru Di, Wen-Xu Wang, and Ying-Cheng Lai. "Exact controllability of complex networks." Nature communications 4, no. 1 (2013): 1-9. 

4. Baggio, Giacomo, Danielle S. Bassett, and Fabio Pasqualetti. "Data-driven control of complex networks." Nature communications 12, no. 1 (2021): 1-13. 

Date: 12-05-2023

Final Review

Network Agreement and Flocking

GENERAL READING

I will add to this list throughout the semester

1. Strogatz SH. "Exploring complex networks." Nature. 2001 Mar;410(6825):268-76.

2. Rajapakse I. "Conversation with Dr. Steve Smale and Dr. Lee Hartwell." NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 68 (9). 

3. Hartwell, Leland H., et al. "From molecular to modular cell biology." Nature 402.6761 (1999): C47-C52.

4. Stankovski T, Pereira T, McClintock PV, Stefanovska A. Coupling functions: universal insights into dynamical interaction mechanisms. Reviews of Modern Physics. 2017 Nov 6;89(4):045001.

5. Too much Coupling and Network Thinking

6. Strogatz, Steven H. "Love affairs and differential equations." Mathematics Magazine 61, no. 1 (1988): 35-35. (FUN read!)

7. Making connections

8. Stephen Hoge: 

https://www.youtube.com/watch?v=Rn9sRkkqGT4

https://www.youtube.com/watch?v=1-kHTzt7EVs