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

Teaching Assistants: MARC ANDREW Choi (machoi@umich.edu) and KEVIN Tracy (kctracy@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

• Wednesday (Marc Andrew Choi), 11:00 AM - 12:00 PM (Remote: https://umich.zoom.us/my/machoi)

• Monday (Kevin Tracy), 12:00 PM - 1:00 PM (Remote: https://umich.zoom.us/j/96821664339) 

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 

• 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

• 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 SETS

PS1: Due September 14

Data: d.csv, Solutions

PS2: Due September 26

• Computing the Normalized Laplacian Matrix

• Solutions

Overleaf

PS3: Due October 21

• Data: PS3_data.mat

• MATLAB Starter Code: PS3_code.mlx

• Solutions

PS4: Due October 31

• Data: fed_fast_refed.mat

• MATLAB Starter Code: PS4_code.mlx

PS5: (Problem 1 Due November 7, Problems 2 and 3 Due November 14)

• Data

PS6: Due December 03

• Data

FINAL Project: Due December 17 (no extensions!)

• Data and Visualization Resources

• LaTex Template

• Slide Template

• Link

• Final Presentation: 12/05/2024

PROBLEM OF THE DAY (Prepared by MARC ANDREW Choi)

POD 1 08/27/24: Introduction

POD 2 08/29/24: Introduction to Graph Theory, Solutions

POD 3 09/03/24: SVD Computation Practice, Solutions

POD 4 09/05/24: Covariance Matrix Data, Solutions

POD 5 09/10/24: Erdos-Renyi Random Graphs,  Solutions

POD 6 09/12/24: Hi-C

POD 7 09/17/24: Normalized Laplacian

POD 8 09/19/24: Network Centrality Measures

POD 9 09/24/24: Differential Equations

POD 10 09/26/24: Dynamic Mode Decomposition

POD 11 10/01/24: Controllability

NOTES, SLIDES, AND PAPERS

Date: 08-27-2024

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: 8-29-2024

Quote of the Day

"Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence" ― Helen Keller 

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: 09-03-2024

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

• 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: 09-10-2024

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)

• Inverse and Pseudoinverse of a Matrix 

• 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. 

Date: 09-12-2024

Quote of the Day

"No great discovery was ever made without a bold guess" ― Isaac Newton

Notes

• Singular Value Decomposition (SVD)

• The Eckhart-Young Theorem

Papers

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). 

3. 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. 

Date: 09-17-2024

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

• • Data: Hi-C and Pore-C

  • The Laplacian

  • K-means

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).

2. 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. 

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

Date: 09-19-2024

Quote of the Day

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

Notes

• • Network Centrality Measures

  • PageRank Algorithm

Papers

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

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: 09-24-2024

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: 10-01-2024

Quote of the Day

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

• DMD and Optimal Hard Threshold

• Network Controllability: Slides and Jamboard

Papers

Optimal hard threshold

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)

Network Controllability

3. 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

4. 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)

Date: 10-03-2024

Hard-Wired Genome (HWG)

Papers

• 1. Luck, Katja, et al. "A reference map of the human binary protein interactome." Nature (2020): 1-7. (DATA: HuRI)

  2. Lambert, Samuel A., et al. "The human transcription factors." Cell 172.4 (2018): 650-665. 

  3. Szklarczyk, Damian, et al. "STRING v11: protein–protein association networks with increased coverage, supporting functional discovery in genome-wide experimental datasets." Nucleic acids research 47.D1 (2019): D607-D613. (DATA: STRING)

Date: 10-08-2024

Quote of the Day

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

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

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: 10-10-2024

Quote of the Day

"It is in this collaboration between people and algorithms that incredible scientific progress lies over the next few decades" ― Demis Hassabis  

Special Lecture by Dr. Lakmal Jayasinghe, SVP - R&D Biologics at Oxford Nanopore Technologies 

Date: 10-17-2024

• Recap and Missed Sections

• Network Controllability: Slides Courtesy of Yang Liu

• Network Agreement and Flocking

Date: 10- 21-2024

Greg Harden ( – September 12, 2024) : Stay Sane in an Insane World: How to Control the Controllables and Thrive

• KL Divergence

• KL Divergence Example

• Entropy

Date: 10-24-2024

Quote of the Day

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

Notes

• Please read this paper: “Transfer learning enables predictions in network biology,” Nature, vol. 618, no. 7965, pp. 616–624, Jun. 2023

More resources: https://rajapakse.lab.medicine.umich.edu/twincell-blueprint

• Human Genome and Data

• Bifurcations and Genetic Networks

Papers

1. 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. 

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

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

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

Date: 10-29-2024

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

• Why Hypergraphs?

• Tensors

• Brain Networks

  • TED Talk:  I am my connectome and Allen Institute for Brain Science 

Tensors = Multi-Dimensional Arrays, Graphs represented with adjacency matrix and Hypergraphs represented with adjacency tensor 

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. 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/

Date: 10-31-2024

"Study hard what interests you the most in the most undisciplined, irreverent and original manner possible" ― Richard Feynmann 

• Beautiful Visualization: Controllability of Complex Networks

• Network Observability: Slides: Courtesy of Yang Liu

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. Liu, Yang-Yu, and Albert-László Barabási. "Control principles of complex systems." Reviews of Modern Physics 88, no. 3 (2016): 035006. 

Date: 11-05-2024

"Stay hungry, stay foolish" ― Steve Jobs 

• Least-squares problems 

• Data-guided Control (DGC)

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. 

3. 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 

Remark: Why are there so many low rank matrices that appear in computational math?

1. Udell, Madeleine, and Alex Townsend. "Why are big data matrices approximately low rank?." SIAM Journal on Mathematics of Data Science 1, no. 1 (2019): 144-160. 

2. Thibeault, Vincent, Antoine Allard, and Patrick Desrosiers. "The low-rank hypothesis of complex systems." Nature Physics 20, no. 2 (2024): 294-302. 

Date: 11-07-2024

"Live as if you were to die tomorrow; learn as if you were to live forever" ― Mahatma Gandhi 

• Foundation models for biology

Papers

1. C. V. Theodoris et al., “Transfer learning enables predictions in network biology,” Nature, vol. 618, no. 7965, pp. 616–624, Jun. 2023

Date: 11-12-2024

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

Methods for Comparing Networks

Papers

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

2. Lindsly S, Chen C, Liu S, Ronquist S, Dilworth S, Perlman M, Rajapakse I. "4DNvestigator: time series genomic data analysis toolbox." Nucleus, 12:1, 58-64, DOI: 10.1080/19491034.2021.1910437  (2021) .

Date: 11-14-2024

“I know what I can do, so I never doubt myself.” ― Usain Bolt

• Why Hypergraphs?

• Tensors and Hypergraphs: Notes and Slides

• HAT: Hypergraph Analysis Toolbox

  • Multi-correlations

Hypergraphs: STEPHEN WOLFRAM  and Wolfram Physics Project Launch

Papers

1. Bick, Christian, Elizabeth Gross, Heather A. Harrington, and Michael T. Schaub. "What are higher-order networks?." SIAM Review 65, no. 3 (2023): 686-731. 

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

4. 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. 

More Papers!

Date: 11-19-2024

“Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.” ― Helen Keller

HAT

A uniform hypergraph has edges with the same number of vertices, while a nonuniform hypergraph has edges with varying numbers of vertices 

Papers

1. Pickard J,  Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “HAT: Hypergraph Analysis Toolbox,” PLOS Computational Biology, 2023

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. 

Date: 11-21-2024

“You don’t understand anything until you learn it more than one way.” ― Marvin Minsky 

Visualizing Networks and Review topics covered so far

Date: 11-26-2024

“Logic will get you from A to B. Imagination will take you everywhere.” ― Albert Einstein

• Network Agreement and Flocking

• Final Review (not complete!)

Date: 12-04-2024

“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” ―William Paul Thurston 

• Final Projects

• Networks and Linear Algebra

• Final Review

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. Too much Coupling and Network Thinking

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

6. Making connections

7. Stephen Hoge: 

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

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