Embedded Files
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)
Links
Canvas, Piazza, and Comments/feedback
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
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
Great Blogs! I visit these from time to time, and they have many great articles
The Advanced Research Projects Agency for Health (ARPA-H)
PROBLEM SETS
PROBLEM SETS
PS1: Due September 14
PS2: Due September 26
Computing the Normalized Laplacian Matrix
PS3: Due October 21
Data: PS3_data.mat
MATLAB Starter Code: PS3_code.mlx
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)
PS6: Due December 03
FINAL Project: Due December 17 (no extensions!)
Final Presentation: 12/05/2024
PROBLEM OF THE DAY (Prepared by MARC ANDREW Choi)
PROBLEM OF THE DAY (Prepared by MARC ANDREW Choi)
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
NOTES, SLIDES, AND PAPERS
Date: 08-27-2024
Date: 08-27-2024
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!)
Date: 8-29-2024
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
Networks: (1) Random, (2) Small-world, (3) Scale-free, (4) Ramanujan
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: 09-03-2024
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
Direct link to YouTube: https://www.youtube.com/watch?v=R9UoFyqJca8
Date: 09-10-2024
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
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.
Date: 09-12-2024
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)
Papers
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).
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
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
Papers
Ng AY, Jordan MI, Weiss Y. "On spectral clustering: Analysis and an algorithm." In Advances in neural information processing systems (2002) (pp. 849-856).
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.
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Date: 09-19-2024
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
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: 09-24-2024
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)
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
Date: 10-01-2024
Quote of the Day
"The best way to have a good idea is to have lots of idea" ― Linus Pauling
Papers
Optimal hard threshold
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.
Excellent book chapter (Please read pages 31 - 32)
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)
Date: 10-03-2024
Date: 10-03-2024
Hard-Wired Genome (HWG)
Papers
Luck, Katja, et al. "A reference map of the human binary protein interactome." Nature (2020): 1-7. (DATA: HuRI)
Lambert, Samuel A., et al. "The human transcription factors." Cell 172.4 (2018): 650-665.
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
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
Turing, Alan Mathison. "The chemical basis of morphogenesis." Philos Trans R Soc Lond B BiolSci 237(1952):37–72.
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.
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.
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
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
Date: 10-17-2024
Recap and Missed Sections
Network Controllability: Slides Courtesy of Yang Liu
Date: 10- 21-2024
Greg Harden ( – September 12, 2024) : Stay Sane in an Insane World: How to Control the Controllables and Thrive
Date: 10-24-2024
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
Papers
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.
Rajapakse I, and Smale S. "Mathematics of the Genome." Foundations of Computational Mathematics 17.5 (2017): 1195-1217.
Timothy Gardner, Charles Cantor, and James Collins. "Construction of a genetic toggle switch in escherichiacoli." Nature, 403(6767): 339, 2000.
Michael Elowitz and Stanislas Leibler. "A synthetic oscillatory network of transcriptional regulators." Nature, 403(6767): 335, 2000.
Date: 10-29-2024
Date: 10-29-2024
"I think one of the things about creativity is not to be afraid of saying the wrong thing " ― Sydney Brenner
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
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.
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
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
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.
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
Date: 11-05-2024
"Stay hungry, stay foolish" ― Steve Jobs
Papers
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.
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.
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?
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.
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
Date: 11-07-2024
"Live as if you were to die tomorrow; learn as if you were to live forever" ― Mahatma Gandhi
Papers
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
Date: 11-12-2024
“The secret of getting ahead is getting started.” ― Mark Twain
Methods for Comparing Networks
Papers
Donnat, Claire, and Susan Holmes. "Tracking network dynamics: A survey using graph distances." The Annals of Applied Statistics 12.2 (2018): 971-1012
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
Date: 11-14-2024
“I know what I can do, so I never doubt myself.” ― Usain Bolt
HAT: Hypergraph Analysis Toolbox
Hypergraphs: STEPHEN WOLFRAM and Wolfram Physics Project Launch
Papers
Bick, Christian, Elizabeth Gross, Heather A. Harrington, and Michael T. Schaub. "What are higher-order networks?." SIAM Review 65, no. 3 (2023): 686-731.
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.
Surana A, Chen C, Rajapakse I. "Hypergraph Similarity Measures." IEEE Transactions on Network Science and Engineering, 2022
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.
Date: 11-19-2024
Date: 11-19-2024
“Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.” ― Helen Keller
A uniform hypergraph has edges with the same number of vertices, while a nonuniform hypergraph has edges with varying numbers of vertices
Papers
Pickard J, Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “HAT: Hypergraph Analysis Toolbox,” PLOS Computational Biology, 2023
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
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
Date: 11-26-2024
“Logic will get you from A to B. Imagination will take you everywhere.” ― Albert Einstein
Final Review (not complete!)
Date: 12-04-2024
Date: 12-04-2024
“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” ―William Paul Thurston
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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