Embedded Files
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
Links
Canvas, Piazza, and Comments/feedback
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
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
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 OF THE DAY
PROBLEM OF THE DAY
PROBLEM SETS
PROBLEM SETS
PS1: Due September 14
MATLAB Starter Code: MATLAB starter code
Python Example: Python Code
Data: D.csv
PS2: Due September 28
Computing the Normalized Laplacian Matrix
PS3: Due October 10
Data: PS3_data.mat
MATLAB Starter Code: PS3_code.mlx
PS4: Due October 26
PS5: Due November 6
PS6: Due November 17
Final Project: Due December 14 (no extensions!)
Slide Template
Final Presentation: 12/13/2023 at 1:30 - 3:30 PM
NOTES, SLIDES, AND PAPERS
NOTES, SLIDES, AND PAPERS
Date: 08-31-2023
Date: 08-31-2023
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: 09-05-2023
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
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: 09-07-2023
Date: 09-07-2023
Quote of the Day
"Think mathematically, act computationally" ― Arthur Krener
Notes
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: 09-12-2023
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
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).
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: 09-14-2023
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
Direct link to YouTube: https://www.youtube.com/watch?v=R9UoFyqJca8
Date: 09-19-2023
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
Papers
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
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
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: 09-26-2023
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)
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
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
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: 10-03-2023
Date: 10-03-2023
Quote of the Day
“The secret of getting ahead is getting started.” ― Mark Twain
Notes
Optimal hard threshold
Papers
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)
Date: 10-05-2023
Date: 10-05-2023
Quote of the Day
"The best way to have a good idea is to have lots of idea" ― Linus Pauling
Papers
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)
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.
Lin, Ching-Tai. "Structural controllability." IEEE Transactions on Automatic Control 19, no. 3 (1974): 201-208. (Beautiful paper!)
Date: 10-10-2023
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
A Tutorial on Spectral Clustering (Excellent Review!)
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).
Date: 10-12-2023
Date: 10-12-2023
Quote of the Day
"Do one thing every day that scares you" ― Eleanor Roosevelt
Notes
TURING System! Mathematics of morphogenesis, the processes by which order is created in the developing organism
Papers
Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158.
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Date: 10-19-2023
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
Papers
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.
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.
Date: 10-24-2023
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
Papers
Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998).
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.
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
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
Entropy
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
Kitano, Hiroaki. "Biological robustness." Nature Reviews Genetics 5.11 (2004): 826-837.
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).
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
Date: 10-31-2023
Network Controllability again...
Please read the following papers carefully!
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) Supporting Information
Date: 11-02-2023
Date: 11-02-2023
Network Controllability
Date: 11-07-2023
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
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.
Bassett, Danielle S., and Olaf Sporns. "Network neuroscience." Nature neuroscience 20, no. 3 (2017): 353-364.
Date: 11-09-2023
Date: 11-09-2023
Lecture summary Jamboard
Notes:
CVX: Matlab-based modeling system for convex optimization
Papers
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/
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.
Chen C, Surana A, Bloch A, Rajapakse I. "Controllability of Hypergraphs." IEEE Transactions on Network Science and Engineering, 2021.
Date: 11-14-2023
Date: 11-14-2023
Lecture summary Jamboard
Homework 6
Notes:
CVX: Matlab-based modeling system for convex optimization
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.
Date: 11-16-2023
Date: 11-16-2023
HAT: Hypergraph Analysis Toolbox
Date: 11-21-2023
Date: 11-21-2023
Hypergraphs: STEPHEN WOLFRAM
Wolfram Physics Project Launch
Papers
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.
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.
Donnat, Claire, and Susan Holmes. "Tracking network dynamics: A survey using graph distances." The Annals of Applied Statistics 12.2 (2018): 971-1012
Surana A, Chen C, Rajapakse I. "Hypergraph Similarity Measures." IEEE Transactions on Network Science and Engineering, 2022
Date: 11-21-2023
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
Observability of Complex Biological Systems: Slides: Courtesy of Yang Liu
Lecture summary Jamboard 1 and Jamboard 2
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.
Pickard J, Surana A, Bloch A, Rajapakse I. Observability of Hypergraphs, arXiv:2304.04883, Accepted (2023 62nd IEEE Conference on Decision and Control (CDC)
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.
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
Date: 12-05-2023
Network Agreement and Flocking
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.
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.
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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