FALL 2022
BIOINF - MATH 540: Mathematics of Biological Networks
Instructor: Prof. INDIKA Rajapakse
Teaching Assistants: JOSHUA Pickard and COOPER Stansbury
Location: 2548, North University Building
Class Zoom Link: https://umich.zoom.us/j/99152694452 (passcode: 1234)
Class Time: Tuesday and Thursday, 8:30 AM - 10:00 AM
In-class lectures (whiteboard) are recorded and uploaded to Canvas shortly after each class.
Office Hours:
Wednesday and Friday (Indika R), 4:00 PM - 5:00 PM: https://meet.google.com/dnm-zipr-tsb or in person after class
Tuesday (Joshua P), 4:00 PM - 5:00 PM: Remote, https://meet.google.com/bov-ghoa-uxo
Monday (Cooper S), 11:00 AM - 12:00 PM: Remote, https://meet.google.com/qic-ybqf-nio
Wednesday (Joshua P and Cooper S together!), 2:00-2:30 PM: Remote, https://meet.google.com/bov-ghoa-uxo
Links
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
Piazza (Please sign in and add yourself to the course if you have not already)
References of Interest
Dr. Gilbert Strang's Book
Great Blogs! I visit these from time to time, and they have many great articles
PROBLEM OF THE DAY
POD2: Eigenvalues of A and L
POD3: Centrality and Controllability: data
PROBLEM SETS
PS1: Due September 13
MATLAB Starter Code: MATLAB starter code
Python Example: Python Code
Data: D.csv
MATLAB Starter Code: MATLAB starter code
Data: PS2_data.mat
PS3: Due October 6
PS5: Due November 3
PS6: Due November 14
PS7: Due December 6
Final Project: Due December 16 (no extensions!)
Slide Template
Final Presentation: 12/13/2022 at 1:30 - 3:00 PM
NOTES, SLIDES, AND PAPERS
Date: 08-30-2022
Introduction: Slides
Papers
Turing, Alan Mathison. "The chemical basis of morphogenesis." Philosophical Transactions of the Royal Society B: Biological Sciences, 370(1666), p.20140218.
Date: 09-01-2022
Quote of the Day
"Ideas only realize their power when people understand them" ― Small Worlds: The Dynamics of Networks between Order and Randomness (Book)
Topics
Networks: (1) Random, (2) Small-world, (3) Scale-free, (4) Ramanujan
Review of Adjacency, Degree matrices
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: 09-06-2022
Quote of the Day
"Simplicity is the ultimate sophistication" ― Leonardo da Vinci
Topics
Date: 09-08-2022
Quote of the Day
"Think mathematically, act computationally" ― Arthur Krener
Topics
Eigenvalues and Eigenvectors
Date: 09-13-2022
Quote of the Day
"One of the really tough things is figuring out what questions to ask. Once you figure out the question, then the answer is relatively easy" ― Elon Musk
Topics
Network Data: Hi-C (Genome-wide Chromosome Conformation Capture)
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: 09-15-2022
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
Direct link to YouTube: https://www.youtube.com/watch?v=R9UoFyqJca8
Date: 09-20-2022
Quote of the Day
"Science and everyday life cannot and should not be separated" ― Rosalind Franklin
SVD and its Applications
Relationship between SVD and PCA
Papers
Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158.
Date: 09-22-2022
Quote of the Day
"Any sufficiently advanced technology is indistinguishable from magic" ― Arthur C. Clarke
SVD and its Applications
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.
Lindsly S, Chen C, Dilworth S, Jeyaraja S, Meixner W, Stansbury C, Cicalo A, Beckloff N, Ryan C, Surana A, Wicha M, Muir L, Rajapakse I. "Deciphering Multi-way Interactions in the Human Genome." Nature Communications (2022).
Date: 09-27-2022
Quote of the Day
"Nature has a great simplicity and therefore a great beauty" ― Richard Feynman
Notes: 1. Norms 2. Matrix Inverse 3. KL Divergence 4. Eckhart-Young Theorem
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.
Date: 09-29-2022
Quote of the Day
"Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence" ― Helen Keller
Lecture summary Jamboard
Poincare Diagram: Stability diagram classifying Poincaré maps as stable or unstable according to their features
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: 10-04-2022
Quote of the Day
"Imagination is more important than knowledge " ― Albert Einstein
Lecture summary Jamboard
Papers
Gleich DF. "PageRank beyond the Web." SIAM Review. 2015;57(3):321-63.
Gómez, Sergio. "Centrality in networks: finding the most important nodes." In Business and consumer analytics: New ideas, pp. 401-433. Springer, Cham, 2019. (Excellent Review!)
Date: 10-06-2022
Quote of the Day
"Live as if you were to die tomorrow. Learn as if you were to live forever " ― Mahatma Gandhi
Lecture summary Jamboard
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: 10-10-2022
Quote of the Day
"If you don’t believe in yourself why is anyone else going to believe in you?" ― Tom Brady
Lecture summary Jamboard
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: 10-12-2022
Quote of the Day
"Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things" ― Sir Isaac Newton
Lecture summary Jamboard
A Tutorial on Spectral Clustering (Excellent Review!)
Date: 10-20-2022
Quote of the Day
"It is not up to you to finish the task, but you are not free to avoid it" ― R. Tarfon
Lecture summary Jamboard
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).
Book Chapter
Network Science: Network Robustness
Date: 10-25-2022
"The best way to have a good idea is to have lots of idea" ― Linus Pauling
Lecture summary Jamboard
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: 10-27-2022
"Science and everyday life cannot and should not be separated" ― Rosalind Franklin
Lecture summary Jamboard
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: 11-01-2022
"The future belongs to those who believe in the beauty of their dreams " ― Eleanor Roosevelt
Lecture summary Jamboard
Papers
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.
Rajapakse I, Groudine M, Mesbahi M. Dynamics and control of state-dependent networks for probing genomic organization. Proceedings of the National Academy of Sciences. 2011 Oct 18;108(42):17257-62.
Date: 11-03-2022
"For the robust, an error is information; for the fragile, an error is an error " ― Nassim Taleb
Lecture summary Jamboard
DMD + Control
Papers
Baggio, Giacomo, Danielle S. Bassett, and Fabio Pasqualetti. "Data-driven control of complex networks." Nature communications 12, no. 1 (2021): 1-13.
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. Slides: Courtesy of Yang Liu
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.
Date: 11-08-2022
"Everything is practice" ― Pele
Lecture summary Jamboard
Networks in Neuroscience and Immunology
TED Talk: I am my connectome and Allen Institute for Brain Science
Notes: Hypergraphs and Tensors
Papers
Please read!
D. L. Barabási and A.-L. Barabási, “A Genetic Model of the Connectome,” Neuron, vol. 105, no. 3, pp. 435-445.e5, Feb. 2020, doi: 10.1016/j.neuron.2019.10.031.
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: 11-10-2022
"I think one of the things about creativity is not to be afraid of saying the wrong thing " ― Sydney Brenner
Lecture summary Jamboard
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: 11-15-2022
"It is not enough to be in the right place at the right time. You should also have an open mind at the right time " ― Paul Erdos
Lecture summary Jamboard
Papers
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. DATA
Date: 11-17-2022
“An expert is a person who has made all the mistakes that can be made in a very narrow field.” ― Neils Bohr
Lecture summary Jamboard
Date: 11-22-2022
“If your life's work can be accomplished in your lifetime, you're not thinking big enough.” ―Wes Jackson
Lecture summary Jamboard
Papers
Pickard J, Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “Hypergraph Analysis Toolbox for Chromosome Conformation,” arXiv:2211.11166
Bapat, R. B. "The Laplacian matrix of a graph." Mathematics Student-India 65, no. 1 (1996): 214-223.
Book (Great book!): Chapter 1
Spielman, Daniel A. "Spectral and Algebraic Graph Theory." (2019)
Date: 11-29-2022
“It always seems impossible until it's done.” ― Nelson Mandela
TED Talk: The science of sync
Date: 12-01-2022
“The secret of getting ahead is getting started.” ― Mark Twain
Lecture summary Jamboard
Clustering and Visualization
Dimension Reduction of Data (Additional Information!)
Papers
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!)
Date: 12-06-2022
“Imagination will often carry us to worlds that never were. But without it we go nowhere.” ― Carl Sagan
Lecture summary Jamboard
Matrix Completion (Additional Material!)
Papers
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.
Cucker, Felipe, and Steve Smale. "Emergent behavior in flocks." IEEE Transactions on automatic control 52.5 (2007): 852-862.
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.
Date: 12-08-2022
“Believe you can and you're halfway there.” ― Theodore Roosevelt
The World’s Largest Matrix Computation (Beautiful article!)
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.
Smale, Steve. "Finding a horseshoe on the beaches of Rio." The Mathematical Intelligencer, 20.1 (1996): 39-44.