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:

Links

References of Interest

NOTES, SLIDES, AND PAPERS

Date: 08-30-2022

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.

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

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: 09-06-2022

Quote of the Day

"Simplicity is the ultimate sophistication" ― Leonardo da Vinci

Lecture summary Jamboard

Topics

Date: 09-08-2022

Quote of the Day

"Think mathematically, act computationally" ― Arthur Krener

Lecture summary Jamboard

Topics

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

Lecture summary Jamboard

Topics

Papers

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


Date: 09-20-2022

Quote of the Day

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

Lecture summary Jamboard

Papers

  1. 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

Lecture summary Jamboard

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. 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

Lecture summary Jamboard

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


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

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

  1. Gleich DF. "PageRank beyond the Web." SIAM Review. 2015;57(3):321-63.

  2. 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

  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: 10-10-2022

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

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: 10-12-2022

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


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

  • K-Means Clustering

  • 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

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

  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: 10-27-2022

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

Lecture summary Jamboard

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: 11-01-2022

"The future belongs to those who believe in the beauty of their dreams " ― Eleanor Roosevelt

Lecture summary Jamboard

Papers

  1. 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.

  2. 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

Papers

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

  2. 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

  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.


Date: 11-08-2022

"Everything is practice" ― Pele

Lecture summary Jamboard

Papers

Please read!

  1. 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.

  2. 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.

  3. 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

  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/

  1. 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.

  2. 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

  1. 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.

  2. 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

  1. Pickard J, Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “Hypergraph Analysis Toolbox for Chromosome Conformation,” arXiv:2211.11166

  2. Bapat, R. B. "The Laplacian matrix of a graph." Mathematics Student-India 65, no. 1 (1996): 214-223.

Book (Great book!): Chapter 1

  1. Spielman, Daniel A. "Spectral and Algebraic Graph Theory." (2019)


Date: 11-29-2022


“It always seems impossible until it's done.” Nelson Mandela


Date: 12-01-2022


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

Lecture summary Jamboard


Papers


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

Papers

  1. 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.

  2. Cucker, Felipe, and Steve Smale. "Emergent behavior in flocks." IEEE Transactions on automatic control 52.5 (2007): 852-862.

  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.























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. Smale, Steve. "Finding a horseshoe on the beaches of Rio." The Mathematical Intelligencer, 20.1 (1996): 39-44.