**FALL 202****2**

## 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****:0****0****A****M -****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 ReferencePiazza (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**

**PROBLEM OF THE DAY**

**POD2**: Eigenvalues of A and L

**POD3**: **Centrality and Controllability:**** **data

**PROBLEM SETS**

**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**

**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**

**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**."*S**cience*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**

**Date: 09-06-2022**

Quote of the Day

"Simplicity is the ultimate sophistication"** **― Leonardo da Vinci

**Topics**

**Date: 09-08-2022**

**Date: 09-08-2022**

Quote of the Day

"Think mathematically, act computationally" ― Arthur Krener

**Topics**

Eigenvalues and Eigenvectors

**Date: 09-****13****-2022**

**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**

**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**

**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**

**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**

**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 TheoremOptimal 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**

**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**

**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.**(****E****xcellent Review!****)**

**Date: 10-06-2022**

**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**

**P****apers**

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**

**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

**(****E****xcellent 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**

**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

**(****E****xcellent Review!****)**

**Date: 10-****20****-2022**

**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**

**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 LiuRonquist 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: 10-2****7-****2022**

**Date: 10-2**

**7-**

**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**

**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**

**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 network**s."*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 LiuYuan, 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**

**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 network**s."*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**

**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**

**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**

**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**

**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:2211.11166Bapat, 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**

**Date: 11-29-2022**

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

TED Talk:

**The science of sync**

**Date: ****12****-01-2022**

**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: 12-0****6****-2022**

**Date: 12-0**

**6**

**-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**

**Date: 12-08-2022**

“Believe you can and you're halfway there.” ― Theodore Roosevelt

The World’s Largest Matrix Computation

**(Beautiful article!)**

**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.Smale, Steve. "Finding a horseshoe on the beaches of Rio."

*The Mathematical Intelligencer*,*20*.1 (1996): 39-44.