Instructor: Prof. INDIKA Rajapakse

Teaching Assistant: STEPHEN Lindsly

Syllabus (PDF)

Reading List (link)

Timeline and Suggested Readings

Digital Library

ASSIGNMENTS

Problem Set 1

Problem Set 2: Solution

Problem Set 3: Solution

Problem Set 4

Problem Set 5: Solution

Problem Set 6: Helpful Code (MATLAB), Solution

Problem Set 7: Solution

Problem Set 8

Problem Set 9: Papers (You need to download to see highlighted sections), Solution

Final Problem Set: Video, MATLAB Data

PROBLEM OF THE DAY

POD1

POD2

POD3

POD4

NOTES, SLIDES, AND PAPERS

Date: 9-3-2020

• Matrices

• Graphs and Digraphs

Papers

1. Gordon, David E., et al. "A SARS-CoV-2 protein interaction map reveals targets for drug repurposing." Nature (2020): 1-13.

2. Hartwell, Leland H., et al. "From molecular to modular cell biology." Nature 402.6761 (1999): C47-C52.

Date: 9-8-2020

• Introduction

Date: 9-10-2020

• Models of Networks

• MATLAB Examples

Papers

1. Barabási, Albert-László. "Scale-free networks: a decade and beyond." Science 325.5939 (2009): 412-413.

2. Erdős, Paul, and Alfréd Rényi. "On the evolution of random graphs." Publ. Math. Inst. Hung. Acad. Sci 5.1 (1960): 17-60.

3. Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.

Date: 9-15-2020

• Creating an Adjacency Matrix

• Network Systems: Emergence (part 1)

Papers

1. Steven Strogatz (2014). "What Should We Be Worried About?: Real Scenarios That Keep Scientists Up at Night" (edited by John Brockman)

2. Rajapakse, Indika, and Stephen Smale. "Emergence of function from coordinated cells in a tissue." Proceedings of the National Academy of Sciences 114.7 (2017): 1462-1467.

Date: 9-17-2020

• Cellular Reprogramming

• Eigenvalues of Graphs

Papers

1. Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.

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: 9-22-2020

• Singular Value Decomposition (SVD)

• Professor SVD

Books

1. Moler CB. "Numerical computing with MATLAB." Society for Industrial and Applied Mathematics; 2004 Jan 1.

Date: 9-24-2020

• Hint for Problem Set 2 part C

• Cleve Moler's answers PDF

• Cleve Moler's MATLAB Files

• SVD

Papers

1. Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998).

2. Lieberman-Aiden, Erez, et al. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." Science 326.5950 (2009): 289-293.

3. Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.

Date: 9-29-2020

• SVD

• BIOINF_MATH_540_PS3

• Controllability

• Hi-C

• Network Data and Visualization

Books

2. Moler CB. "Numerical computing with MATLAB." Society for Industrial and Applied Mathematics; 2004 Jan 1.

Date: 10-1-2020

• BIOINF_MATH_540_PS3

• Controllability

• Self-organization

Papers

1. Rajapakse, Indika, and Mark Groudine. "On emerging nuclear order." Journal of Cell Biology 192.5 (2011): 711-721.

2. Ronquist, Scott, et al. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences 114.45 (2017): 11832-11837.

3. Tero, Atsushi, et al. "Rules for biologically inspired adaptive network design." Science 327.5964 (2010): 439-442.

Date: 10-6-2020

• BIOINF_MATH_540_PS3

• Controllability

• Agreement in a Network

• Network Centrality

• Inverse and Moore–Penrose inverse

Date: 10-8-2020

• Network Centrality

• Controllability 9-29

• Network Controllability 10-6

• Bifurcations and Genetic Networks

Date: 10-13-2020

• Network Centrality

• Controllability 9-29

• Bifurcations and Genetic Networks

Papers

1. Michael Elowitz and Stanislas Leibler. "A synthetic oscillatory network of transcriptional regulators." Nature, 403(6767): 335, 2000.

2. Timothy Gardner, Charles Cantor, and James Collins. "Construction of a genetic toggle switch in escherichiacoli." Nature, 403(6767): 339, 2000.

3. Egerstedt M. "Degrees of control." Nature. 2011 May;473(7346):158-9.

Date: 10-15-2020

• Beautiful Biology!

• Agreement in a Network

• Controllability 9-29

• Network Controllability 10-6

• Controllability Metrics for Networks: Controllability Gramian

Papers

1. Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.

COMMENTARY

Egerstedt M. "Degrees of control." Nature. 2011 May;473(7346):158-9.

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.

COMMENTARY

Abdallah, Chaouki T. "Mathematical controllability of genomic networks." Proceedings of the National Academy of Sciences 108.42 (2011): 17243-17244.

FUN readings.....

1. Buchanan, Mark. "The best is yet to come." Nature 447.7140 (2007): 39-39.

2. More papers: Connections in 2007

Date: 10-20-2020

• Network Controllability 10-6

• Controllability Metrics for Networks: Controllability Gramian

Papers

1. 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.

2. Alon, Uri. "Biological networks: the tinkerer as an engineer." Science 301.5641 (2003): 1866-1867.

3. Nurse, Paul, and Jacqueline Hayles. "The cell in an era of systems biology." Cell 144.6 (2011): 850-854.

Date: 10-22-2020

• Cell Cycle Network

• Controllability Metrics for Networks: Controllability Gramian

• Graph Distances

Papers

1. Rajapakse I, Perlman MD, Scalzo D, Kooperberg C, Groudine M, Kosak ST. "The emergence of lineage-specific chromosomal topologies from coordinate gene regulation." Proceedings of the National Academy of Sciences. 2009 Apr 21;106(16):6679-84.

COMMENTARY

Misteli T. "Self-organization in the genome." Proceedings of the National Academy of Sciences. 2009 Apr 28;106(17):6885-6.

2. Rajapakse I, Groudine M, Mesbahi M. "What can systems theory of networks offer to biology?" PLoS Comput Biol. 2012 Jun 28;8(6):e1002543.

Date: 10-27-2020

• Controllability Metrics for Networks: Controllability Gramian

• Graph Distances

• Large networks and graph limits (see chapter 8) : This is very TECHNICAL!

Papers

1. 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.

2. Donnat C, Holmes S. "Tracking network dynamics: A survey using graph distances." The Annals of Applied Statistics. 2018;12(2):971-1012.

Date: 10-29-2020

• Controllability Metrics for Networks: Controllability Gramian

• Graph Distances

Extra Readings

1. Hardy, Godfrey H. "Mendelian proportions in a mixed population." Science 28.706 (1908): 49-50.

2. Hardy, G. H. "A Mathematician’s Apology." University of Alberta Mathematical Sciences Society. (2005).

3. Rajapakse, Indika, Lindsey Muir, and Paul Martin. "Hardy’s “Small” Discovery Remembered." Notices of the AMS 55.3 (2008).

Date: 11-3-2020

• Network Visualization and Gephi Tutorial

  • Data for Tutorial: nodes.csv and edges.csv

• In-class Network Visualization Example (MATLAB)

  • Data Generated: nodes_cent.csv and edges_cent.csv

• Dynamic Mode Decomposition (DMD)

Papers

1. Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161.

Date: 11-5-2020

• Poincare Diagram: Stability diagram classifying Poincaré maps as stable or unstable according to their features

• Dynamic Mode Decomposition (DMD)

• Inverse and Moore–Penrose inverse

Papers

1. Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161.

Date: 11-10-2020

• Problem Set 6 - Helpful Code (MATLAB)

• Dynamic Mode Decomposition (DMD)

• Inverse and Moore–Penrose inverse

Book Chapter: Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems

• Dynamic Mode Decomposition: An Introduction

MATLAB Code: DMD Function and DMD Example

Papers

1. Lambert SA, Jolma A, Campitelli LF, Das PK, Yin Y, Albu M, Chen X, Taipale J, Hughes TR, Weirauch MT. "The human transcription factors." Cell. 2018 Feb 8;172(4):650-65.

2. Kunert-Graf JM, Eschenburg K, Galas D, Kutz JN, Rane S, Brunton BW. "Extracting reproducible time-resolved resting state networks using dynamic mode decomposition." Frontiers in computational neuroscience. 2019;13:75.

Date: 11-12-2020

• Graph Distances

• Network Motifs

• Additional Insights into Problem Set 6

Papers

1. Benson, Austin R., David F. Gleich, and Jure Leskovec. "Higher-order organization of complex networks." Science 353.6295 (2016): 163-166.

2. Chen C, Rajapakse I. "Tensor Entropy for Uniform Hypergraphs." IEEE Transactions on Network Science and Engineering. (2020).

Date: 11-17-2020

• Topic Timeline and Suggested Readings

• Problem Set 7

• Problem Set 8

• k-means clustering

• Spectral Clustering Example

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: 11-19-2020

• Tensors (slides)

• Tensors and Hypergraphs

• Network Neuroscience (slides)

Papers

1. Bassett, Danielle S., and Olaf Sporns. "Network neuroscience." Nature neuroscience 20.3 (2017): 353-364.

Date: 12-01-2020

• Entropy (from biology): Please read the yellow highlighted section

• Entropy

  • Part 1: Entropy and Hypergraphs

  • Part 2: Slides from ICML 2019

Papers

1. Chen, Pin-Yu, et al. "Fast incremental von neumann graph entropy computation: Theory, algorithm, and applications." International Conference on Machine Learning. PMLR, 2019.

Supplementary materials

• Dan Spielman's excellent lecture notes for his semester-long course on Spectral Graph Theory. The notes include a number of helpful plots.

Date: 12-03-2020

• Emergence: Alan Turing's paper "The chemical basis of morphogenesis " is a beautiful example of a network system which can guide us to talk about emergence. Please read these pages carefully and internalize the ideas! I will discuss tomorrow.

  • Application: Dynamics of Obesity

• Problem Set 9

  • Answer Key

  • Code

Papers

1. Rajapakse, Indika, and Stephen Smale. "Emergence of function from coordinated cells in a tissue." Proceedings of the National Academy of Sciences 114.7 (2017): 1462-1467.

2. Cucker F, Smale S. On the mathematics of emergence. Japanese Journal of Mathematics. 2007 Mar 1;2(1):197-227.

• Application: Wound Healing

3. Biological Controllability and Templating

Date: 12-08-2020

• Perron Frobenius Theorem

• Community Structure

• Controllability of Network Systems

• Matrix World : The Picture of All Matrices

Papers

1. Chen C, Surana A, Bloch A, Rajapakse I. Controllability of Hypergraphs. Submitted (2020).

2. Strogatz SH. "Exploring complex networks." nature. 2001 Mar;410(6825):268-76.

3. Hartwell, Leland H., et al. "From molecular to modular cell biology." Nature 402.6761 (1999): C47-C52.

Extra (don't read)

1. Aral, Sinan, and Dylan Walker. "Identifying influential and susceptible members of social networks." Science 337.6092 (2012): 337-341.

2. Shimada, Yutaka, et al. "Graph distance for complex networks." Scientific reports 6 (2016): 34944.

Digital Library