Fall 2013      MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology

Instructor:  Dr. Isabel K. Darcy
Email: idarcybiomath AT gmail.com

Live lectures are held MWF 17:30 - 18:20 GMT (11:30am - 12:20pm CST, Iowa time).

To join a live lecture, e-mail me (idarcybiomath AT gmail.com) for the URL.

The live lectures are recorded and posted on youtube. See links below or my youtube page. Powerpoint slides (also in pdf) are also available below.

     Preparatory videos introducing algebraic topology are available here.

     The links below include both recommended as well as supplementary reading for those who wish to go deeper into a subject. Recommended vs supplementary reading will be distinguished at a later date.

Tentative Schedule:

Week 1 Topological Data Analysis: Software Mapper
Aug 26 video, pptx, pdf Extracting insights from the shape of complex data using topology P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, G. Carlsson (2013)
Aug 28 video, pptx, pdf Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival M. Nicolau, A. J. Levine, G. Carlsson (2011)
Aug 30 video, pptx, pdf Download Mapper for Matlab
Python Mapper
Web tool: Progression Analysis of Disease - PAD (includes Mapper)
Ayasdi Iris, academic trial
Additional readings:
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition G. Singh , F. Memoli, G. Carlsson (2007)
Topology and data, G Carlsson (2009) (Mapper: p. 281 - 289)
How to Analyze DNA Microarray Data, Howard Hughes Medical Institute
Pearson Product-Moment Correlation
Week 2 Homology
Sept 2 Holiday: No class
Sept 4 video, pptx, pdf Section 2 in H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and simpliction, Discrete and Computational Geometry 28, 2002, 511-533.
Discriminative persistent homology of brain networks, Hyekyoung Lee; Chung, M.K.; Hyejin Kang; Bung-Nyun Kim; Dong Soo Lee, Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on , vol., no., pp.841,844, March 30 2011-April 2 2011.
Sept 6 video, pptx, pdf A. Zomorodian and G. Carlsson , Computing persistent homology, Discrete and Computational Geometry, 33 (2), pp. 247-274. Jan 2005
4.1 - 4.3 in Herbert Edelsbrunner and John L. Harer, Computational Topology, American Mathematical Society (December 8, 2009) google books preview
Ch 4 and sect 7.3.1 in Afra J. Zomorodian, Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics), Cambridge University Press (September 28, 2009) google books preview
Additional readings (for Sept 4)
Persistent Brain Network Homology From the Perspective of Dendrogram, Hyekyoung Lee; Hyejin Kang; Chung, M.K.; Bung-Nyun Kim; Dong Soo Lee, Medical Imaging, IEEE Transactions on , vol.31, no.12, pp.2267,2277, Dec. 2012.
Week 3
Sept 9 video, pptx, pdf Create your own homology
Ghrist's A Sequence of Homologies video (pdf). From IMA New Directions Short Course Applied Algebraic Topology June 15-26, 2009
Sept 11 video, pptx, pdf Persistent homology
Topology and data, G Carlsson (2009)
H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and simpliction, Discrete and Computational Geometry 28, 2002, 511-533.
Ch 7 in Afra J. Zomorodian, Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics), Cambridge University Press (September 28, 2009) google books preview
Sept 13 video, pptx, pdf Persistance homology (cont.)
Additional readings
Klein bottle
Topological analysis of population activity in visual cortex, Gurjeet Singh, Facundo Memoli, Tigran Ishkhanov, Guillermo Sapiro, Gunnar Carlsson, Dario L. Ringach, J Vis. 2008 Jun 30;8(8):11.1-18
Persistent Homology - a Survey. Herbert Edelsbrunner and John Harer, Contemporary Mathematics 453 (2008), 257 - 282
Week 4
Sept 16 video, pptx, pdf Persistent homology III
Javaplex,     Javaplex tutorial
Sept 18 video, pptx, pdf JavaPlex
NKI data, Array5yr.csv FIX LINK
Sept 20 video, pptx, pdf Persistent homology IV
On the Local Behavior of Spaces of Natural Images, Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, Afra Zomorodian, International Journal of Computer Vision January 2008, Volume 76, Issue 1, pp 1-12.
Additional readings
Mathworks Matlab Tutorials
Kaggle data analysis competitions
Data for MATLAB hackers (pre-2010)
Using the MNIST Dataset
Week 5
Sept 23 video, pptx, pdf Image data Application
Sept 25video, pptx, pdf Applicable Triangulations
Sept 27video, pptx, pdf Phom
Additional readings
Week 6
Sept 30video, pptx, pdf Multidimensional Persistence
Oct 2-4
IMA pre-workshop (Oct 2-4): An Introduction to Statistics and Probability for Topologists
Additional readings
Week 7
Oct 7 - 11 IMA workshop: Topological Data Analysis
Week 8
Oct 14 video, pdf Persistent Holes in the Universe
Oct 16 video, pptx, pdf Zigzag Persistence and installing Dionysus part I
Oct 18 video, Oct18_Dionysus.pptx, pdf Dionysus (and a brief intro to Perseus)
Additional readings
Week 9
Oct 21 video, pptx, pdf Persistent Cohomology and Circular Coordinates, Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson, Discrete & Computational Geometry June 2011, Volume 45, Issue 4, pp 737-759. ,
Oct 23 video, pptx, pdf
Oct 25 video, pptx, pdf
Additional readings
Week 10
Oct 28 - Nov 1 IMA workshop: Modern Applications of Homology and Cohomology
Week 11
Nov 4 video, pptx, pdf DNA, ethics, and stability
Nov 6 video, pptx, pdf Stable Persistence and time series
Comparison of Pattern Detection Methods in Microarray Time Series of the Segmentation Clock
Nov 8 video, pptx, pdf DNA topology
Additional readings
Week 12
Nov 11 alternate video, pdf Topological molecular symmetries
Nov 13 video, pptx, pdf DNA Topology II
Nov 15 video, pptx, pdf The Topology of Viral Evolution
Joseph Minhow Chan, Gunnar Carlsson, and Raúl Rabadán, Topology of viral evolution, PNAS 2013
IAS video October 2, 2013, Raúl Rabadán
Additional readings
Week 13
Nov 18 video, pptx, pdf Viral Evolution II and Crickets via cubical homology
Structure of the Afferent Terminals in Terminal Ganglion of a Cricket and Persistent Homology Jacob Brown, Tomas Gedeon
Nov 20 video, pptx, pdf Intro to RNA & Topological Landscapes for Visualization of Scalar-Valued Functions.
Generating and exploring a collection of topological landscapes for visualization of scalar-valued functions. by W. Harvey and Y. Wang, Comput. Graphics Forum (Special issue from EuroVis) 2010
Nov 22 video, pptx, pdf Topological methods for exploring low-density states in biomolecular folding pathways

An eQTL biological data visualization challenge and approaches from the visualization community

G. Bowman, X. Huang, Y. Yao, J. Sun, G. Carlsson, L. Guibas and V. Pande, “Structural insight into RNA Hairpin Folding Intermediates”, Journal of American Chemical Society (Communications). Jul 2008

Additional readings
Nov 25 - 29 Thanksgiving break
Week 14
Dec 2 video, pptx, pdf Curto, C., & Itskov, V. (2008). Cell groups reveal structure of stimulus space. PLoS Computational Biology, 4, e1000205.
Dec 4 video, pptx, pdf Dabaghian, Y., Memoli, F., Frank, L. M., & Carlsson, G. (2012). A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS Computational Biology, 8, e1002581.
Topology and Neuroscience: Data analysis, Yuri Dabaghian
Dec 6 video, pptx, pdf Journal of Theoretical Biology, Volume 335, 21 October 2013, Pages 130–146; Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks; Atsushi Mochizuki, Bernold Fiedler, Gen Kurosawa, Daisuke Saito
Additional readings
Week 15
Dec 9-13 IMA workshop: Topological Structures in Computational Biology

Spring Activities: While the official course will end in December, we can continue online seminars/discussion meetings.

My tentative locations: I will be at the IMA (staying at the Wales house) October 1 - November 2 as well as December 2 - December 14. I will be at a conference Nov 17 - 22 and will likely visit a colleague before and/or after this conference (but the class is online, so we will still have regular class meetings). All other times, I will be at UI.

Recommended books/online notes:

Recommended textbooks (note these textbooks are NOT required as we will focus on published papers). Online notes/textbooks: Classic texts: