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.
|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
|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||
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)
DNA MICROARRAY VIRTUAL LAB, youtube video
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.
|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 |
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
|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
|Sept 23 video, pptx, pdf||Image data Application|
|Sept 25video, pptx, pdf||Applicable Triangulations|
|Sept 27video, pptx, pdf||Phom|
|Sept 30video, pptx, pdf||Multidimensional Persistence|
IMA pre-workshop (Oct 2-4): An Introduction to Statistics and Probability for Topologists
|Oct 7 - 11||IMA workshop: Topological Data Analysis|
|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)|
|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|
|Oct 28 - Nov 1||IMA workshop: Modern Applications of Homology and Cohomology|
|Nov 4 video, pptx, pdf||DNA, ethics, and stability|
|Nov 6 video, pptx, pdf||Stable
Comparison of Pattern Detection Methods in Microarray Time Series of the Segmentation Clock
|Nov 8 video, pptx, pdf||DNA topology|
|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
|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
states in biomolecular folding pathways |
|Nov 25 - 29||Thanksgiving break|
|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|
|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.