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
(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
Graphviz
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.
|
| 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)
http://yann.lecun.com/exdb/mnist/
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)
Dionysus
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.