http:// www.ima.umn.edu /2008-2009/ND6.15-26.09/activities/ Carlsson -Gunnar/lecture14.pdf

1. MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology Oct 16, 2013: Zigzag Persistence and installing Dionysus part I. Fall 2013 course offered through the University of Iowa Division of Continuing Education Isabel K. Darcy, Department of Mathematics Applied Mathematical and Computational Sciences, University of Iowa http://www.math.uiowa.edu/~idarcy/AppliedTopology.html

2. http://www.ima.umn.edu/videos/?id=863 http://www.ima.umn.edu/2008-2009/ND6.15-26.09/activities/Carlsson-Gunnar/lecture14.pdf

3. http://geometrica.saclay.inria.fr/workshops/TGDA_07_2009/workshop_files/slides/deSilva_TGDA.pdfhttp://geometrica.saclay.inria.fr/workshops/TGDA_07_2009/workshop_files/slides/deSilva_TGDA.pdf

4. Lee-Mumford-Pedersen [LMP] study only high contrast patches. Collection: 4.5 x 106high contrast patches from a collection of images obtained by van Hateren and van der Schaaf Recall from Sept 20 lecture

7. M(100, 10) U Q where |Q| = 30 On the Local Behavior of Spaces of Natural Images, Gunnar Carlsson, TigranIshkhanov, Vin de Silva, AfraZomorodian, International Journal of Computer Vision 2008, pp 1-12.

9. The Theory of Multidimensional Persistence, Gunnar Carlsson, AfraZomorodian "Persistence and Point Clouds" Functoriality, diagrams, difficulties in classifying diagrams, multidimensional persistence, Gröbnerbases, Gunnar Carlsson http://www.ima.umn.edu/videos/?id=862

10. Computing Multidimensional Persistence, Gunnar Carlsson, GurjeetSingh, and AfraZomorodian

12. S(1, 1) Z2[x1, x2]/x2

17. Witness Complexes

18. Witness Complexes

19. Time varying data X[t0, t1] = data points existing at time t for t in [t0, t1] X[t1, t2] X[t2, t3] X[t0, t2] X[t1, t3] X[t2, t4]

21. Time varying data X[t0, t1] = data points existing at time t for t in [t0, t1] VR(X[t1, t2], ε) VR(X[t2, t3], ε) X[t1, t2] X[t2, t3] VR(X[t0, t2], ε) VR(X[t1, t3], ε) VR(X[t2, t4], ε) X[t0, t2] X[t1, t3] X[t2, t4]

22. Time varying data X[t0, t1] = data points existing at time t for t in [t0, t1] VR(X[t1, t2], ε) VR(X[t2, t3], ε) X[t1, t2] X[t2, t3] VR(X[t0, t2], ε) VR(X[t1, t3], ε) VR(X[t2, t4], ε) X[t0, t2] X[t1, t3] X[t2, t4] C0 C1  C2  C3 C4

23. C1 C3 H1 H3 C0 C2 C4 H0H2 H4

24. Persistent Homology: C0C1  C2 C3 C4 H0H1 H2 H3 H4 Zigzag Homology: C0 C1  C2  C3 C4 H0 H1 H2  H3 H4 Hki, p = Zki /(Bki+pZki) = L(i, i+p)( Hki) U

25. H0 H1 H2  H3 H4

26. H0 H1 H2  H3 H4 Z2 Z2  0 00

27. H0 H1 H2  H3 H4 Z2 Z2  0 00 0 Z2 Z2 Z2 0

28. H0 H1 H2  H3 H4 Z2 Z2  0 00 0 Z2 Z2 Z2 0 Z2Z2 × Z2 Z2 Z2 0 x

29. Gabriel (1972) For Dynkin-Coxeter graphs: H0 H1 H2  H3 H4 F F 0 00 0 FF F0 FF× FF F0 x

30. F F 0 00 0 FF F0 FF× FF F0 x I(0, 2) I(1, 4)

32. http://www.mrzv.org/software/dionysus/

33. http://www.mrzv.org/software/dionysus/get-build-install.html

34. http://mercurial.selenic.com/

35. idarcy$ hg clone http://hg.mrzv.org/Dionysus/ destination directory: Dionysus requesting all changes adding changesets adding manifests adding file changes added 278 changesets with 1396 changes to 388 files updating to branch default 82 files updated, 0 files merged, 0 files removed, 0 files unresolved idarcy$ cd Dionysus :Dionysus idarcy$ hg up tip 277 files updated, 0 files merged, 18 files removed, 0 files unresolved

36. idarcy$ man hg HG(1) Mercurial Manual HG(1) NAME hg - Mercurial source code management system SYNOPSIS hg command [option]... [argument]... DESCRIPTION The hg command provides a command line interface to the Mercurial system. COMMAND ELEMENTS files... indicates one or more filename or relative type q to quit

37. http://www.mrzv.org/software/dionysus/get-build-install.html

38. Need C-compiler first For example: http://www.macports.org/

39. http://www.macports.org/install.php

40. http://www.macports.org/install.php go to app store for free app

41. 2. From within xcode preferences (or download directly from web per next slide)

42. https://developer.apple.com/downloads/ Log in with Free apple ID

44. http://www.cmake.org/

46. Clicking on downloads should install Depending on your security settings, you may need to control click to install

47. http://www.boost.org/ See Oct 18 lecture for easier way to download and install Boost

48. http://www.mrzv.org/software/dionysus/python/zigzag-persistence.html#ZigzagPersistencehttp://www.mrzv.org/software/dionysus/python/zigzag-persistence.html#ZigzagPersistence See Oct 18 & 21 lecture.