Peer-Timo Bremer  Ingrid Hotz 
Valerio Pascucci  Ronald Peikert
Editors
Topological Methods in Data  Analysis and Visualization III
Theory, Algorithms, and Applications

Contents
Part I Robust Topological Analysis
Robust Detection of Singularities in Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Harsh Bhatia, Attila Gyulassy, Hao Wang, Peer-Timo Bremer,
and Valerio Pascucci
Interpreting Feature Tracking Through the Lens of Robustness . . . . . . . . . . . 19
Primoz Skraba and Bei Wang
Simplification of Morse Decompositions Using Morse Set Mergers . . . . . . . . 39
Levente Sipeki and Andrzej Szymczak
Toward the Extraction of Saddle Periodic Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Jens Kasten, Jan Reininghaus, Wieland Reich,
and Gerik Scheuermann
Part II Efficient Computation of Topology
Computational Topology via Functional Programming:
A Baseline Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
David Duke and Hamish Carr
Distributed Contour Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Dmitriy Morozov and Gunther H. Weber
Clear and Compress: Computing Persistent Homology in Chunks . . . . . . . . 103
Ulrich Bauer, Michael Kerber, and Jan Reininghaus
Parallel Computation of Nearly Recurrent Components
of Piecewise Constant Vector Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Nicholas Brunhart-Lupo and Andrzej Szymczak
Part III Simplification, Approximation, and Distance
Measures
Notes on the Simplification of the Morse-Smale Complex. . . . . . . . . . . . . . . . . . . 135
David Günther, Jan Reininghaus, Hans-Peter Seidel,
and Tino Weinkauf
Measuring the Distance Between Merge Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Kenes Beketayev, Damir Yeliussizov, Dmitriy Morozov,
Gunther H. Weber, and Bernd Hamann
Topological Integrity for Dynamic Spline Models During
Visualization of Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Hugh P. Cassidy, Thomas J. Peters, Horea Ilies, and Kirk E. Jordan
Part IV Time-Dependent Analysis
A Comparison of Finite-Time and Finite-Size Lyapunov Exponents . . . . . . 187
Ronald Peikert, Armin Pobitzer, Filip Sadlo,
and Benjamin Schindler
Development of an Efficient and Flexible Pipeline
for Lagrangian Coherent Structure Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Siavash Ameli, Yogin Desai, and Shawn C. Shadden
Topological Features in Time-Dependent Advection-Diffusion Flow. . . . . . . 217
Filip Sadlo, Grzegorz K. Karch, and Thomas Ertl
Part V Applications
Definition, Extraction, and Validation of Pore Structures
in PorousMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Ulrike Homberg, Daniel Baum, Alexander Wiebel,
Steffen Prohaska, and Hans-Christian Hege
Visualization of Two-Dimensional Symmetric Positive Definite
Tensor Fields Using the Heat Kernel Signature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Valentin Zobel, Jan Reininghaus, and Ingrid Hotz
Topological Features in Glyph-Based Corotation Visualization . . . . . . . . . . . . 263
Sohail Shafii, Harald Obermaier, Bernd Hamann,
and Kenneth I. Joy
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277