Publications

Note: In my research community, we tend to list authors of joint publications in alphabetical order, unless dictated by submission circumstances. All authors are expected to have equally substantial intellectual contribution to the paper. In particular, we kindly request not to apply the algorithm of This Cartoon to our lists ;-)

Book: T. Kaczynski, K. Mischaikow, et M. Mrozek, Computational Homology , Appl. Math. Sci. Vol. 157, Springer Verlag , NY 2004.

Recent research papers (Titles in blue are linked to PDF files of either author's preprint versions or open access publications)
37.
 N. Cavazza, M. Ethier, P. Frosini, T. Kaczynski, and Claudia Landi, Comparison of persistent homologies for vector functions: from continuous to discrete and back, preprint January 2012, arXiv:1201.3217v1 [cs.CG] (open access).
36.
 T. Kaczynski and M. Mrozek, Cubical cohomology ring: an algorithmic approach, preprint November 2011.
35.
 M. Allili, D. Corriveau, S. Derivière, M. Ethier, and T. Kaczynski, Detecting critical regions in multidimensional data sets, published version in Computers & Math. Appl. 61 (2) (2011), 499-512.
34.
 T. Kaczynski (presenter), P. Dłotko, and M. Mrozek, Computing The Cubical Cohomology Ring, in Proc. Computational Topology in Image Context, Chipiona 2010, Image-A 1(1) (2010), 137-142 (open access).
33.
 P. Dłotko, T. Kaczynski, M. Mrozek, and T. Wanner, Coreduction homology algorithm for regular CW-complexes, Discrete & Comput. Geom. 46 (2) (2011), 361-388 (open access).
32.
 M. Allili, M. Ethier, and T. Kaczynski, Critical region analysis of scalar fields in arbitrary dimensions, published version in Proc. SPIE-IS&T Electronic Imaging, Visualization and Data Analysis, 7530 (2010), 7530–7537.
31.
 S. Derivière, T. Kaczynski, and P.O. Vallerand, On the decomposition and local degree of multiple saddles, published version in Annales Sci. Math. Qué. 33 (1) (2009), 45-62.
30.
 T. Kaczynski, Multivalued maps as a tool in modeling and rigorous numerics, published version in Browder Festschrift, J. Fixed Point Theory and Appl., 4 (2) (2008), 151-176.
29.
 M. Allili, D. Corriveau, S. Derivière, T. Kaczynski, and A. Trahan, Discrete dynamical system framework for construction of connections between critical regions in lattice height data, published version in J. Mathematical  Imaging and Vision, 28 (2) (2007), 99-111.

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Papers popularizing mathematics

4.
 S. Derivière, A. Trahan, and T. Kaczynski, Comment compter les trous dans une meule de fromage suisse : ou, l'homologie pour les gourmands, in Actes du Congrès AMQ Sherbrooke 2006 (open access), (2008), 127-131.
3.
 T. Kaczynski, Vivre en dimension 4 and Voyager en dimension 4, Accromath (open access), 1 (2006), 30-35.
2.
 T. Kaczynski, Life and travel in 4D, Pi in the Sky (open access), Dec. 2001.
1.
 T. Kaczynski, The red violin of science, Pi in the Sky (open access), Dec. 2000.