Recent work by Konstantin Mischaikow


Computational Homology

Conley Index

Computational Homology

Computational Dynamics

Mathematical Biology

Computer Graphics

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I am interested in developing efficient algorithms for computing homology and homology maps. My original interest in the subject was motivated by my work in rigorous computer assisted proofs in dynamics. However, these tools are proving to be useful in the study of geometric properties of either numerically or experimentally generated data sets.

  • Book

    • T. Kaczynski, K. Mischaikow, and  M. Mrozek, Computational Homology Applied Mathematical Sciences 157 Springer-Verlag, 2004.
  • Theory

    • S. Harker, K. Mischaikow, M. Mrozek, and V. Nanda, Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps, (2012) preprint.
    • K. Mischaikow and V. Nanda, Reconstructing the Induced Map on Homology from Images of Random Samples, (2012) preprint.
    • K. Mischaikow and V. Nanda, Morse Theory for Filtrations and Efficient Computation of Persistent Homology, (2011) preprint.
    • S. Harker, K. Mischaikow, M. Mrozek, V. Nanda, H. Wagner, M. Juda, P. Dlotko, The Eciency of a Homology Algorithm based on Discrete Morse Theory and Coreductions, Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010, (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 1(2010), 41-47.
    • K. Mischaikow and T. Wanner, Topology-Guided Sampling of Nonhomogeneous Random Processes, Annals of Applied Probability, 20 1068-1097 (2010).
    • S. Day, W. Kalies, K. Mischaikow, and T. Wanner, Probabilistic and Numerical Validation of Homology Computations for Nodal Domains, Electronic Research Announcements, 13 (2007) 60-73.
    • K. Mischaikow and T. Wanner, Probabilistic validation of homology computations for nodal domains, Annals of Applied Probability 17 (2007) 980-1018.
    • K. Mischaikow, M. Mrozek and Pawel Pilarczyk, Graph Approach to the Computation of the Homology of Continuous Maps, Foundations of Computational Mathematics 5 (2005) 199-229.
    • W. Kalies, K. Mischaikow, and G. Watson, Cubical Approximation and Computation of Homology   (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
  • Applications - Condensed Matter

    • M. Kramar, A. Goullet, L. Kondic, K. Mischaikow, Persistence of Force Networks in Compressed Granular Media, (2012).
    • L. Kondic, A. Goullet, C. S. O'Hern, M. Kramar, K. Mischaikow, and R. P. Behringer, Topology of force networks in compressed granular media, EPL, 97 (5) 54001 (2012).
    • Huseyin Kurtuldu, Konstantin Mischaikow, and Michael F. Schatz, Measuring the departures from the Boussinesq approximation in Rayleigh-Benard convection experiments, J. Fluid Mechanics, (2011) 682: 543-557.
    • Huseyin Kurtuldu, Konstantin Mischaikow, and Michael F. Schatz, Extensive scaling from computational homology and Karhunen-Loeve decomposition analysis of Rayleigh-Benard convection experiments, Physical Review Letters, 107 034503 (2011).
    • James R.Wilson, Marcio Gameiro, Konstantin Mischaikow, William Kalies, Peter W. Voorhees, and Scott A. Barnett, Three-Dimensional Analysis of Solid Oxide Fuel Cell Ni-YSZ Anode Interconnectivity, Microscopy and Microanalysis 15 (2009) 71-77.
    • K. Krishan, H. Kurtuldu, M. F. Schatz, M. Gameiro, K. Mischaikow, and S. Madruga, Homological and symmetry breaking in Rayleigh-Benard convection: Experiments and simulations, Physics of Fluids, 19 117105 (2007).
    • M. Gameiro,  K. Mischaikow and T. Wanner, Evolution of Pattern Complexity in the Cahn-Hilliard Theory of Phase Separation, (A revised version will appear in Acta Materialia).
    • M. Gameiro, W. D. Kalies, and K. Mischaikow, Topological Characterization of Spatial Temporal Chaos, (The final version can be found in Phys. Rev. E.

Last Modified on July 21, 2012