Papers

  1. M. Kramar, L. Kovalcinova, L. Kondic and K. Mischaikow, Quantitative measure of memory loss in complex spatio-temporal systems, arXiv:1903.03562v1 (2019).
  2. S. Harker, M. Kramar, R. Levanger and K. Mischaikow,  A comparison framework for interleaved persistence modules, Journal of Applied and Computational Topology, 3 (2019).
  3. C. Colonnello and M. Kramar, Dynamics of silo deformation under granular dischargePhys. Rev. E, 98 (2018).
  4. J. Dijksman, L. Kovalcinova, J. Ren, R.P. Behringer, M. Kramar, K. Mischaikow and L. Kondic, Characterizing granular networks using topological metrics,  Phys. Rev. E, 97 (2018).
  5. L. Kondic, M. Kramar, L. Kovalcinova and  K. Mischaikow, Evolution of force networks in dense granular matter close to jamming, Powders & Grains (2017).
  6. J. Jaquette and M. Kramar, On 𝜖 approximations of persistence diagrams,  Mathematics of Computation, 86   (2017).
  7.  L. Kondic,  M. Kramar, L. A. Pugnaloni, C. M. Carlevaro and   K. Mischaikow, Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysisPhys. Rev. E, 93  (2016).
  8. L. A. Pugnaloni, C. M. Carlevaro,  M. Kramar, K. Mischaikow and L. Kondic, Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops Phys. Rev. E, 93  (2016).
  9. M. Kramar, R. Levanger, J. Tithof, B. Suri, M. Xu, M. Paul, M. F. Schatz and K. Mischaikow, Analysis of Kolmogorov flow and Rayleigh-Benard convection using persistent homology,  Phys. D,  334 (2016).
  10. D. Taylor, F. Klimm, H.A. Harrington, M. Kramar, K Mischaikow, M.A. Porter and P.J. Mucha, Topological data analysis of contagion maps for examining spreading processes on networks, Nature Communications, 6  (2015).
  11.  M. Kramar, A. Goullet,  L. Kondic and K. Mischaikow, Evolution of force networks in dense particulate media, Phys. Rev. E, 90  (2014).
  12. M. Gameiro, Y. Hiraoka, S. Izumi, M. Kramar, K. Mischaikow and V. Nanda, A topological measurement of protein compressibility, Japan Journal of Industrial and Applied Mathematics, 32 (2014).
  13. M. Kramar, A. Goullet, L. Kondic and K. Mischaikow, Quantifying force networks in particulate systems, Phys. D,  283  (2014).
  14. M. Kramar, A. Goullet, L. Kondic and K. Mischaikow, Persistence of force networks in compressed granular media, Phys. Rev. E, 87  (2013).
  15. 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  (2012).
  16. J. B. van den Berg, M. Kramar‡ and R. C. Vandervorst, Oscillatory solutions of fourth order conservative systems via the Conley index, Journal of Differential Equations, 252  (2012).
  17. J. B. van den Berg, M. Kramar  and R. C. Vandervorst,  The order of bifurcation points in fourth order conservative systems via braids, SIAM Journal on Applied Dynamical Systems, 10  (2011).
  18. M. Kramar,  Generic and stability properties of reciprocal and pseudogradient vector fields,  Math. Slovaca,  54 (2004).

In Preparation

  1. M. Kramar, J. Dijksman and L. Kondic, Topical Review on Characterizing Granular Networks Using Topological Metrics. 
  2. M. Kramar, M. Gameiro, H. Kokubu and H. Oka, Morse decompostion of the dynamics from observations.
  3. R. Levanger, T. Ishihara, P. Dlotko, M. Kramar and K. Mischaikow,  A new relation between enstrophy and higher order statistic in incompressible homogeneous isotropic turbulence.