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Published:

  1. There are no chaotic mappings with residual scrambled sets,
    Bull. Austral. Math. Soc. 36 (1987),411-416
  2. Generic chaos can be large,
    Acta Math. Univ. Comenianae, LIV-LV-1988
  3. A counterexample to a Fedorenko statement,
    Acta Math. Univ. Comenianae,vol. LX, 1(1991), pp. 15-18.
  4. Stable and non-stable non-chaotic maps of the interval,
    Math. Slovaca 41, 1991, 4, 379-391.
  5. Shadowing property of continuous maps,
    Proceedings of the AMS, 115, 1(1992) ( with Milan Kuchta)
  6. Structure of the global attractor of cyclic feedback systems
    ( with Konstantin Mischaikow ) J. Dynam. Diff. Eq. 7, 141-190. (1995)
  7. Dynamics of cyclic feedback systems (with Konstantin Mischaikow)
    Resenhas IME-USP, Vol.1, No. 4, 495-515. (1994)
  8. A class of convergent neural networks (with Bernold Fiedler)
    Physica D 111 (1998), 288-294.
  9. Cyclic feedback systems
    Memoirs of AMS, vol. 134, No. 637 (1998)
  10. Continuity of resetting curves for FitzHugh-Nagumo equations on a circles
    (with Leon Glass)
    Fields Institute Communications, Vol.21, (1999).
  11. Structure and dynamics of artificial neural networks
    Fields Institute Communications, Vol.21, (1999).
  12. Upper-semicontinuity properties of the discretization of scalar differential delay equation (with Gwendolen Hines)
    JDE 151, (1999), 36-78.
  13. Additive neural networks and periodic patterns
    Neural Networks 12 (1999), 617-626.
    (only old version available here because of copy rights. Write me to get the final version of the paper)
  14. The Conley index for fast-slow systems I: One dimensional slow variable
    (with Kontantin Mischaikow, Hiroshi Kokubu, Hiroe Oka and Jim Reineck)
    J. Dynam. Diff. Eq. 11 (1999), 427-470.
  15. A Lyapunov function for tridiagonal competitive-cooperative systems
    (with Bernold Fiedler), SIAM J. Math. Anal. 30, No. 3, (1999), 469-478.
  16. The global dynamics of neural networks with infinite gain
    Physica D, 146, (2000), 200-212.
  17. Non-uniform quantization of neural spike sequences through an information distortion measure
    , Neurocomputing 38-40, 175-181 (2001).
    (by A. G. Dimitrov, J.P. Miller, Z. Aldworth, and T. Gedeon)
  18. Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing
    (with Hiroshi Kokubu, Konstantin Mischaikow and Hiroe Oka)
    J. of Dynamics and Diff. Eq., vol. 14, 1, (2002)
  19. Upper-semicontinuity properties of the discretization of scalar differential delay equation: An improvement (with G. Hines)
    Journal of Diff. Equations 179, 369-383 (2002),
  20. Analysis of neural coding using quantization with an information-based distortion measure , ( A. Dimitrov, J. Miller,T.G, Z. Aldworth and A. Parker)
    Network 14, pp. 151-176, (2003)
  21. Attractors in continuous-time switching networks
    Communications on Pure and Applied Analysis (CPAA) vol. 2, No. 2, 187-209, (2003).
  22. Attractor reconstruction from interspike intervals is incomplete (with Matt Holzer and Mark Pernarowski)
    Physica D, vol. 178/3-4, 149-172, (2003).
  23. Annealing and the rate distortion problem ( Al Parker, T.G and Alex Dimitrov)
    In S. Thrun, S. Becker and K. Obermayer, editors, Advances in Neural Information Processing Systems 15, 969-976, MIT Press, 2003.
  24. Information distortion and neural coding, (T.G, Al Parker and Alex Dimitrov), Canadian Applied Math. Q. vol 10, 1, 33-70, (2003).
  25. Derivation of natural stimulus feature set uing a data-diven model,(A. Dimitrov,T.G, B. Mumey, R. Snider, Z. Aldworth, A. Parker and J. P. Miller),
    ICCS 2003, P.M.A., Sloot et. al Eds., Springer-Verlag, Berlin, pp. 337-345.
  26. Finding neural codes using random projections, (B. Mumey, A. Sarkar, T.G, A. Dimitrov and J. Miller)
    Neurocomputing 58-60:19-25 (2004)
  27. Bifurcation structure of a class of S_N-invariant constrained optimization problems , (T.G.and A. Parker) J. Dynamics and Differential Equations, vol. 16, 3, (2004), 629-678.
  28. Phase locking in integrate-and-fire models with refractory periods and modulation , (T. G. and Matt Holzer), J. Math. Biology, Volume 49, Number 6, 577 - 603, (2004)
  29. Structure Theorems and the Dynamics of Nitrogen Catabolite Repression in Yeast (For supplemental material click here)
    (with E. Boczko, T. Cooper, K. Mischaikow, D. Murdock, S. Pratap and S Wells)
    Proceedings of National Academy of Science 2005 102: 5647-5652; published online before print as 10.1073/pnas.0501339102
  30. Z. Aldworth, J.P. Miller, T. Gedeon, G. Cummins and A. Dimitrov, Dejittered spike-conditioned stimulus waveforms yield improved estimates of neuronal feature sensitivity and Spike-Timing Precision of Sensory Interneurons
    The Journal of Neuroscience, June 1, (2005), 25(22):5323-5332; doi:10.1523/JNEUROSCI.0359-05.2005
  31. A. Dimitrov and T. Gedeon, Effects of stimulus transformations on estimates of sensory neuron functions , Journal of Computat. Neurosci. (2006) 20:265-283
  32. T. Gedeon, Hiroshi Kokubu, Kontantin Mischaikow and Hiroe Oka, The Conley index for fast-slow systems II: Multi dimensional slow variable, J. Differential Equations 225 (2006) 242-307.
  33. T. Gedeon and K. Mischaikow, Singular boundary value problems via the Conley index , Topological Methods in Nonlinear Analysis vol. 28., No.2 (2006)m 263-284.
  34. B. Cummins, T. Gedeon, I. Klapper and R. Cortez, Interaction between arthropod filiform hairs in a fluid enviroment,, Journal of Theoretical Biology, Volume 247, Issue 2, 21 July 2007, Pages 266-280
  35. M. Gameiro, T. Gedeon, W. Kallies, H. Kokubu, K. Mischaikow and H. Oka, Topological horseshoes of travelling waves for fast-slow predator-prey system , Journal of Dynamics and Diff. Eq., Volume 19, Number 3,September, 623-654. (2007) online first 10.1007/s10884-006-9013-6.
  36. T. Gedeon, Ch. Hayes and R. Swanson, Genericity of the fixed point set for the infinite population genetic algorithm , in Foundations of genetic algorithms, LCNS No. 4436, Springer-Verlag 2007
  37. T. Gedeon,C. Campion, A. Parker and Z. Aldworth, Annealing an information type cost function computes the normalized cut, Pattern Recognition 41 (2):592-606, February 2008
  38. E. Boczko, T. Gedeon and K. Mischaikow, Dynamics of a simple regulatory switch,Journal of Mathematical Biology 55: No. 5-6 (2007), DOI 10.1007/s00285-007-0102-x.
  39. S. Harker, C.R. Vogel and T. Gedeon, A multilinear optimization problem associated with correspondence maximization, Journal of Mathematical Imaging and Vision 29:49-62 (2007)
  40. T. Gedeon and E. Sontag, Oscillation in multi-stable monotone system with slowly varying positive feedback, J.Diff. Eq. Volume 239, Issue 2, 15 August 2007, Pages 273-295
  41. T. Gedeon and D. Arathorn, Convergence in map finding circuits, Journal of Math. Imaging Vis. 29, p. 235-248, (2007)
  42. K. Patterson,T. Gedeon, K. Mischaikow and Traldi, E., Why does the positive regulation in bacteriophage affect isomerization of the RNAP-DNA complex?, Proc. Appl. Math. Mech. 2007 7(1):1120101-1120102.
  43. T. Gedeon, E. Boczko and K. Mischaikow, Dynamics of transport mediated switch, Proc. Appl. Math. Mech. 2007 7(1):1120103-1120104.
  44. B. Cummins and T. Gedeon, A refined model of viscous coupling between filiform hairs in the cricket cercal system, Proceedings of IMECE2007, #41075, (2007).
  45. T. Gedeon, J.J. Heys, B.C. Knott and J. Mulder-Rosi, Modeling insect hair motion using the penalty immersed boundary method, Proceedings of IMECE2007, #41076, (2007).
  46. Gedeon, T., Mischaikow, K., Patterson, K., and Traldi, E., When Activators Repress and Repressors Activate: A Qualitative Analysis of the Shea-Ackers Model, The Eighth International Conference on Systems Biology (ICSB-2007) Proceedings, 2007.
  47. T. Gedeon, K. Mischaikow, K. Patterson and E. Traldi, When activators repress and repressors activate: a qualitative analysis of Shea-Ackers model, Bulletin of Mathematical Biology, 70:6 (2008), p. 1660-1683. doi 10.1007/s11538-008-9313-6 
  48. T. Gedeon, K. Mischaikow, K. Patterson and E. Traldi, Binding cooperativity in phage lambda is not sufficient to produce an effective switch, Biophysical J. 94(9), May 2008
  49. J.J. Heys, T. Gedeon, B.C. Knott and Y. Kim, Modeling arthropod hair motion using the penalty immersed boundary method, Journal of Biomechanics, Vol. 41, Issue 5, Pages 977-984, February 2008.
  50. T. Gedeon and G. Hines, Multi-valued characteristics and Morse decompositions, J. Differential Equations, vol. 247, 4, pp. 1013-1042 (2009)
  51. T. Gedeon, C. Bodelon and A. Kuenzi, Hantavirus transmission in sylvan and peridomestic environment, Bull. of Mathematical Biology 72:3, pp.541 (2010), DOI 10.1007/s11538-009-9460-4
  52. T. Gedeon, Oscillations in monotone systems with negative feedback, SIAM Dynamical Systems vol.9, No.1, (2010)
  53. Ch. Hayes and T. Gedeon, Hyperbolicity of the fixed point set for the simple genetic algorithm, Theoretical Computer Science 411 (2010), pp. 2368-2383.
  54. M. Campanelli and T. Gedeon, Somitogenesis clock-wave initiation requires differential decay and multiple binding sites for clock protein, a PLoS Comput. Biol. 6(4) e10000728 (2010)
  55. E. Boczko, T. Gedeon, C. Stowers and T. Young, ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast J. Biological Dynamics, Vol.4, No.4, July 2010, 328-345
  56. A. Dimitrov, A. Parker and T. Gedeon, Symmetry breaking in soft clustering decoding of neural codes , IEEE Transactions on Information Theory,Vol. 56, No. 2, Feb 2010, 901-927.
  57. P. De Leenheer, J. Dockery, T. Gedeon and S. Pilyugin, The chemostat with lateral gene transfer, Journal of Biological Dynamics, Vol. 4, (6), p.607-620 (2010)
  58. P. De Leenheer, J. Dockery, T. Gedeon and S. Pilyugin, Senescence and antibiotic resistance in an age-structured population model, J. of Math. Biology, 61(4) 475-499 (2010)
  59. A. Wright, T. Gedeon and N. Richter, On the movement of vertex points in the simple GA, FOGA 2011 (Foundations of genetic Algorithms), 193-208 (2011)
  60. Z. Aldworth, A. Dimitrov, G. Cummins, T. Gedeon and J.P. Miller, Temporal coding in a nervous system , PLoS Comput. Biol. 7(5) e1002041 (2011) 
  61. Z. Arai, M. Gameiro, T. Gedeon, H. Kokubu, K. Mischaikow and H. Oka, Graph-based topogical approximation of saddle-node bifurcation in maps, RIMS Kokyuroku Bessatsu, B 31 (2012), pp.225-241
  62. B. Cummins and T. Gedeon, Assessing the mechanical response of groups of arthropod filiform flow sensors, In Frontiers in Sensing, F. Barth, J. Humprhey and M. Srinavasan (eds.), Springer-Verlag 2012.
  63. J. P. Miller, S. Krueger, J. Heys and T. Gedeon, Quantitative characterization of the filiform mechanosensory hair array on the cricket cercus, PloS ONE 6(11) e27873. doi:10.1371/journal.pone.0027873 (2011) 
  64. T. Gedeon, A.E. Parker and A. G. Dimitrov, The mathematical structure of information bottleneck methods, Entropy 2012 14(3), 456-479; doi:10.3390/e14030456 
  65. J. Brown and T. Gedeon, Structure of the afferent terminals in terminal ganglion of a cricket and persistent homology, PLoS ONE 7(5): e37278. doi:10.1371/journal.pone.0037278, 2012 
  66. J. Berwald, T. Gedeon and J. Sheppard, Using machine learning to predict catastrophes in dynamical systems, J. Computational and Applied Mathematics, 236(9), March 2012, 2235-2245.
  67. P. Bokes and T. Gedeon, Delayed protein synthesis reduces the correlation between mRNA and protein fluctuations, Biophys. J. 103(3), August 8 2012, pp. 377-385 
  68. T. Gedeon, G. Cummins and J. Heys, Effect of model selection on prediction of periodic behavior in gene regulatory networks, Bull. Math. Biology 74(8), 2012, 
  69. J. Heys, P.K. Rajaraman, T. Gedeon and J.P. Miller, A model of filiform hair distribution on the cricket cercus, PLoS ONE 7(10): e46588, doi:10.1371/journal.pone.0046588 2012
    Submitted:
  70. L.Davis, J. Gedeon, T. Gedeon and J. Thorenson, Traffic flow model for bio-polymerization processes 
  71. K. Patterson, K. Mischaikow and T. Gedeon, A comprehensive biophysical model of transcriptional control in the lac operon
  72. K. Spendlove, J. Berwald and T. Gedeon, Predicting Critical Transitions in Dynamical Systems Using Active Learning
    In preparation:
  73. J. Berwald, T. Gedeon, K. Mischaikow,M. Costa and A. Goldberger, Modeling complexity of physiological time series in-silico 
  74. B. Cummins, T. Gedeon, G. Cummins and J.P. Miller, Predicted effects of viscosity coupling on filifirm hair motion in the cricket cercal system using an unsteady Stokes model
  75. K. Patterson, K. Mischaikow and T. Gedeon, Minimal biophysical model of lac operon