Michael C. Mackey

Publications

Last update: December 28, 2008
 Please note: The copyrights to these publications are held by their publishers. The pdf files provided here may be used only for single copies for personal use, as though they were reprints provided by mail. They may not be reposted on other web sites or used for any other purpose without the express permission of the appropriate publishers.

  • Theses
    1. M.C. Mackey. "Excitable membrane models: Statistical mechanical analysis of current-electric field relationships", Ph.D. Dissertation, University of Washington, 1968.

  • Book Chapters
    1. J.W. Woodbury, S.H. White, M.C. Mackey, W.L. Hardy, & D. Chang. "Bioelectrochemistry", Chapter 9 in Electrochemistry (eds. H. Erying, W. Jost, and D. Henderson) Academic Press, New York (1970).
    2. M.C. Mackey. "Mathematical models of hematopoietic cell replication and control", in The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids (eds. H.G. Othmer, F.R. Adler, M.A. Lewis, and J.C. Dallon) Prentice Hall, pp. 149-178 (1997). pdf file

    3. M.C. Mackey. “Microscopic dynamics and the second law of thermodynamics”, in Time’s Arrows, Quantum Measurement and Superluminal Behavior (eds. C. Mugnai, A. Ranfagni, L.S. Schulman) Consiglio Nazionale Delle Ricerche (Roma), pp. 49-65 (2001).

    4. M.C. Mackey, C. Haurie & J. Bélair. "Cell replication and control", Chapter 9 in Nonlinear Dynamics in Physiology and Medicine (eds. A. Beuter, L. Glass, M.C. Mackey & M. Titcombe), Springer-Verlag, New York (2003).
    5. M. Santillan, E. S. Zeron, M. C. Mackey. "Systems biology of the tryptophan operon", Chapter 8 in Mathematical Biology Research Trends (ed: Lachlan B. Wilson), Nova Science Publishers, Inc., 2008, pp. 1-19. pdf file
  • Books
    1. M.C. Mackey. Ion Transport Through Biological Membranes: An Integrated Theoretical Approach, Springer-Verlag, Berlin, Heidelberg, New York, 1975.

    2. A. Lasota & M.C. Mackey. Probabilistic Properties of Deterministic Systems, Cambridge University Press, New York-Cambridge, 1985.

    3. L. Rensing, U. an der Heiden & M.C. Mackey (eds). Temporal Disorder in Human Oscillatory Systems, Springer-Verlag, New York, Berlin, Heidelberg, 1987.

    4. L. Glass & M.C. Mackey. From Clocks to Chaos: The Rhythms of Life. Princeton University Press, 1988.

    5. M.C. Mackey. Time's Arrow: The Origins of Thermodynamic Behaviour. Springer-Verlag, 1992.

    6. A. Lasota & M.C. Mackey. Chaos, Fractals and Noise: Stochastic Aspects of Dynamics. Springer-Verlag, 1994.
    7. A. Beuter, L. Glass, M. C. Mackey & M. Titcombe (eds). Nonlinear Dynamics in Physiology and Medicine. Springer Verlag, 2003.
    8. M.C. Mackey. Time’s Arrow: The Origins of Thermodynamic Behaviour. Dover Publications, 2003 (reprint of the Springer-Verlag 1992 edition).

  • Papers
    1. M.C. Mackey. "On the division of one polynomial by another", J. Pi Mu Epsilon (1960) 3, 114-117.

    2. M.C. Mackey. "Kinetic theory model for ion movement through biological membranes: I. Field dependent conductances in the presence of solution symmetry", Biophys. J. (1971) 11, 75-90. pdf file

    3. M.C. Mackey. "Kinetic theory model for ion movement through biological membranes: II. Inter-ionic selectivity", Biophys. J. (1971) 11, 91-97. pdf file

    4. M.C. Mackey & M. McNeel. "Kinetic theory model for ion movement through biological membranes: III. Steady state electrical properties with solution asymmetry", Biophys. J. (1971) 11, 664-674. pdf file

    5. M.C. Mackey & M. McNeel. "The independence principle: A reconsideration", Biophys. J. (1971) 11, 675-680. pdf file

    6. R.I. Birks, M.C. Mackey, & P.W. Weldon. "Organelle formation from pinocytotic elements in neurites of cultured sympathetic ganglia", J. Neurocytol. (1972) 1, 311-340. pdf file

    7. M.C. Mackey & M. McNeel. "Determinants of time - dependent membrane conductance: The non-role of classical ion-membrane molecule interactions", Biophys. J. (1973) 13, 733-746. pdf file

    8. M.C. Mackey & J.W. Combs. "Tissue growth and homeostasis: Consequences of control in synchronous cell populations", Growth (1974) 38, 477-494.

    9. M.C. Mackey. "Admittance properties of electrodiffusion membrane models", Math. Biosci. (1975) 25, 67-80. pdf file

    10. M.C. Mackey & L. Glass. "Oscillation and chaos in physiological control systems", Science (1977) 197, 287- 289. pdf file

    11. M.C. Mackey. "A unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis", Blood (1978) 51, 941-956. pdf file

    12. L. Glass & M.C. Mackey. "Pathological conditions resulting from instabilities in physiological control systems", Ann. N.Y. Acad. Sci. (1979) 316, 214-235.

    13. M.C. Mackey. "Dynamic haematological disorders of stem cell origin", in Biophysical and Biochemical Information Transfer in Recognition (eds. J.G. Vassileva-Popova, E.V. Jensen), Plenum Publishing Corp., New York. 1979, pp. 373-409.

    14. L. Glass & M.C. Mackey. "A simple model for phase locking of biological oscillators", J. Math. Biol. (1979) 7, 339-352. pdf file

    15. M.C. Mackey. "Periodic auto-immune hemolytic anemia: An induced dynamical disease", Bull. Math. Biol. (1979) 41, 829-834. pdf file

    16. A. Lasota & M.C. Mackey. "The extinction of slowly evolving dynamical systems", J. Math. Biol. (1980) 10, 333-345. pdf file

    17. L. Glass, C. Graves, G. Petrillo & M.C. Mackey. "Unstable dynamics of a periodically driven oscillator in the presence of noise", J. Theor. Biol. (1980) 86, 455-475. pdf file

    18. M.C. Mackey & P. Dörmer. "Enigmatic hemopoiesis", in Biomathematics and Cell Kinetics (ed. M. Rotenberg), Elsevier/North Holland, 1981, pp 87-103.

    19. U. an der Heiden, M.C. Mackey, & H.O. Walther. "Complex oscillations in a simple deterministic neuronal network", Lectures App. Math (1981) 19, 355-360.

    20. A. Lasota, M.C. Mackey & M. Wazewska-Czyzewska. "Minimizing therapeutically induced anemia", J. Math. Biol. (1981) 13, 149-158. pdf file

    21. M.C. Mackey. "Some models in hemopoiesis: Predictions and problems", in Biomathematics and Cell Kinetics (ed. M. Rotenberg), Elsevier/North Holland, 1981, pp. 23-38. pdf file

    22. M.C. Mackey & P. Dörmer. "Continuous maturation of proliferating erythroid precursors", Cell and Tissue Kinetics (1982) 15, 381-392.

    23. M.C. Mackey & U. an der Heiden. "Dynamic diseases and bifurcations in physiological control systems", Funk. Biol. Med. (1982) 1, 156-164. pdf file

    24. U. an der Heiden & M.C. Mackey. "The dynamics of production and destruction: Analytic insight into complex behaviour", J. Math. Biol. (1982) 16, 75-101. pdf file

    25. M.R. Guevara, L. Glass, M.C. Mackey & A. Shrier. "Chaos in neurobiology", IEEE Trans. on Systems, Man and Cybernetics (1983) SMC--13, 790-798.

    26. M.C. Mackey & U. an der Heiden. "The dynamics of recurrent inhibition", J. Math. Biol. (1984) 19, 211- 225. pdf file

    27. A. Lasota & M.C. Mackey. "Globally asymptotic properties of proliferating cell populations", J. Math. Biol. (1984) 19, 43-62. pdf file

    28. M.C. Mackey. "A deterministic cell cycle model with transition probability like behaviour", in Temporal Order (eds. L. Rensing and N.I. Jaeger), Springer- Verlag, Berlin-Heidelberg-New York, 1985, 315-320.

    29. M.C. Mackey, M. Santavy & P. Selepova. "A mitotic oscillator model for the cell cycle with a strange attractor", in Nonlinear Oscillations in Biology and Chemistry (ed. H. Othmer), Lecture Notes in Biomathematics, volume 66, 1986, pp. 34-45. Springer- Verlag, Berlin-Heidelberg-New York.

    30. A. Lasota & M.C. Mackey. "Noise and statistical periodicity", Physica (1987), 28D, 143-154. pdf file

    31. M.C. Mackey & J.G. Milton. "Dynamical diseases", Ann. N.Y. Acad. Sci. (1987), 504, 16-32.

    32. J. Bélair & M.C. Mackey. "A model for the regulation of mammalian platelet production", Ann. N.Y. Acad. Sci. (1987), 504, 280-282. pdf file

    33. U. an der Heiden & M.C. Mackey. "Mixed feedback: A paradigm for regular and irregular oscillations", in Temporal Disorder in Human Oscillatory Systems (eds. L. Rensing, U. an der Heiden, and M.C. Mackey), Springer- Verlag, New York, Berlin, Heidelberg 1987, pp 30-36.

    34. A. Lasota & M.C. Mackey. "Stochastic perturbation of dynamical systems: The weak convergence of measures", J. Math. Anal. and Applic. (1989), 138, 232-248. pdf file

    35. M.C. Mackey. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors", J. Econ. Theory (1989), 48, 497-509. pdf file

    36. J. Milton, A. Longtin, A. Beuter, M.C. Mackey & L. Glass. "Complex dynamics and bifurcations in neurology", J. Theor. Biol. (1989), 138, 129-147. pdf file

    37. J. Bélair & M.C. Mackey. "Consumer memory and price fluctuations in commodity markets: An integrodifferential model", J. Dynam. & Diff. Eqns. (1989), 1(3), 299-325. pdf file

    38. J. Milton & M.C. Mackey. "Periodic haematological diseases: Mystical entities or dynamical disorders?", J. Roy. Coll. Phys. (Lond) (1989), 23, 236-241. pdf file

    39. M.C. Mackey. "The dynamic origin of increasing entropy", Rev. Mod. Phys. (1989) 61, 981-1016. pdf file

    40. M.C. Mackey & J.G. Milton. "A deterministic approach to survival statistics", J. Math. Biol. (1990) 28, 33-48. pdf file

    41. M.C. Mackey & J. G. Milton. "Feedback, delays, and the origins of blood cell dynamics", Comm. on Theor. Biol. (1990) 1, 299-327.

    42. M.C. Mackey, A. Longtin, & A. Lasota. "Noise-induced global asymptotic stability", J. Stat. Phys. (1990), 60, 735-751. pdf file

    43. A. Longtin, J.G. Milton, J.E. Bos & M.C. Mackey. "Noise and critical behaviour of the pupil light reflex at oscillation onset'', Phys. Rev. A. (1990), 41, 6992-7005. pdf file

    44. J.G. Milton, U. an der Heiden, A. Longtin, & M.C. Mackey. "Complex dynamics and noise in simple neural networks with delayed mixed feedback", Biomed. Biochim. Acta (1990). 49, 697-707.

    45. U. an der Heiden, A. Longtin, M.C. Mackey, J.G. Milton, & R. Scholl. "Oscillatory modes in a nonlinear second order differential equation with delay", J. Dynam. & Diff. Eqns. (1990), 2, 423-449. pdf file

    46. A. Lasota, K. Loskot, & M.C. Mackey. "Stability properties of proliferatively coupled cell replication models", Acta Biotheor. (1991), 39, 1-14. pdf file

    47. N. Provatas & M.C. Mackey. "Noise induced asymptotic periodicity in a piecewise linear map." J. Stat. Phys. (1991), 63, 661-688. pdf file

    48. M.C. Mackey. "The second law of thermodynamics: Comments from ergodic theory", in Nonlinear Fields: Classical, Random, Semiclassical (eds. P. Garbaczewski & Z. Popowicz), Proceedings of the XXVII Karpacz Winter School in Theoretical Physics, World Scientific, 1991, pp. 384-415.

    49. N. Provatas & M.C. Mackey. "Asymptotic periodicity and banded chaos." Physica D (1991), 53, 295-318. pdf file

    50. A. Rey & M.C. Mackey. "Bifurcations and traveling waves in a delayed partial differential equation", Chaos (1992), 2, 231-244. pdf file

    51. J. Losson & M.C. Mackey. "A Hopf-like equation and perturbation theory for differential delay equations", J. Stat. Phys. (1992), 69, 1025-1046. pdf file

    52. A. Lasota, M.C. Mackey, & J. Tyrcha. "The statistical dynamics of recurrent biological events", J. Math. Biol. (1992), 30, 775-800. pdf file

    53. A. Rey & M.C. Mackey. "Multistability and boundary layer development in a transport equation with delayed arguments", Can. Appl. Math. Quar. (1993), 1, 1-21.

    54. M.C. Mackey & H. Schwegler. "Ensemble and trajectory statistics in a nonlinear partial differential equation", J. Stat. Phys. (1993), 70, 281-295. pdf file

    55. J. Losson, M.C. Mackey, & A. Longtin. "Solution multistability in first order nonlinear differential delay equations", Chaos (1993), 3, 167-176. pdf file

    56. H. Schwegler & M.C. Mackey. "A Simple Model for the Approach of Entropy to Thermodynamic Equilibrium", J. Phys. A: Math. Gen. (1994), 27, 1939-1951. pdf file

    57. J. Losson & M.C. Mackey. "Coupling induced statistical cycling in two diffusively coupled maps", Physica D (1994), 72, 324-342. pdf file

    58. M.C. Mackey & I. Nechayeva. "Noise and stability in differential delay equations", J. Dynam. & Diff. Eqns. (1994), 6, 395-426. pdf file

    59. M.O. Vlad, M.C. Mackey & J. Ross. "A generating functional approach to space and time dependent colored noise", Phys. Rev. E. (1994), 50, 798-821. pdf file

    60. J. Losson & M.C. Mackey. "Statistical cycling in coupled map lattices", Phys. Rev. E. (1994), 50, 843-856. pdf file

    61. R. Rudnicki & M.C. Mackey. "Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations", J. Math. Anal. Applic. (1994), 187, 548-566. pdf file

    62. H. Schwegler & M.C. Mackey. "Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant", J. Math. Biol. (1994) 32, 761-770. pdf file

    63. M.O. Vlad & M.C. Mackey. "Multiple logarithmic oscillations for statistical fractals on ultrametric spaces with application to recycle flows in hierarchial porous media", Physica Scripta (1994) 50, 615-623.

    64. M.C. Mackey & R. Rudnicki. "Global stability in a delayed partial differential equation describing cellular replication", J. Math. Biol. (1994), 33, 89-109. pdf file

    65. J. Losson, J.G. Milton, & M.C. Mackey. "Phase transitions in networks of chaotic elements with short and long range interactions", Physica D (1995) 81, 177-203. pdf file

    66. M.C. Mackey, & J.G. Milton. "Asymptotic stability of densities in coupled map lattices", Physica D (1995), 80, 1-17. pdf file

    67. A. Rey & M.C. Mackey. "Transitions and kinematics of reaction-convection fronts in a cell population model", Physica D. (1995), 80, 120-139. pdf file

    68. M.O. Vlad & M.C. Mackey. "Generating functional approach to multichannel parallel relaxation with application to the problem of direct energy transfer in fractal systems with dynamic disorder", J. Math. Phys. (1995), 36, 1834-1853. pdf file

    69. M.O. Vlad & M.C. Mackey. "Stochastic renormalization group approach to space dependent supercritical branched chain processes", Phys. Rev. A. (1995), 51, 3104-3119. pdf file

    70. M.O. Vlad & M.C. Mackey. "Jump clustering, Shlesinger-Huges stochastic renormalization, and interacting Levy flights", Phys. Rev. A. (1995), 51, 3120-3125. pdf file

    71. M.O. Vlad & M.C. Mackey. "Maximum information entropy approach to non-Markovian random jump processes with long memory: Application to surprisal analysis in molecular dynamics", Physica A (1995), 215, 339-360. pdf file

    72. J. Losson & M.C. Mackey. "Coupled map lattices as models of deterministic and stochastic differential delay equations", Phys. Rev. E. (1995), 52, 115-128. pdf file

    73. M.O. Vlad & M.C. Mackey. "Passage over a random energy barrier with dynamical disorder", Phys. Lett. A. (1995), 203, 292-299. pdf file

    74. J. Bélair, M.C. Mackey, & J.M. Mahaffy. "Age-structured and two delay models for erythropoiesis", Math. Biosci. (1995), 128, 317-346. pdf file

    75. P.K. Kamthan & M.C. Mackey. "Asymptotic behaviour of densities in random maps and its thermodynamic implications", Random and Computational Dynamics (1995), 3, 157-212.

    76. J. Losson & M.C. Mackey. "Evolution of probability densities in stochastic coupled map lattices", Phys. Rev. E. (1995), 52, 1403-1417. pdf file

    77. M.C. Mackey & I.G. Nechayeva. "Solution moment stability in stochastic differential delay equations", Phys. Rev. E. (1995) 52, 3366-3376. pdf file

    78. A. Rey & M.C. Mackey. "Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function", Physica D. (1995), 86, 373-395. pdf file

    79. M.O. Vlad, C. Lacoursiére & M.C. Mackey. "Long memory and scaling for multiplicative stochastic processes with application to the study of population oscillations", Phys. Lett. A. (1995), 208, 99-107. pdf file

    80. M.C. Mackey & J.G. Milton. "Lattices with spatially extended coupling and the statistical properties of neural populations", Proc. First Inter. Conf. Nonlin. Anal. (1996), 4, 3119-3124, de Gruyter, Berlin.

    81. R. Crabb, J. Losson, & M.C. Mackey. "Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems", Proc. First Inter. Conf. Nonlin. Anal. (1996), 4, 3125-3136, de Gruyter, Berlin.

    82. M.O. Vlad, J. Ross, & M.C. Mackey. "Nonequilibrium fluctuation-dissipation relations for independent random rate processes with dynamical disorder", J. Math. Phys. (1996), 37, 803-835.

    83. M.O. Vlad, M.C. Mackey, & B. Schönfisch. "Statistical fractals with cutoffs, Shlesinger--Hughes renormalization, and the onset of an epidemic", Phys. Rev. E. (1996), 53, 1382-1398. pdf file

    84. M.O. Vlad & M.C. Mackey. "Crossover from geometrical to stochastic fractal statistics for translationally invariant random distributions of independent particles in N-dimensional Euclidean space", Chaos, Solitons, & Fractals (1996), 7, 337-348. pdf file

    85. M.O. Vlad, R. Metzler, T.F. Nonnenmacher, & M.C. Mackey. "Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential", J. Math. Phys. (1996), 37, 2279-2306.

    86. M.O. Vlad, B. Schönfisch, & M.C. Mackey. "Fluctuation dissipation relations and universal behavior for relaxation processes in systems with static disorder and in the theory of mortality", Phys. Rev. E. (1996), 53, 4703-4710. pdf file

    87. M.O. Vlad, B. Schönfisch, & M.C. Mackey. "Fractal time, long-range correlations and stretched or compressed exponential survival statistics", Fractals (1996), 4, 59-72.

    88. J. Losson & M.C. Mackey. "Thermodynamic properties of coupled map lattices", in Stochastic and Spatial Structures of Dynamical Systems (eds. S.J. van Strien & S.M. Verduyn Lunel), North Holland, Amsterdam, 1996, pp 41-69.

    89. R. Crabb, M.C. Mackey, & A. Rey. "Propagating fronts, chaos and multistability in a cell replication model", Chaos (1996) 6, 477-492. pdf file

    90. M.O Vlad, B. Schönfisch, & M.C. Mackey. "Fluctuating Poissonian clocks, fractal random processes and dynamical Porter-Thomas distributions--Applications to evolutionary molecular biology, enhanced diffusion and dynamical relaxation", Physica Scripta (1996), 54, 581-593. pdf file

    91. M.O Vlad, B. Schönfisch, & M.C. Mackey. "Industrial replacement, communication networks and fractal time statistics", Phys. A (1996), 229, 295-311. pdf file

    92. M.O Vlad, B. Schönfisch, & M.C. Mackey. "Evolution towards ergodic behavior of stationary fractal random processes with memory--Application to the study of long-range correlations of nucleotide sequences in DNA", Phys. A (1996), 229, 312-342. pdf file

    93. M.O Vlad, B. Schönfisch, & M.C. Mackey. "Self-similar potentials in random media, fractal evolutionary landscapes and Kimura's theory of molecular evolution", Phys. A (1996), 229, 343-364. pdf file

    94. M.O. Vlad, J. Ross, & M.C. Mackey. "Jump statistics, sojourn times, fluctuation dynamics and ergodic behaviour for Markov processes in continuous time with a finite number of states", Physica A. (1997), 243, 319-339. pdf file

    95. M.O. Vlad, J. Ross, & M.C. Mackey. "Fluctuation dynamics, thermodynamic analogies and ergodic behaviour for nonequilibrium independent rate processes with dynamical disorder", Physica A. (1997), 243, 340-361. pdf file

    96. J.M. Mahaffy, J. Bélair, & M.C. Mackey. "Hematopoietic model with moving boundary condition and state dependent delay", J. Theor. Biol. (1998), 190, 135-146. pdf file

    97. T. Hearn, C. Haurie, & M.C. Mackey. "Cyclical neutropenia and the peripheral control of white blood cell production", J. Theor. Biol. (1998), 192, 167-181. pdf file

    98. C. Haurie, D.C. Dale, & M.C. Mackey. "Cyclical neutropenia and other periodic hematological disorders: A review of mechanisms and mathematical models", Blood (1998), 92, 2629-2640. pdf file

    99. A. Lasota & M.C. Mackey. "Statistical stability of strongly perturbed dynamical systems", Fields Institute Communications (1999), 21, 363-376.

    100. M.C. Mackey & R. Rudnicki. "A new criterion for the global stability of simultaneous cell replication and maturation processes", J. Math. Biol. (1999), 38,195-219. pdf file

    101. A. Lasota & M.C. Mackey. "Cell division and the stability of cellular replication", J. Math. Biol. (1999), 38, 241-261. pdf file

    102. C. Haurie, D.C. Dale, & M.C. Mackey. "Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF", Exper. Hematol. (1999), 27, 401-409. pdf file

    103. C. Haurie, R. Person, D.C. Dale, & M.C. Mackey. "Hematopoietic dynamics in grey collies", Exper. Hematol. (1999), 27, 1139-1148. pdf file

    104. P. Fortin & M.C. Mackey. "Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and aetiological implications", Brit. J. Haematol. (1999), 104, 336-345.pdf file

    105. J. Swinburne & M.C. Mackey. "Cyclical thrombocytopenia: Characterization by spectral analysis and a review", J. Theor. Med. (2000), 2, 81-91.

    106. C. Haurie, D.C. Dale, R. Rudnicki & M.C. Mackey. "Modeling of complex neutrophil dynamics in the grey collie", J. Theor. Biol. (2000), 204, 505-519. pdf file

    107. M. Santillan, J. Bélair, J.M. Mahaffy, & M.C. Mackey. "Regulation of platelet production: The normal response to perturbation and cyclical platelet disease", J. Theor. Biol. (2000), 206, 585-603. pdf file

    108. J.G. Milton & M.C. Mackey. "Neural ensemble coding and statistical periodicity: Speculations on the operation of the mind's eye", J. Physiol. (Paris) (2000), 94, 489-503. pdf file

    109. M. Santillan & M.C. Mackey. "Dynamic regulation of the tryptophan operon: A modelling study and comparison with data", Proc. Nat. Acad.Sci. (2001), 98, 1364-1369. pdf file and Supplement

    110. M. Santillan & M.C. Mackey. "Dynamic behaviour in mathematical models of the tryptophan operon", Chaos (2001), 11, 261-268. pdf file

    111. M.C. Mackey. "Cell kinetic status of hematopoietic stem cells", Cell Prolif. (2001), 34, 71-83. pdf file

    112. Louise Kold-Andersen & M.C. Mackey. "Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia", J. Theor. Biol. (2001), 209, 113-130. pdf file

    113. M.C. Mackey. "Microscopic dynamics and the second law of thermodynamics", published in "Time's Arrows, Quantum Measurement and Superluminal Behavior" (eds. C. Mugnai, A. Ranfagni, L.S. Schulman), (2001), Consiglio Nazionale Delle Ricerche (Roma), 49-65. pdf file

    114. S. Bernard, J. Bélair & M.C. Mackey. "Sufficient conditions for stability of linear differential equations with distributed delay ", Cont. and Disc. Dynam. Sys. (2001), 1, 233-256. pdf file

    115. C. Eurich, M.C. Mackey & H. Schwegler. "Recurrent inhibitory dynamics: The role of state dependent distributions of conduction delay times ", J. Theor. Biol. (2002), 216, 31-50. pdf file

    116. A. Fowler & M.C. Mackey. "Relaxation oscillations in a class of delay differential equations ", SIAM J. Appl. Math. (2002), 63, 299-323. pdf file

    117. M. C. Mackey, A.A.G. Aprikyan and D.C. Dale. " The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans " , Cell Prolif. (2003), 36, 27-34. pdf file

    118. C. Hauptmann, H. Touchette, M. C. Mackey. "Information capacity and pattern formation in a tent map network featuring statistical periodicity", Phys. Rev. E. (2003), 67, 026217. pdf file

    119. N. Yildirim & M.C. Mackey." Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data ", Biophy. J.(2003), 84, 2841-2851. pdf file

    120. S. Bernard, L. Pujo-Menjouet, and M. C. Mackey. " Analysis of cell kinetics using a cell division marker: Mathematical analysis of experimental data ", Biophy. J. (2003), 84, 3414-3424. pdf file

    121. C. Hauptmann & M.C. Mackey. "Stimulus dependent onset latency of the inhibitory recurrent activity", Biol. Cyber. (2003), 88, 457-459. pdf file
    122. S. Bernard, J. Bélair & M.C. Mackey. ''Oscillations in cyclical neutropenia: New evidence for origins based on mathematical modeling'', J. Theor. Biol. (2003), 223, 283-298. pdf file

    123. M. Santillan & M.C. Mackey. " Why the lysogenic state of l phage is so stable: a mathematical modelling approach", Biophy. J. (2004), 86, 75-84. pdf file
    124. M. Santillan & M.C. Mackey. "Influence of catabolic repression and inducer exclusion on the bistable behavior of the lac operon", Biophy. J. (2004), 86, 1282-1292. pdf file
    125. S. Bernard, J. Bélair & M.C. Mackey. ''Bifurcations in a white blood cell production model'', Comptes Rendus Biologiques (2004), 327, 201–210. pdf file
    126. L. Pujo-Menjouet & M. C. Mackey. "Contribution to the study of periodic chronic myelogenous leukemia", Comptes Rendus Biologiques (2004), 327, 235–244. pdf file

    127. M.C. Mackey, M. Santillan & N. Yildirim. "Modeling operon dynamics: The tryptophan and lactose operon as paradigms", Comptes Rendus Biologiques (2004), 327, 211–224. pdf file
    128. N.Yildirim, M. Santillan, D. Horike & M.C. Mackey. "Dynamics and bistability in a reduced model of the lactose operon", Chaos (2004), 14(2), 279-292. pdf file

    129. M.C. Mackey & M. Santillán. "Mathematics, biology and physics: interactions and interdependence", Notices of the American Mathematical Society (2005), 52(8), 832-840. pdf file

    130. L. Pujo-Menjouet, S. Bernard, M. C. Mackey. "Long period oscillations in a G0 model of hematopoietic stem cells", SIAM J. Appl. Dynam. Sys. (2005), 4(2), 312-332. pdf file

    131. C. Beck & M. C. Mackey. "Could dark energy be measured in the lab?", Physics Letters B (2005), 605, 295–300. pdf file

    132. M. Santillan & M.C. Mackey. "Dynamic behaviour of the B12 riboswitch", Phys. Biol. (2005), 2, 29–35. pdf file
    133. C. Colijn, M.C. Mackey. "A mathematical model of hematopoiesis: Periodic chronic myelogenous leukemia, part I, J. Theor. Biol. (2005), 237, 117–132 pdf file

    134. C. Colijn, M.C. Mackey. " A mathematical model of hematopoiesis: Cyclical neutropenia", part II, J. Theor. Biol. (2005), 237, 133–146. pdf file

    135. M. C. Mackey & M. Tyran-Kaminska. "Temporal behavior of the conditional and Gibbs’ entropies", J. Stat. Phys (2006), 124(6). pdf file

    136. C. Colijn, A.C. Fowler & M.C. Mackey. "High frequency spikes in long period blood cell oscillations", J. Math. Biol. (2006), 53(4), 499–519 pdf file
    137. C. Foley, S. Bernard, M.C. Mackey. "Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses", J. Theor. Biol. (2006), 238, 754-763. pdf file

    138. I. Drobnjak, A.C. Fowler & M.C. Mackey. "Oscillations in a maturation model of blood cell production", SIAM J. Appl. Math. (2006), 66(6), 2027–2048. pdf file

    139. M. C. Mackey & M. Tyran-Kaminska. "Noise and conditional entropy evolution", Physica A (2006) 365, 360-382. pdf file

    140. M.C. Mackey & M. Tyran-Kaminska."Deterministic brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system", Physics Reports (2006), 422, 167–222. pdf file
    141. S. Bernard, B. Cajavek, L. Pujo-Menjouet, M.C. Mackey, H. Herzel. "Modeling transcriptional feedback loops: The role of Gro/TLE1 in Hes1 oscillations", Phil. Trans. R. Soc. A (2006), 364, 1155-1170. pdf file
    142. M.C. Mackey, C. Ou, L. Pujo-Menjouet, & J. Wu. "Periodic oscillations of blood cell populations in chronic myelogenous leukemia", SIAM J. Math. Anal. (2006), 38(1), 166–187. pdf file

    143. C. Colijn, D.C. Dale, C. Foley & M.C. Mackey. “Observations on the pathophysiology and mechanisms for cyclic neutropenia”, Math. Model. Natur. Phenom. (2006), 1(2) , 45-69. pdf file

    144. J. Lei & M.C. Mackey. "Stochastic differential delay equation, moment stability, and appplication to hematopoietic stem cell regulation system", SIAM J. Appl. Math. (2007), 67(2), 387–407. pdf file

    145. M. Santillan, M.C. Mackey & E.S. Zeron. “Origin of bistability in the lac operon”, Biophy. J. (2007), 92, 3830–3842. pdf file
    146. C. Colijn, C. Foley & M.C. Mackey. “G-CSF treatment of canine cyclical neutropenia: A comprehensive mathematical model”, Exper. Hematol. (2007), 35, 898–907 pdf file
    147. C. Colijn & M.C. Mackey. "Bifurcation and bistability in a model of hematopoietic regulation", SIAM J. App. Dynam. Sys. (2007), 6(2), 378–394. pdf file

    148. C. Beck & M.C. Mackey. “Zeropoint fluctuations and dark energy in Josephson junctions”, Fluc. Noise. Lett. (2007), 7(2), C27-C35. pdf file

    149. C. Beck & M.C. Mackey. “Measurability of vacuum fluctuations and dark energy”, Physica A (2007), 379, 101–110. pdf file

    150. J.G. Rodriguez-Gonzalez, M. Santillan, A.C. Fowler & M.C. Mackey. "The segmentation clock in mice: Interaction between the Wnt and Notch signalling pathways", J. Theor. Biol. (2007), 248, 37-47. pdf file

    151. M. C. Mackey. "Adventures in Poland: Having fun and doing research with Andrzej Lasota", Matematyka Stosowana (2007), 8, 5-32. pdf file

    152. C. Foley & M.C. Mackey. "Dynamic hematological disease: A review", J. Math. Biol. (2008, in press), DOI: 10.1007/s00285-008-0165-3. pdf file

    153. M. Santillan, M. C. Mackey. "A proposed mechanism for the interaction of the segmentation clock and the determination front in somitogenesis", PLoS One (2008), 3(2). pdf file

    154. M.J. Piotrowska, H. Enderling, U. an der Heiden & M.C. Mackey. "Mathematical modeling of stem cells related to cancer", in Cancer and stem cells (eds. T. Dittmar & K. S. Zänker), Nova Science Publisher, Hauppauge, NY (2008, in press). pdf file

    155. M.C. Mackey & M. Tyran-Kaminska. "Dynamics and density evolution in piecewise deterministic growth processes", Annales Polonici Mathematici (2008, in press). pdf file

    156. C. Beck & M.C. Mackey. “Electromagnetic dark energy”, International Journal of Modern Physics D (2008), 17(1), 71–80. pdf file

    157. M.C. Mackey & M. Tyran-Kaminska. “Central limit theorems for non-invertible measure preserving maps”, Colloquium Mathematicum (2008), 110, 167–191. pdf file

    158. R. Apostu & M.C. Mackey. "Understanding Cyclical Thrombocytopenia: A mathematical modeling approach", J. Theor. Biol. (2008), 251, 297–316. pdf file

    159. M. Santillan & M.C. Mackey. "Quantitative approaches to the study of bistability in the lac operon of Escherichia coli", J. R. Soc. Interface (2008) 5, 29–39. pdf file

    160. M.C. Mackey & M. Tyran-Kaminska. “Central limit theorem behavior in the skew tent map”, Chaos, Solitons and Fractals (2008), 38, 789–805. pdf file

    161. C. Foley & M.C. Mackey. "Mathematical model for G-CSF administration after chemotherapy", J. Theor. Biol. (2008), DOI:10.1016/j.jtbi.2008.09.043 pdf file

    162. M. Santillan & M.C. Mackey. "Dynamic stability versus thermodynamic performance in a simple model for a Brownian motor", Phys. Rev. E(2008) 78, 061122. pdf file