PRINCIPAL RESEARCH FINDINGS TO DATE: keyed to list of publications
  1. Mutual entrainment in a population of coupled non-linear oscillators (biological clocks), and unexpected distinctive modes (e.g., splitting and twinning) (1965-1968),: papers 5-8, 15, 38
  2. Topologically peculiar "strong" or "Type 0" mode of phase-resetting in circadian clocks, unexpected while data were traditionally interpreted in qualitatively different way (1967-1968): papers 9-10, 57
  3. Newly predicted implication of "strong" resetting, the phase singularity, confirmed in my laboratory using fruit-flies (Drosophila pseudoobscura) and using yeast cells (1968-1972): papers 11-14, 25, 35, 57, 91, 98,133 ... (then in other labs in several other species, now including human circadian clocks (1989) and heart muscle (1989-2000)
  4. Unexpected: Drosophila circadian clock photoreceptor is not rhodopsin and dark-adapts on a slow time-course of days and becomes sensitive enough to be arrested by prolonged very dim light: papers 18, 19, 29, 37
  5. Unexpected: Drosophila circadian clock is acutely sensitive to small temperature changes: paper 21
  6. Unexpected: 19-hour mutant melanogaster hardly differs from D. pseudoobscura: paper 44
  7. Isochrons and phaseless manifolds of arbitrary-dimensional limit-cycle dynamics (1968-1978): papers 12, 22, 57
  8. Spiral waves (1970) and cylindrically  vortex-rings (1972-1974) and their spontaneous evolution by shrinkage to extinction discovered in a laboratory excitable medium: papers 17, 20, 27-28, 30, 34
  9. Replacement of malonic acid substrate of chemical excitable media by 1-3 cyclohexane dione and other substrates to eliminate bubbling in 3d gels of silica, poly-acrylamide, agar (around 1975, unpublished)
  10. "Strong" resetting in neural and cardiac pacemakers, and prediction of the rhythm-extinguishing impulse subsequently found and clinically employed by others (1976-1979): papers 47, 58, 75, 77
  11. 3-dimensional phase singularities: topologically exotic organizing centers in excitable media (1978-1983), with symmetries other than cylindrical enabled by discovering a new physical intensive scalar, "twist": papers 27, 30, 34, 72-74, 77-78, 81-84
  12. Interpretation of the onset of cardiac fibrillation as reentry around a 2-dimensional phase singularity: a rotating arrhythmia (1979-1983), confirmed experimentally (by others) in dog (1986) and sheep (1990) myocardium: papers 57, 61, 64, 77, 94, 103
  13. Interpretation of ventricular fibrillation as an indispensably 3-dimensional topological problem in electrical activation patterns, the subject of much medical laboratory work by 1996: summary books 77, 91 and papers 61, 64, 67 94, 103, 109, 110, 112, 114, 118, 128, 136-8, 141, 142, 145, 147
  14. Discontinuity in human sleep duration vs circadian rhythm phase, discovered in the literature and theoretically interpreted (1980-1982): papers 62, 63, 65, 66, 69, 90
  15. Theoretical anticipation of: the "bull's-eye" structure of the vulnerable zone of mammalian heart to fibrillation, confirmed experimentally by others in 1986; and of the 3d 'singular filament' of vortex activity in fibrillation, confirmed experimentally by others in 1987: papers 77, 103, 112
  16. Dynamical properties and stability of the topologically-predicted organizing centers in excitable media; computational 'discovery' (in supercomputers) of topologically distinct stable organizing centers in diverse 3d excitable media (1985-1988), in particular, finding that "twist" enhances local spin frequency and that beyond an unforeseen threshold of twist, filaments spontaneously "sproing" helically: 87-89, 94, 97, 100, 102,103, 106,109, 110, 112-114, 119, 121, 127, 132, 135, 137, 139, 143-4, 146-7
  17. Computational discovery of orderly 'meander' in chemically excitable media, followed in the laboratory by discovery of similar patterns in the Belousov-Zhabotinsky medium (1988), then discovery of disorderly "hyper-meander" (1990): papers 107, 108, 126
  18. First laboratory measurement of laws of motion of the simplest 3d organizing center in a chemically excitable medium (1988); quantitative confirmation of anticipated shrinkage and first qualitative observation of anticipated 'drift' though without strict proof that gradients and boundaries played no role: papers 34, 111, 115
  19. An attempt to quantitatively account for major electrical thresholds of healthy cardiac muscle (1989): papers 118, 128, 138
  20. Prediction that myocardial fibrillation must have an "excitable gap" and will prove to have quantitatively the same intercellular electrical coupling as in sinus rhythm (contrary to all evidence at the time) (1989-1991): papers 118, 128 etc (experimentally confirmed 1992-1995)
  21. Demonstration, violating former dogma, of multiple alternative stable organizing centers in a 2d excitable medium (1990): papers 129-132
  22. Numerical experiments demonstrating the generic pattern of rotor behaviors in familiar 2d excitable media, for triage among contending mathematical theories (1991): papers 108, 126
  23. Computational discovery of disorderly meander reminiscent of the onset of fibrillation, in an electrophysiologically detailed ionic model of myocardium (1990-1991): papers 103, 122-124 (then in simpler models: 136, 141, 143-147)
  24. Experimental demonstration of predicted spatial patterns in the "invisible" chemical constitutents of chemical waves, by on-line numerical processing of video microscope observations; applicable (?) to Ca2+ waves in cerebral tissues or to electrical activations in myocardium (1992-4): papers 135, 137, 138
  25. Reconstruction in 1993 of the un-published 1964 Moe-Rheinboldt-Abildskov cellular automaton model of atrial fibrillation reveals that the published conclusion drawn from its operation, that complicated behavior emerges if and only if the substrate is suitably heterogeneous in its cellular parameters, is false (paper 141).
  26. Computational discovery that no current mathematical approximations quantitatively capture the dynamics of movement of vortex filaments with non-0 "twist" in generic excitable media, and that such media harbor topologically diverse persistent tangles of vortex rings (different from "stable" organzing center a above) (1992-1994): papers 144 and 146
  27. Experimentally testable interpretation of the overlooked paradox that ventricular fibrillation does not occur in 2-dimensional healthy heart muscle, but does in mathematical models (1994): papers 136, 141, 142, 145, 147
  28. Built optical tomographic microscope for 100-micron resolution of 3d chemical waves, and C/UNIX code for backprojection and 3d graphics display: paper 150 and 5 seminars (1994-97). This might be used to look for the first time for topologically exotic organizing centers as predicted in papers 113, 127, 137, 144, 146,  if a stable batch medium can be found (cyclohexane dione recipe?) A copy has been built at the Max-Planck lab in Magdeburg.
  29. Observation of gas-phase excitability in three-dimensional phosphorus vapor (1998, web site and book 158).
  30. Logical consequences (1996-98) of what is understood about electrical anisotropy in myocardium include that an intuitively natural determination of the electrical coupling coefficient in longitudinal direction in fact measures the order-of-magnitude smaller transverse coefficient (papers 148, 149) and that propagation is not perpendicular to the activation front so evaluation in that direction can produce an under-estimate (paper 149), and that activation fronts generally meet boundaries non-perpendicularly, contrary to most computer simulations (paper 149).
  31. That many ostensible contradictions between published experiments and theories about electrical propagation in myocardium can be resolved (1998) by using a value for "D" (diffusion of electrical potential) much nearer to 1 cm2/sec longitudinally (papers 149, 151).
  32. The Virtual Electrode Induced Phase Singularities of Efimov, Chang, Roth, Lindblom, and others in bidomain anisotropic media seem to arise not from those features per se so much as from the adjacency of positive and negative stimuli in a medium with only one local state variable diffusing (1999-2000). Bidomain anisotropy enables a monopolar point stimulus to evoke such patterned stimulation (web site, paper 156, book 158).
  33. My biggest solo discovery: 31 Dec 1999, a whole galaxy  :)   (unpublished, subsequently found to have a name already: NGC 2805)
  34. While engineering the CCD device for optical tomography,  I frequently discussed with Frank Witkowski (d. 2000) his engineering of one for myocardial fluorescence during fibrillation, and what might ultimately be seen when it works. At his Edmonton lab in April 1997 we found we could preserve normal electrophysiology by refraining from use of DAM in the dog heart (and not otherwise). After much elaborate image-processing on his Windows and my SGI unix machine, under these conditions we saw regular action potentials propagating periodically from 130-msec sources which I take to be the "rotors" predicted a decade ago. More intriguingly, after 10 minutes these movies show more complex geometry that I take to be surface eruptions of 3d from the anticipated "vortex filaments" (papers 153, 154, book 158)
  35. Biggest personal abrupt surprise in the lab, unforeseen in (my) concept: my Sikhote-Alin meteorite is a piece of an enormous single crystal of iron (March 2001, unpublished: turns out others had found bigger a century ago.)
  36. Computational behavior of persistent organizing centers in 3d presented some mysteries, including a stability unaccountable except in terms of non-local "slap-jump" mechanisms (2000-01) not included in present-day analytical theory (paper 157, book 158), and an incipient instability explored by Paul Sutcliffe's much longer computation (paper 160).

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