Epstein Secrets

ence not distance preserving ) representation of a difficult to characterize system of “geodesics on surfaces of negative curvature” (Hadamard, 1898; Morse, 1917; Morse and Hedlund, 1938). Geodesics here are the shortest lines in this curved, non-Euclidean space in which nearby lines spread apart and far

with active (REM) sleep in fetal sheep: presence of recurrent fractal organization. Brain Res. 787:351-357 Arnold, V.|. (1984) Catastrophe Theory. Springer-Verlag. N.Y. Arnold, V.|., Avez, A. (1968) Ergodic Problems in Classical Mechanics. Addison- Wesley. Redwood City, CA Babloyantz, A. (1986) Evidence of ch

. (1986) Evidence of chaotic dynamics of brain activity during the sleep cycle. In (ed. Mayer-Kress, G) Dimensions and Entropies in Chaotic Systems. Springer-Verlag, 1986 252 HOUSE_OVERSIGHT_013752 Babloyantz, A., Destexhe, A. (1986) Low dimensional chaos in an instance of epilepsy. Proc. Natl. Acad. Sci. 83:3

ence for synergetic dynamics in a mammalian pituitary cell perfusion system in (ed. E.Basar, H. Flohr, H. Haken, A.J. Mandell) Synergetics of Brain. Springer-Verlag. pp 155-162 Gupta, V., Suryanarayanan, S., Reddy, N.P. (1997) Fractal analysis of surface EMG signals from the biceps. Int J Med Inf 45:185-192 Guz

ns of probability), we notice that /og70(0.5) = 0.693147 and /og70(0.25) = 1.386294 and that 0.693147 + 0.693147 = 1.386294. The dot-dash choices of Morse code machines, the go, no-go gates of transistors, the open versus closed ion channel-mediated neuronal membrane discharge and the left, right spins

Press, Oxford, 1994 62 HOUSE_OVERSIGHT_013562 The Shape of Space, Jeffrey Weeks, Dekker, NY, 1985 The Topological Picture Book, George K. Francis, Springer-Verlag, NY 1988 Mathematical Models of Morphogenesis, Rene Thom, Wiley, NY 1983 Catastrophe Theory, Selected Papers, 1972-1977, Christopher Zeeman, Addison

spects of Neurological Disease, D. Frank Benson and Dietrich Blumer, Grune and Straton, N.Y. 1975. Mathematics —The Music of Reason, Jean Dieudonne, Springer-Verlag, N.Y. 1991 Mathematics for the Liberal Arts, F. Richman, C.L. Walker, R.J. Wisner and J.W Brewer, Simon and Schuster, N.Y. 1998 The Feynman Lecture

mical system, such as nerve membrane equations as above, or in the aggregate, the middle layer of a completely connected neural network, can encode, Morse code-like, messages (Paulus et al, 1989). Bifurcations in Biologically Relevant Dynamical Systems Bifurcations, “splitting into (two) branches,” ar

tion, time as recorded as the number of small pouring events may stretch. In aa comparable system, as elegantly described by Detrich Stauffer in his Springer-Verlag book on percolation, multiple hot spots in the woods can suddenly fuse into a forest fire. Isaiah said, “...glorify the Lord in the growing fires of