Cielo's research program in the Neurosciences has involved the analysis of a variety of data streams from real dynamical systems including brain enzyme and receptor fluctuations, single brain stem biogenic amine and reticular neuron discharge patterns, brain field electrical potentials, and EEG and MEG generated regional and global data series. Most recently, in collaboration with the NIMH Core MEG Laboratory, we are treating MEG recordings as delocalized electromagnetic flux fields using symmetric sensor difference series. Our data analytic approaches incorporate both stochastic, distributional statistical mechanical techniques and phase space oriented measures from the ergodic theory of (nonuniform hyperbolic) dynamical systems. Our current work also deals with the conservation of (multi-measured) brain entropy and loss of the entropies associated with pathological emergence of aberrant dynamical structure in brain disorders, such a schizophrenia and epilepsy.
Mandell, A.J., Russo, P.V., Knapp, S. Strange stability in hierarchically coupled neuropsychobiological systems In (Haken, H. ed.) Evolution of Chaos and Order in Physics, Chemistry and Biology Springer. NY 1982.
Mandell, A.J. From intermittency to transitivity in neuropsychobiological flows Am. J. Physiol. (Reg. Integ.Compar. Physiol.)245; R485-95, 1983.
Basar, E, Flohr, H., Haken, H., Mandell, A.J. Synergetics of Brain Springer-Verlag, Berlin, 1983.
Mandell, A.J., Knapp, S, Ehlers, C. Russo, P. The stability of constrained randomness: lithium prophylaxis at several neurobiological levels (Post, R., Ballenger, J.C. eds) Neurobiology of Mood Disorders, Williams and Wilkins, Baltimore, 1984 pp744-76.
Russo, P, Mandell, A.J. Metrics from nonlinear dynamics adapted for characterizing the behavior of nonequilibrium enzymatic rate functions Anal Biochem139: 91-9, 1984.
Goldberger, A., Findley, L.J., Blackburn, M.R., Mandell, A.J. Nonlinear dynamics in heart failure: implications of long-wavelength cardiopulmonary oscillations Am Heart J 107:612-615, 1984.
Mandell, A.J. Non-equilibrium behavior of some brain enzymes and receptor systems 24:237-274, 1984.
Goldberger, A., Bhargava, V, West, B.J. Mandell, A.J. On a mechanism of cardiac electrical stability. The fractal hypothesis Biophys. J. 48;525-28, 1985.
Mandell, A.J. Dynamical complexity and pathological order in the cardiac monitoring problem Physica D 27 235-42, 1987.
Paulus, M., Gass, S., Mandell, A.J. A realistic, minimal "middle layer" for neural networks Physica D 40: 135-55, 1989.
Paulus, M., Geyer, M.A., Gold, LH Mandell, A.J. Application of entropy measures from the ergodic theory of dynamical systems to animal behavior Proc. Natl. Acad. Sci 87 723-727, 1990.
Mandell, A.J. Shlesinger, M.F. Lost choices; parallelism and topological entropy decrements in neurobiological aging.( Krasner, S ed.) The Ubiquity of Chaos AAAS Press, Washington, DC, pp 10-22, 1990.
Selz, K.A., Mandell, A.J. Bernoulli partition equivalence of intermittent neuronal discharge patterns Int. J. Bifurcation and Chaos 1:717-722, 1991.
Mandell, A.J., Selz, K.A., Shlesinger, M.F. Some comments on the weaving of contemporaneous minds; Resonant neuronal quasiperiodicity, period adding and 0(2) symmetry in the EEG (Duke, D.W., Pritchard, W eds.) Chaos in the Brain World Scientific Press, Singapore pp 137-155, 1991.
Mandell, A.J. Selz, K.A. Period adding, hierarchical protein modes and electroencephalographically defined states of consciousness (Vohra, S, Spano, M., Shlesinger, M.F., Pecora, L. Ditto, W eds)In Proceedings of the First Experimental Conference on Chaos World Scientific Press, Singapore,1992.
Selz, K.A., Mandell, A.J. Critical coherence and characteristic times in brain stem neuronal discharge patterns.I (McKenna, T ed) Single Neuron Computation Neural Nets: Foundations to ApplicationsAcademic Press, NY pp 525-560. 1992.
Mandell, A.J., Selz, K.A. Brain stem neuronal noise and neocortical "resonance" J. Stat. Phys. 70: 355-373, 1993.
Selz, K.A., Mandell, A.J. Bursting intermittency and microwave popcorn: comments on the "reporting out" of neuron-like firing behavior. In (J.M. Garcia-Ruiz ed) Growth Patterns in Physical Sciences and Biology Plenum, NY.pp 363-372, 1993.
Selz, K.A. Mandell, A.J. Style as mechanism: from man to a map of the interval and back. In (Ditto, W, ed) Chaos in Medicine and Biology Proc. SPIE 2036: 174-182, 1993.
Selz, K.A., Mandell, A.J. A family of autocorrelation graph equivalence classes on symbolic dynamics as models of individual differences in human behavioral style. In (Vallacher, RR, Nowak, A eds) Dynamical Systems in Social Psychology Academic Press, San Diego, 169-195, 1994.
Selz, K.A., Mandell, A.J., Anderson, C., Smotherman, W., Teicher, M. Distribution of local Mandelbrot-Hurst exponents: motor activity in cocaine treated fetal rats and manic depressive patients Fractals 3: 893-904, 1995.
Mandell, A. J., Selz, K.A. Nonlinear dynamical patterns as personality theory for neurobiology and psychiatry Psychiatry 58: 371-90, 1995. Yang, W., Ding, M., Mandell, A.J., Ott, E. Preserving chaos; control strategies to preserve complex dynamics with potential relevance to biological disorders Phys. Rev. E 51: 102-110, 1995.
Smotherman, W.P., Selz, K.A., Mandell, A.J. Dynamical entropy is conserved during cocaine-induced changes in fetal rat motor patterns Psychoneuroendocrinology 21: 173-187, 1996.
Selz, K.A., Mandell, A.J. The power of style: differential operator scaling in the lexical compression of sequences generated by psychological, content free tasks. Complexity2: 50-55,1997.
DiMarzio, E.A, Mandell, A.J. Phase transition behavior of a linear macromolecule threading a membrane J. Chem. Phys. 14:5510-14, 1997.
Anderson, C., Mandell, A.J., Selz, K.A., Terry, L.M., Wong, C.H., Robinson, S.R. Robertson, S.S, Smotherman, W.P. The development of nuchal atonia associated with active (REM) sleep in fetal sheep: presence of recurrent fractal organization Brain Res 787: 351-7, 1998.
Kinkead, B, Selz, K.A., Owens, M.J., Mandell, A.J. Algorithmically designed peptides ameliorate behavioral defects in animal model of ADHD by an allosteric mechanism J Neurosci Methods 151: 68-81, 2006.
Mandell, A.J., Selz, K.A., Holroyd, T., Rutter, L., Coppola, R. Intermittent vorticity, power spectral scaling and dynamical measures on resting brain magnetic field fluctuations. In The Dynamic Brain. (M. Ding ed) 2009 pg 296-337.
Mandell, A.J., Selz, K.A., Aven, J., Holroyd, T., Coppola, R. Daydreaming, thought blocking and strudels in the taskless, resting Human Brain's Magnetic fields. American Institute of Physics Proceedings: International Conference on Applications of Nonlinear Dynamics II, 2011, In Press.