Dennis W. Duke

Measuring Chaos in the Brain: A Tutorial Review of Nonlinear Dynamical Eeg Analysis

Nonlinear dynamical systems that are open, dissipative, and subject to strong non-equilibrium constraints are capable of self-organization, the spontaneous emergence of large scaJe, complex behavior (Nicolis & Prigogine, 1989). One variety of self-organization that can be produced by such systems is deterministic chaos (popularly, “chaos”). Although chaos was first described by Poincar6 in the 1800s, recent years have witnessed major developments in the physics of chaotic systems (Crutchfield, Farmer, Packard, & Shaw, 1986; Eubank & Farmer, 1990; Glass & Mackey, 1988; Gleick, 1987; Guevara, Glass, Mackey, & Shrier, 1983; Middleton, 1990; Schuster, 1988; Stewart, 1989; Tsonis & Tsonis, 1989; van Rossum & de Bie, 1991). Beginning in the mid 1980s, scientists began to apply chaos theory to the human electroencephalogram, or EEG (Albano et al., 1986; Babloyantz & Destexhe, 1986; Bab-loyantz, Salazar, & Nicolis, 1985; Dvořak & SIska, 1986; Dvořak, SIska, Wackermann, Hrudova, & Dostalek, 1986; Holzfuss & Mayer-...

Altered EEG Dynamical Responsivity Associated with Normal Aging and Probable Alzheimer's Disease

The Takens-Ellner method was employed to estimate the dimensional complexity of topographic EEG data (resting, eyes-closed and eyes-open) in 3 subject groups: normal young, normal elderly, and elderly

A fast algorithm for the Cyber 205 to simulate the 3D Ising model

We describe a computer program that performs the Metropolis algorithm for the 3D Ising model at a peak speed of 98 million spin updates per second on a 2-pipe CDC Cyber 205. This speed is achieved using the special vector capabilities of the Cyber 205 and multispin coding techniques.

No effect of cigarette smoking on electroencephalographic nonlinearity.

The Gaussian surrogate-date procedure was applied to the measurement of the effect of cigarette smoking on the dimensional complexity of normal, resting EEG. Evidence of significant nonlinearity in the EEG was obtained, replicating previous results. However, unlike EEG dimensional complexity, EEG nonlinearity (difference between original and surrogate data) was not affected by smoking. This indicates that, under resting conditions, smoking/nicotine may have a modulating effect on input from the reticular activating system, with such input having a global, linearizing effect on cortical dynamics. Nonlinear dynamics resulting from intracortical processes appear not to be affected.

Deep inelastic scattering and asymptotic freedom: A detailed analysis and confrontation

Abstract We have performed a detailed calculation of the moments of electron, muon and neutrino deep inelastic scattering data. We have analyzed the Q 2 dependence of the moments in the context of asymptotic freedom. Also, in an alternative approach, we have analyzed the Q 2 dependence of the data at fixed x . In general we find very good agreement between all the various data and the predictions of asymptotic freedom, at least for Q 2 >2 GeV 2 , with the possible exception of the flavor singlet electron moments at Q 2 >10 GeV 2 and n >3.

Flexible effects of quantified cigarette-smoke delivery on EEG dimensional complexity

A quantified smoke delivery system (QSDS) was used to experimentally control the administration of inhaled cigarette smoke to 28 male smokers. One puff (2 s, 35 cc) was taken every 30 s on a cigarette (nicotine yield 1.0 mg) until the char line reached 3 mm from the filter wrap. The smoke was inhaled for 5 s. Resting eyes-closed and eyes-open EEG was recorded from F3, F4, P3, and P4 before and after quantified smoke delivery (QSD). EEG dimensional complexity (DCx, a measure derived from chaos theory) was computed using the Takens-Ellner method. QSD appeared to have a ‘flexible’ effect on EEGDCx, primarily lowering it in subjects whose pre-smoking level was high, not affecting it in subjects whose pre-smoking level was intermediate, and tending to raise it in subjects whose pre-smoking level was low. This replicates previous results obtained with ad libitum smoking, suggesting the hypothesis that smoking may have an “optimizing” effect on the complexity of brain dynamics.

Analysis of Nucleon Structure Function Moments From Electron and Muon Data and Critical Tests of Asymptotic Freedom

Abstract We evaluate the Nachtmann moments of the nucleon structure functions from electron and muon scattering on proton and deuterium targets for 2 GeV 2 ⩽ Q 2 ⩽30 GeV 2 . The Q 2 dependence of the nonsinglet moments agrees with the predictions of asymptotic freedom only if higher-order effects are included. The Q 2 dependence of the singlet moments, however, differs from simple expectations based on asymptotic freedom alone.

Fractals and interpolating dimensions

Abstract We describe a computer study of Ising models on a generalization of Sierpinsky carpets of Hausdorf dimension between one and four. We measure the critical coupling and the exponent γ as a function of dimension. We also show how finite size scaling analyses can be done using fractals. Our results strongly suggest that fractals of the Sierpinsky carpet type can be used to interpolate between integer dimensions to study the critical behavior of statistical systems.

Momentum distributions for Jψ photoproduction

Abstract The contributions to heavy quark pair production from the subprocesses γg → QQg and γq → QQq have been calculated using perturbative quantum chromodynamics. The results have been used to obtain predictions for the longitudinal and transverse momentum distributions for J ψ photoproduction. The comparison with data from a recent muon scattering experiment is encouraging.

Analysis of the Farnese Globe

The constellations on the Farnese Atlas are based on the now-lost star catalogue of Hipparchus. This is proved by S1.1) the virtually perfect match with the constellation figures used by Hipparchus and only for these, S1.2) the perfect match with the date of Hipparchus (with the exclusion of all other known candidate sources), S1.3) the requirement that the source be a star catalogue such as that compiled by Hipparchus, and S1.4) the many points of consistency with what we know about ancient Greek astronomy.