Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review

Heightened Delta Power during Slow-Wave-Sleep in Patients with Rett Syndrome Associated with Poor Sleep Efficiency.

Sleep problems are commonly reported in Rett syndrome (RTT); however the electroencephalographic (EEG) biomarkers underlying sleep dysfunction are poorly understood. The aim of this study was to analyze the temporal evolution of quantitative EEG (qEEG) biomarkers in overnight EEGs recorded from girls (2-9 yrs. old) diagnosed with RTT using a non-traditional automated protocol. In this study, EEG spectral analysis identified high delta power cycles representing slow wave sleep (SWS) in 8-9h overnight sleep EEGs from the frontal, central and occipital leads (AP axis), comparing age-matched girls with and without RTT. Automated algorithms quantitated the area under the curve (AUC) within identified SWS cycles for each spectral frequency wave form. Both age-matched RTT and control EEGs showed similar increasing trends for recorded delta wave power in the EEG leads along the antero-posterior (AP). RTT EEGs had significantly fewer numbers of SWS sleep cycles; therefore, the overall time spent in SWS was also significantly lower in RTT. In contrast, the AUC for delta power within each SWS cycle was significantly heightened in RTT and remained heightened over consecutive cycles unlike control EEGs that showed an overnight decrement of delta power in consecutive cycles. Gamma wave power associated with these SWS cycles was similar to controls. However, the negative correlation of gamma power with age (r = -.59; p<0.01) detected in controls (2-5 yrs. vs. 6-9 yrs.) was lost in RTT. Poor % SWS (i.e., time spent in SWS overnight) in RTT was also driven by the younger age-group. Incidence of seizures in RTT was associated with significantly lower number of SWS cycles. Therefore, qEEG biomarkers of SWS in RTT evolved temporally and correlated significantly with clinical severity

Comparison of control EEGs’ and RTT EEGs’ delta power.

<p>(A) Representative 8.5 hour EEG traces were scored as high delta power (black) and low delta power (grey). Comparison of RTT EEG with control EEGs revealed significantly higher delta power as well as fewer cycles. (B) RTT EEGs had significantly greater delta power in all three lead positions (frontal, central, occipital). (C) Patients with RTT had no significant difference in gamma power but revealed a trend of greater power reading in all three lead positions compared to control group.</p

Clinical severity scores.

<p>Severity Score = SS; SZ = seizures; Mild = 0–7; Moderate = 8–14; Severe = 15–21.</p><p>Clinical severity scores.</p

SWS percent in Age Group.

<p>Patients with RTT have significantly lower SWS percent compared to control group. Significance is driven in the age group 2–5 year old. The significance in SWS percent is lost in 6–9 years ago. Comparison of SWS percent reveals an increasing tread in SWS percent for patients with RTT instead of the decreasing trend in the control group.</p

Age-dependent evolution.

<p>Because occipital lead displayed the greater difference between genotypes, occipital line graphs were used to display age related comparison. (A) Comparison of delta power revealed no significant difference between ages. Difference in delta power between Control EEGs and RTT EEGs seems to be driven by 2–5 year age group. (B) Gamma power in control group had a significant decrease from age group 2–5 year to 6–9 year group. The sharp decrease in gamma power is lost in patients with RTT as age increases.</p