Gamma-hydroxybutyrate (GHB) is an endogenous GHB/GABAB receptor agonist, which has demonstrated potency in consolidating sleep and reducing excessive daytime sleepiness in narcolepsy. Little is known whether GHB's efficacy reflects the promotion of physiological sleep mechanisms and no study has investigated its sleep consolidating effects under low sleep pressure. GHB (50 mg/kg p.o.) and placebo were administered in 20 young male volunteers at 2:30 a.m., the time when GHB is typically given in narcolepsy, in a randomized, double-blinded, crossover manner. Drug effects on sleep architecture and electroencephalographic (EEG) sleep spectra were analyzed. In addition, current source density (CSD) analysis was employed to identify the effects of GHB on the brain electrical sources of neuronal oscillations. Moreover, lagged-phase synchronization (LPS) analysis was applied to quantify the functional connectivity among sleep-relevant brain regions. GHB prolonged slow-wave sleep (stage N3) at the cost of rapid eye movement (REM) sleep. Furthermore, it enhanced delta-theta (0.5-8 Hz) activity in NREM and REM sleep, while reducing activity in the spindle frequency range (13-15 Hz) in sleep stage N2. The increase in delta power predominated in medial prefrontal cortex, parahippocampal and fusiform gyri, and posterior cingulate cortex. Theta power was particularly increased in the prefrontal cortex and both temporal poles. Moreover, the brain areas that showed increased theta power after GHB also exhibited increased lagged-phase synchronization among each other. Our study in healthy men revealed distinct similarities between GHB-augmented sleep and physiologically augmented sleep as seen in recovery sleep after prolonged wakefulness. The promotion of the sleep neurophysiological mechanisms by GHB may thus provide a rationale for GHB-induced sleep and waking quality in neuropsychiatric disorders beyond narcolepsy.

Background Multisensor fitness trackers offer the ability to longitudinally estimate sleep quality in a home environment with the potential to outperform traditional actigraphy. To benefit from these new tools for objectively assessing sleep for clinical and research purposes, multisensor wearable devices require careful validation against the gold standard of sleep polysomnography (PSG). Naturalistic studies favor validation. Objective This study aims to validate the Fitbit Charge 2 against portable home PSG in a shift-work population composed of 59 first responder police officers and paramedics undergoing shift work. Methods A reliable comparison between the two measurements was ensured through the data-driven alignment of a PSG and Fitbit time series that was recorded at night. Epoch-by-epoch analyses and Bland-Altman plots were used to assess sensitivity, specificity, accuracy, the Matthews correlation coefficient, bias, and limits of agreement. Results Sleep onset and offset, total sleep time, and the durations of rapid eye movement (REM) sleep and non–rapid-eye movement sleep stages N1+N2 and N3 displayed unbiased estimates with nonnegligible limits of agreement. In contrast, the proprietary Fitbit algorithm overestimated REM sleep latency by 29.4 minutes and wakefulness after sleep onset (WASO) by 37.1 minutes. Epoch-by-epoch analyses indicated better specificity than sensitivity, with higher accuracies for WASO (0.82) and REM sleep (0.86) than those for N1+N2 (0.55) and N3 (0.78) sleep. Fitbit heart rate (HR) displayed a small underestimation of 0.9 beats per minute (bpm) and a limited capability to capture sudden HR changes because of the lower time resolution compared to that of PSG. The underestimation was smaller in N2, N3, and REM sleep (0.6-0.7 bpm) than in N1 sleep (1.2 bpm) and wakefulness (1.9 bpm), indicating a state-specific bias. Finally, Fitbit suggested a distribution of all sleep episode durations that was different from that derived from PSG and showed nonbiological discontinuities, indicating the potential limitations of the staging algorithm. Conclusions We conclude that by following careful data processing processes, the Fitbit Charge 2 can provide reasonably accurate mean values of sleep and HR estimates in shift workers under naturalistic conditions. Nevertheless, the generally wide limits of agreement hamper the precision of quantifying individual sleep episodes. The value of this consumer-grade multisensor wearable in terms of tackling clinical and research questions could be enhanced with open-source algorithms, raw data access, and the ability to blind participants to their own sleep data.

We study a high-dimensional regression model. Aim is to construct a confidence set for a given group of regression coefficients, treating all other regression coefficients as nuisance parameters. We apply a one-step procedure with the square-root Lasso as initial estimator and a multivariate square-root Lasso for constructing a surrogate Fisher information matrix. The multivariate square-root Lasso is based on nuclear norm loss with 1penalty. We show that this procedure leads to an asymptotically χ 2 -distributed pivot, with a remainder term depending only on the 1 -error of the initial estimator. We show that under 1 -sparsity conditions on the regression coefficients β 0 the square-root Lasso produces to a consistent estimator of the noise variance and we establish sharp oracle inequalities which show that the remainder term is small under further sparsity conditions on β 0 and compatibility conditions on the design. arXiv:1502.07131v2 [math.ST] 15 Sep 2015 Ω * (z j ).Thus, when Ω is the 1 -norm we have A 1,Ω = A 1 and Z ∞,Ω * = Z ∞ . We let the multivariate square-root Ω -sparse estimator bêThis estimator equals (6) when Ω is the 1 -norm.We let, as in (7), (8) and (10) but now with the newΓ J , the quantitiesT J ,T J and M be defined asTThe Ω -de-sparsified estimator of β 0 J is as in Definition 1but now withβ not necessarily the square root Lasso but a suitably chosen initial estimator and withΓ J the multivariate square-root Ω -sparse estimator. The normalized de-sparsified estimator is Mb J with normalization matrix M given above. We can then easily derive the following extension of Theorem 1. Proof of the main result in Subsection 3.2Proof of Theorem 1. We havewhere we invoked the KKT-conditions (9). We thus arrive atwhere rem = − √ nλẐ T J (β −J − β 0 −J )/σ 0 .The co-variance matrix of the first termT −1/2 J (X J − X −JΓJ ) T ε/ √ n in (15) is equal to

In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al. [18] and van de Geer and Stucky [17], then using an appropriate estimator for the precision matrix Θ. In order to estimate the precision matrix a corresponding structured matrix norm penalty has to be introduced. After normalization the result is an asymptotic pivot. The asymptotic behavior is studied and simulations are added to study the differences between the two schemes.Applying equation (3.3) to the optimal solution of equation (3.1) leads to the KKT conditions (in the case of X J − X J cB J nuc = 0):Here we denoteΣ J := (X J − X J cB J ) T (X J − X J cB J )/n (assumed to be nonsingular). Let us additionally define the |J| de-sparsified Ω structured estimator with the help of the following notations.The normalizing matrix can then be written asThis leads to the definition of the |J| de-sparsified Ω structured estimator. Defining a de-sparsified estimator in this way lets us deal with group-wise confidence sets.Definition 3. The |J| de-sparsified Ω structured estimator iŝWith these definitions we are now ready to describe the asymptotic behavior of the estimator (3.5) in the following Theorem.As we can see from Lemma 2 (4) we can upper bound part of the reminder term from Theorem 1 as g(β J c − β 0 J c ) ≤ g(β − β 0 ). By the definition of the gauge function g, from Lemma 2 (2) we get thatWe can simplify the termThat is why we can conclude thatwhere Z comes from the KKT conditions which fulfills:. The remainder term can be bounded with the generalized Cauchy Schwartz inequality in the ∞ -norm byThe last inequality comes directly from the weak decomposability of the allowed 20 set J:Now with the calculation in the proof of Lemma 3 and by dividing everything by σ 0 the proof is finished.

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