A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

Covert Waking Brain Activity Reveals Instantaneous Sleep Depth

The neural correlates of the wake-sleep continuum remain incompletely understood, limiting the development of adaptive drug delivery systems for promoting sleep maintenance. The most useful measure for resolving early positions along this continuum is the alpha oscillation, an 8–13 Hz electroencephalographic rhythm prominent over posterior scalp locations. The brain activation signature of wakefulness, alpha expression discloses immediate levels of alertness and dissipates in concert with fading awareness as sleep begins. This brain activity pattern, however, is largely ignored once sleep begins. Here we show that the intensity of spectral power in the alpha band actually continues to disclose instantaneous responsiveness to noise—a measure of sleep depth—throughout a night of sleep. By systematically challenging sleep with realistic and varied acoustic disruption, we found that sleepers exhibited markedly greater sensitivity to sounds during moments of elevated alpha expression. This result demonstrates that alpha power is not a binary marker of the transition between sleep and wakefulness, but carries rich information about immediate sleep stability. Further, it shows that an empirical and ecologically relevant form of sleep depth is revealed in real-time by EEG spectral content in the alpha band, a measure that affords prediction on the order of minutes. This signal, which transcends the boundaries of classical sleep stages, could potentially be used for real-time feedback to novel, adaptive drug delivery systems for inducing sleep

Sleep in the Human Hippocampus: A Stereo-EEG Study

Background. There is compelling evidence indicating that sleep plays a crucial role in the consolidation of new declarative, hippocampus-dependent memories. Given the increasing interest in the spatiotemporal relationships between cortical and hippocampal activity during sleep, this study aimed to shed more light on the basic features of human sleep in the hippocampus. Methodology/Principal Findings. We recorded intracerebral stereo-EEG directly from the hippocampus and neocortical sites in five epileptic patients undergoing presurgical evaluations. The time course of classical EEG frequency bands during the first three NREM-REM sleep cycles of the night was evaluated. We found that delta power shows, also in the hippocampus, the progressive decrease across sleep cycles, indicating that a form of homeostatic regulation of delta activity is present also in this subcortical structure. Hippocampal sleep was also characterized by: i) a lower relative power in the slow oscillation range during NREM sleep compared to the scalp EEG; ii) a flattening of the time course of the very low frequencies (up to 1 Hz) across sleep cycles, with relatively high levels of power even during REM sleep; iii) a decrease of power in the beta band during REM sleep, at odds with the typical increase of power in the cortical recordings. Conclusions/Significance. Our data imply that cortical slow oscillation is attenuated in the hippocampal structures during NREM sleep. The most peculiar feature of hippocampal sleep is the increased synchronization of the EEG rhythms during REM periods. This state of resonanc

The thalamic mGluR1-PLC??4 pathway is critical in sleep architecture

The transition from wakefulness to a nonrapid eye movement (NREM) sleep state at the onset of sleep involves a transition from low-voltage, high-frequency irregular electroencephalography (EEG) waveforms to large-amplitude, low-frequency EEG waveforms accompanying synchronized oscillatory activity in the thalamocortical circuit. The thalamocortical circuit consists of reciprocal connections between the thalamus and cortex. The cortex sends strong excitatory feedback to the thalamus, however the function of which is unclear. In this study, we investigated the role of the thalamic metabotropic glutamate receptor 1 (mGluR1)-phospholipase C ??4 (PLC??4) pathway in sleep control in PLC??4-deficient (PLC??4-/-) mice. The thalamic mGluR1-PLC??4 pathway contains synapses that receive corticothalamic inputs. In PLC??4-/- mice, the transition from wakefulness to the NREM sleep state was stimulated, and the NREM sleep state was stabilized, which resulted in increased NREM sleep. The power density of delta (??) waves increased in parallel with the increased NREM sleep. These sleep phenotypes in PLC??4-/- mice were consistent in TC-restricted PLC??4 knockdown mice. Moreover, in vitro intrathalamic oscillations were greatly enhanced in the PLC??4-/- slices. The results of our study showed that thalamic mGluR1-PLC??4 pathway was critical in controlling sleep architecture.ope

Adjunctive dexamethasone for the treatment of HIV-uninfected adults with tuberculous meningitis stratified by Leukotriene A4 hydrolase genotype (LAST ACT): Study protocol for a randomised double blind placebo controlled non-inferiority trial [version 1; referees: 2 approved]

Background: Tuberculosis kills more people than any other bacterial infection worldwide. In tuberculous meningitis (TBM), a common functional promoter variant (C/T transition) in the gene encoding leukotriene A4 hydrolase (LTA4H), predicts pre-treatment inflammatory phenotype and response to dexamethasone in HIV-uninfected individuals. The primary aim of this study is to determine whether LTA4H genotype determines benefit or harm from adjunctive dexamethasone in HIV-uninfected Vietnamese adults with TBM. The secondary aim is to investigate alternative management strategies in individuals who develop drug induced liver injury (DILI) that will enable the safe continuation of rifampicin and isoniazid therapy.  Methods: We will perform a parallel group, randomised (1:1), double blind, placebo-controlled,  multi-centre Phase III non-inferiority trial, comparing dexamethasone versus placebo for 6-8 weeks in addition to standard anti-tuberculosis treatment in HIV-uninfected patients with TBM stratified by LTA4H genotype. The primary endpoint will be death or new neurological event. The trial will enrol approximately 720 HIV-uninfected adults with a clinical diagnosis of TBM, from two hospitals in Ho Chi Minh City, Vietnam. 640 participants with CC or CT- LTA4H genotype will be randomised to either dexamethasone or placebo, and the remaining TT- genotype participants will be treated with standard-of-care dexamethasone. We will also perform a randomised comparison of three management strategies for anti-tuberculosis DILI. An identical ancillary study will also be perfomed in the linked randomised controlled trial of dexamethasone in HIV-infected adults with TBM (ACT HIV).  Discussion: Previous data have shown that LTA4H genotype may be a critical determinant of inflammation and consequently of adjunctive anti-inflammatory treatment response in TBM. We will stratify dexamethasone therapy according to LTA4H genotype in HIV-uninfected adults, which may indicate a role for targeted anti-inflammatory therapy according to variation in LTA4H C/T transition. A comparison of DILI management strategies may allow the safe continuation of rifampicin and isoniazid

Human Gamma Oscillations during Slow Wave Sleep

Neocortical local field potentials have shown that gamma oscillations occur spontaneously during slow-wave sleep (SWS). At the macroscopic EEG level in the human brain, no evidences were reported so far. In this study, by using simultaneous scalp and intracranial EEG recordings in 20 epileptic subjects, we examined gamma oscillations in cerebral cortex during SWS. We report that gamma oscillations in low (30–50 Hz) and high (60–120 Hz) frequency bands recurrently emerged in all investigated regions and their amplitudes coincided with specific phases of the cortical slow wave. In most of the cases, multiple oscillatory bursts in different frequency bands from 30 to 120 Hz were correlated with positive peaks of scalp slow waves (“IN-phase” pattern), confirming previous animal findings. In addition, we report another gamma pattern that appears preferentially during the negative phase of the slow wave (“ANTI-phase” pattern). This new pattern presented dominant peaks in the high gamma range and was preferentially expressed in the temporal cortex. Finally, we found that the spatial coherence between cortical sites exhibiting gamma activities was local and fell off quickly when computed between distant sites. Overall, these results provide the first human evidences that gamma oscillations can be observed in macroscopic EEG recordings during sleep. They support the concept that these high-frequency activities might be associated with phasic increases of neural activity during slow oscillations. Such patterned activity in the sleeping brain could play a role in off-line processing of cortical networks

Statistical Analysis of Sleep Spindle Occurrences

Spindles - a hallmark of stage II sleep - are a transient oscillatory phenomenon in the EEG believed to reflect thalamocortical activity contributing to unresponsiveness during sleep. Currently spindles are often classified into two classes: fast spindles, with a frequency of around 14 Hz, occurring in the centro-parietal region; and slow spindles, with a frequency of around 12 Hz, prevalent in the frontal region. Here we aim to establish whether the spindle generation process also exhibits spatial heterogeneity. Electroencephalographic recordings from 20 subjects were automatically scanned to detect spindles and the time occurrences of spindles were used for statistical analysis. Gamma distribution parameters were fit to each inter-spindle interval distribution, and a modified Wald-Wolfowitz lag-1 correlation test was applied. Results indicate that not all spindles are generated by the same statistical process, but this dissociation is not spindle-type specific. Although this dissociation is not topographically specific, a single generator for all spindle types appears unlikely