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Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated information quantifies how much of the causal powers of a subset of units in a state, also referred to as a mechanism, cannot be accounted for by its parts. If the causal powers of the mechanism can be fully explained by its parts, it is reducible and its integrated information is zero. Here, we study the upper bound of this measure and how it is achieved. We study mechanisms in isolation, groups of mechanisms, and groups of causal relations among mechanisms. We put forward new theoretical results that show mechanisms that share parts with each other cannot all achieve their maximum. We also introduce techniques to design systems that can maximize the integrated information of a subset of their mechanisms or relations. Our results can potentially be used to exploit the symmetries and constraints to reduce the computations significantly and to compare different connectivity profiles in terms of their maximal achievable integrated information.

Summary: The cerebral cortex is widely considered part of the neural substrate of consciousness, but direct causal evidence is missing. Here, we tested in mice whether optogenetic activation of cortical neurons in posterior parietal cortex (PtA) or medial prefrontal cortex (mPFC) is sufficient for arousal from three behavioral states characterized by progressively deeper unresponsiveness: sleep, a coma-like state induced by muscimol injection in the midbrain, and deep sevoflurane-dexmedetomidine anesthesia. We find that cortical stimulation always awakens the mice from both NREM sleep and REM sleep, with PtA requiring weaker/shorter light pulses than mPFC. Moreover, in most cases light pulses produce both cortical activation (decrease in low frequencies) and behavioral arousal (recovery of the righting reflex) from brainstem coma, as well as cortical activation from anesthesia. These findings provide evidence that direct activation of cortical neurons is sufficient for behavioral and/or cortical arousal from sleep, brainstem coma, and anesthesia.

This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system's irreducible cause-effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

Study Objectives: Sleep slow wave activity, as measured using EEG delta power (

When we are asleep, we lose the ability to promptly respond to external stimuli, and yet we spend many hours every day in this inherently risky behavioral state. This simple fact strongly suggests that sleep must serve essential functions that rely on the brain going offline, on a daily basis, and for long periods of time. If these functions did not require partial sensory disconnection, it would be difficult to explain why they are not performed during waking. Paradoxically, despite its central role in defining sleep and what sleep does, sensory disconnection during sleep remains a mystery. We have a limited understanding of how it is implemented along the sensory pathways; we do not know whether the same mechanisms apply to all sensory modalities, nor do we know to what extent these mechanisms are shared between non-rapid eye movement (NREM) sleep and REM sleep. The main goal of this contribution is to review some knowns and unknowns about sensory disconnection during sleep as a first step to fill this gap.

Summary: Exploring the neurobiology of the profound changes in consciousness induced by classical psychedelic drugs may require novel neuroimaging methods. Serotonergic psychedelic drugs such as psilocybin produce states of increased sensory-emotional awareness and arousal, accompanied by increased spontaneous electroencephalographic (EEG) signal diversity. By directly stimulating cortical tissue, the altered dynamics and propagation of the evoked EEG activity can reveal drug-induced changes in the overall brain state. We combine Transcranial Magnetic Stimulation (TMS) and EEG to reveal that psilocybin produces a state of increased chaotic brain activity which is not a result of altered complexity in the underlying causal interactions between brain regions. We also map the regional effects of psilocybin on TMS-evoked activity and identify changes in frontal brain structures that may be associated with the phenomenology of psychedelic experiences.

Neurophysiological differentiation (ND), a measure of the number of distinct activity states that a neural population visits over a time interval, has been used as a correlate of meaningfulness or subjective perception of visual stimuli. ND has largely been studied in non-invasive human whole-brain recordings where spatial resolution is limited. However, it is likely that perception is supported by discrete neuronal populations rather than the whole brain. Therefore, here we use Neuropixels recordings from the mouse brain to characterize the ND metric across a wide range of temporal scales, within neural populations recorded at single-cell resolution in localized regions. Using the spiking activity of thousands of simultaneously recorded neurons spanning 6 visual cortical areas and the visual thalamus, we show that the ND of stimulus-evoked activity of the entire visual cortex is higher for naturalistic stimuli relative to artificial ones. This finding holds in most individual areas throughout the visual hierarchy. Moreover, for animals performing an image change detection task, ND of the entire visual cortex (though not individual areas) is higher for successful detection compared to failed trials, consistent with the assumed perception of the stimulus. Together, these results suggest that ND computed on cellular-level neural recordings is a useful tool highlighting cell populations that may be involved in subjective perception.

Abstract Unlike sleep-walkers, patients with rapid-eye-movement-behaviour disorder (RBD) rarely leave the bed during the re-enactment of their dreams. RBD movements may be independent of spatial co-ordinates of the ‘outside-world’, and instead rely on (allocentric) brain-generated virtual space-maps, as evident by patients’ limited truncal/axial movements. To confirm this, a semiology analysis of video-polysomnography records of 38 RBD patients was undertaken and paradoxically restricted truncal/thoraco-lumbar movements during complex dream re-enactments demonstrated.

The authors propose an explainable consciousness indicator using deep learning to quantify arousal and awareness under sleep, anesthesia, and in patients with disorders of consciousness.

The relationship between conscious experience and brain activity has intrigued scientists and philosophers for centuries. In the last decades, several theories have suggested different accounts for these relationships. These theories have developed in parallel, with little to no cross-talk among them. To advance research on consciousness, we established an adversarial collaboration between proponents of two of the major theories in the field, Global Neuronal Workspace and Integrated Information Theory. Together, we devised and preregistered two experiments that test contrasting predictions of these theories concerning the location and timing of correlates of visual consciousness, which have been endorsed by the theories' proponents. Predicted outcomes should either support, refute, or challenge these theories. Six theory-impartial laboratories will follow the study protocol specified here, using three complementary methods: Functional Magnetic Resonance Imaging (fMRI), Magneto-Electroencephalography (M-EEG), and intracranial electroencephalography (iEEG). The study protocol will include built-in replications, both between labs and within datasets. Through this ambitious undertaking, we hope to provide decisive evidence in favor or against the two theories and clarify the footprints of conscious visual perception in the human brain, while also providing an innovative model of large-scale, collaborative, and open science practice.

Multiple evidence in rodents shows that the strength of excitatory synapses in the cerebral cortex and hippocampus is greater after wake than after sleep. The widespread synaptic weakening afforded by sleep is believed to keep the cost of synaptic activity under control, promote memory consolidation, and prevent synaptic saturation, thus preserving the brain’s ability to learn day after day. The cerebellum is highly plastic and the Purkinje cells, the sole output neurons of the cerebellar cortex, are endowed with a staggering number of excitatory parallel fiber synapses. However, whether these synapses are affected by sleep and wake is unknown. Here, we used serial block face scanning electron microscopy to obtain the full 3D reconstruction of more than 7000 spines and their parallel fiber synapses in the mouse posterior vermis. This analysis was done in mice whose cortical and hippocampal synapses were previously measured, revealing that average synaptic size was lower after sleep compared to wake with no major changes in synapse number. Here, instead, we find that while the average size of parallel fiber synapses does not change, the number of branched synapses is reduced in half after sleep compared to after wake, corresponding to ~16% of all spines after wake and ~8% after sleep. Branched synapses are harbored by two or more spines sharing the same neck and, as also shown here, are almost always contacted by different parallel fibers. These findings suggest that during wake, coincidences of firing over parallel fibers may translate into the formation of synapses converging on the same branched spine, which may be especially effective in driving Purkinje cells to fire. By contrast, sleep may promote the off-line pruning of branched synapses that were formed due to spurious coincidences.

The synaptic mechanisms of how sleep benefits cognitive functions are not well characterised. Here, the authors show that sleep leads to an overall net decrease in spine-surface GluA1-containing AMPA receptors and that this is correlated with changes in performance after sleep.

Abstract Rapid eye movement (REM) sleep behavior disorder (RBD) is characterized by disrupting motor enactments during REM sleep, but also cognitive impairments across several domains. In addition to REM sleep abnormalities, we hypothesized that RBD patients may also display EEG abnormalities during NREM sleep. We collected all-night recordings with 256-channel high-density EEG in nine RBD patients, predominantly early-onset medicated individuals, nine sex- and age- matched healthy controls, and nine additional controls with matched medications and comorbidities. Power spectra in delta to gamma frequency bands were compared during both REM and NREM sleep, between phasic and tonic REM sleep, and between the first versus last cycle of NREM sleep. Controls, but not RBD patients, displayed a decrease in beta power during phasic compared to tonic REM sleep. Compared to controls, RBD patients displayed a reduced decline in SWA from early to late NREM sleep. Overnight changes in the distribution of the amplitude of slow waves were also reduced in RBD patients. Without suppression of beta rhythms during phasic REM sleep, RBD patients might demonstrate heightened cortical arousal, favoring the emergence of behavioral episodes. A blunted difference between REM sleep sub-stages may constitute a sensitive biomarker for RBD. Moreover, reduced overnight decline in SWA suggests a reduced capacity for synaptic plasticity in RBD patients, which may favor progression towards neurodegenerative diseases.

Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause–effect structure unfolded from a maximally irreducible substrate (a Φ-structure). In this work we introduce a definition for the integrated information of a system (φs) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the φs of which is greater than the φs of any overlapping candidate systems.

We have previously demonstrated that, in rested subjects, extensive practice in a motor learning task increased both electroencephalographic (EEG) theta power in the areas involved in learning and improved the error rate in a motor test that shared similarities with the task. A nap normalized both EEG and performance changes. We now ascertain whether extensive visual declarative learning produces results similar to motor learning. Thus, during the morning, we recorded high-density EEG in well rested young healthy subjects that learned the order of different visual sequence task (VSEQ) for three one-hour blocks. Afterward, a group of subjects took a nap and another rested quietly. Between each VSEQ block, we recorded spontaneous EEG (sEEG) at rest and assessed performance in a motor test and a visual working memory test that shares similarities with VSEQ. We found that after the third block, VSEQ induced local theta power increases in the sEEG over a right temporo-parietal area that was engaged during the task. This local theta increase was preceded by increases in alpha and beta power over the same area and was paralleled by performance decline in the visual working memory test. Only after the nap, VSEQ learning rate improved and performance in the visual working memory test was restored, together with partial normalization of the local sEEG changes. These results suggest that intensive learning, like motor learning, produces local theta power increases, possibly reflecting local neuronal fatigue. Sleep may be necessary to resolve neuronal fatigue and its effects on learning and performance.

Abstract The neuronal connectivity patterns that differentiate consciousness from unconsciousness remain unclear. Previous studies have demonstrated that effective connectivity, as assessed by transcranial magnetic stimulation combined with electroencephalography (TMS–EEG), breaks down during the loss of consciousness. This study investigated changes in EEG connectivity associated with consciousness during non-rapid eye movement (NREM) sleep following parietal TMS. Compared with unconsciousness, conscious experiences during NREM sleep were associated with reduced phase-locking at low frequencies (

Background: Slow-wave activity (SWA) during non-rapid eye movement (NREM) sleep reflects synaptic potentiation during preceding wakefulness. Epileptic activity may induce increases in state-dependent SWA in human brains, therefore, localization of SWA may prove useful in the presurgical workup of epileptic patients. We analyzed high-density electroencephalography (HDEEG) data across vigilance states from a reflex epilepsy patient with a clearly localizable ictal symptomatogenic zone to provide a proof-of-concept for the testability of this hypothesis.Methods: Overnight HDEEG recordings were obtained in the patient during REM sleep, NREM sleep, wakefulness, and during a right facial motor seizure then compared to 10 controls. After preprocessing, SWA (i.e., delta power; 1–4 Hz) was calculated at each channel. Scalp level and source reconstruction analyses were computed. We assessed for statistical differences in maximum SWA between the patient and controls within REM sleep, NREM sleep, wakefulness, and seizure. Then, we completed an identical statistical comparison after first subtracting intrasubject REM sleep SWA from that of NREM sleep, wakefulness, and seizure SWA.Results: The topographical analysis revealed greater left hemispheric SWA in the patient vs. controls in all vigilance states except REM sleep (which showed a right hemispheric maximum). Source space analysis revealed increased SWA in the left inferior frontal cortex during NREM sleep and wakefulness. Ictal data displayed poor source-space localization. Comparing each state to REM sleep enhanced localization accuracy; the most clearly localizing results were observed when subtracting REM sleep from wakefulness.Conclusion: State-dependent SWA during NREM sleep and wakefulness may help to identify aspects of the potential epileptogenic zone. Future work in larger cohorts may assess the clinical value of sleep SWA to help presurgical planning.

Beta oscillations (13.5−25 Hz) over the sensorimotor areas are characterized by a power decrease during movement execution (event-related desynchronization, ERD) and a sharp rebound after the movement end (event-related synchronization, ERS). In previous studies, we demonstrated that movement-related beta modulation depth (peak ERS-ERD) during reaching increases within 1-h practice. This increase may represent plasticity processes within the sensorimotor network. If so, beta modulation during a reaching test should be affected by previous learning activity that engages the sensorimotor system but not by learning involving other systems. We thus recorded high-density EEG activity in a group of healthy subjects performing three 45-min blocks of motor adaptation task to a visually rotated display (ROT) and in another performing three blocks of visual sequence-learning (VSEQ). Each block of either ROT or VSEQ was followed by a simple reaching test (mov) without rotation. We found that beta modulation depth increased with practice across mov tests. However, such an increase was greater in the group performing ROT over both the left and frontal areas previously involved in ROT. Importantly, beta modulation values returned to baseline values after a 90-min of either nap or quiet wake. These results show that previous practice leaves a trace in movement-related beta modulation and therefore such increases are cumulative. Furthermore, as sleep is not necessary to bring beta modulation values to baseline, they could reflect local increases of neuronal activity and decrease of energy and supplies.

Brain function requires the flexible coordination of billions of neurons across multiple scales. This could be achieved by scale-free, critical dynamics balanced at the edge of order and disorder. Criticality has been demonstrated in several, often reduced neurophysiological model systems. In the intact human brain criticality has yet been only verified for the resting state. A more direct link between the concept of criticality and oscillatory brain physiology, which is strongly related to cognition, is yet missing. In the present study we therefore carried out a frequency-specific analysis of criticality in the MEG, recorded while subjects were in a defined cognitive state through mindfulness meditation. In a two-step approach we assessed whether the macroscopic neural avalanche dynamics is scale-free by evaluating the goodness of a power-law fits of cascade size and duration distributions of MEG deflections in different frequency bands. In a second step we determined the closeness of the power-law exponents to a critical value of -1.5. Power-law fitting was evaluated by permutation testing, fitting of alternative distributions, and cascade shape analysis. Criticality was verified by defined relationships of exponents of cascade size and duration distributions. Behavioral relevance of criticality was tested by correlation of indices of criticality with individual scores of the Mindful Attention Awareness Scale. We found that relevant scale-free near-critical dynamics originated only from broad-band high-frequency (> 100 Hz) MEG activity, which has been associated with action potential firing, and therefore links criticality on the macroscopic level of MEG to critical spike avalanches on a microscopic level. Whereas a scale-free dynamics was found under mindfulness meditation and rest, avalanche dynamics shifted towards a critical point during meditation by reduction of neural noise. Together with our finding that during mindfulness meditation avalanches show differences in topography relative to rest, our results show that self-regulated attention as required during meditation can serve as a control parameter of criticality in scale-free brain dynamics.

Abstract By identifying endogenous molecules in brain extracellular fluid metabolomics can provide insight into the regulatory mechanisms and functions of sleep. Here we studied how the cortical metabolome changes during sleep, sleep deprivation and spontaneous wakefulness. Mice were implanted with electrodes for chronic sleep/wake recording and with microdialysis probes targeting prefrontal and primary motor cortex. Metabolites were measured using ultra performance liquid chromatography-high resolution mass spectrometry. Sleep/wake changes in metabolites were evaluated using partial least squares discriminant analysis, linear mixed effects model analysis of variance, and machine-learning algorithms. More than 30 known metabolites were reliably detected in most samples. When used by a logistic regression classifier, the profile of these metabolites across sleep, spontaneous wake, and enforced wake was sufficient to assign mice to their correct experimental group (pair-wise) in 80–100% of cases. Eleven of these metabolites showed significantly higher levels in awake than in sleeping mice. Some changes extend previous findings (glutamate, homovanillic acid, lactate, pyruvate, tryptophan, uridine), while others are novel (D-gluconate, N-acetyl-beta-alanine, N-acetylglutamine, orotate, succinate/methylmalonate). The upregulation of the de novo pyrimidine pathway, gluconate shunt and aerobic glycolysis may reflect a wake-dependent need to promote the synthesis of many essential components, from nucleic acids to synaptic membranes.

The ventromedial thalamus (VM) is thought to control cortical arousal through its diffuse projections to cortex. Here the authors record and manipulate the activity of calbindin1-positive matrix cells in VM and show that they bidirectionally regulate the sleep-wake transition.

Background: Making an accurate diagnosis in patients with disorders of consciousness remains challenging. 18F-fluorodeoxyglucose (FDG)–PET has been validated as a diagnostic tool in this population, and allows identifying unresponsive patients with a capacity for consciousness. In parallel, the perturbational complexity index (PCI), a new measure based on the analysis of the electroencephalographic response to transcranial magnetic stimulation, has also been suggested as a tool to distinguish between unconscious and conscious states. The aim of the study was to cross-validate FDG–PET and PCI, and to identify signs of consciousness in otherwise unresponsive patients. Methods: We jointly applied the Coma Recovery Scale-Revised, FDG–PET and PCI to assess 24 patients with non-acute disorders of consciousness or locked-in syndrome (13 male; 19–54 years old; 12 traumatic; 9 unresponsive wakefulness syndrome, 11 minimally conscious state; 2 emergence from the minimally conscious state, and 2 locked-in syndrome). Results: FDG–PET and PCI provided congruent results in 22 patients, regardless of their behavioural diagnosis. Notably, FDG–PET and PCI revealed preserved metabolic rates and high complexity levels in four patients who were behaviourally unresponsive. Conclusion: We propose that jointly measuring the metabolic activity and the electrophysiological complexity of cortical circuits is a useful complement to the diagnosis and stratification of patients with disorders of consciousness.

The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT—existence, intrinsicality and information—and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT—integration and exclusion—and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience.

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.

Transcriptomic studies revealed that hundreds of mRNAs show differential expression in the brains of sleeping relative to awake rats, mice, flies, and sparrows. Although these results have offered clues regarding the molecular consequences of sleep and sleep loss, their functional significance thus far has been limited. This is probably because the previous studies pooled transcripts from all brain cells, including neurons and glia. In Bellesi et al. (2015) [1], we used the translating ribosome affinity purification technology (TRAP) and microarray analysis to obtain a genome-wide mRNA profiling of astrocytes as a function of sleep and wake. We used bacterial artificial chromosome (BAC) transgenic mice expressing eGFP tagged ribosomal protein L10a under the promoter of the Aldh1L1 gene, a highly expressed astrocytic gene. Using this approach, we could extract only the astrocytic mRNAs, and only those already committed to be translated into proteins (L10a is part of the translational machinery). Here, we report a detailed description of the protocol used in the study (Bellesi et al., 2015 [1]). Array data have been submitted to NCBI GEO under accession number (GSE69079).

Astrocytic glycogen represents the only form of glucose storage in the brain, and one of the outcomes of its breakdown is the production of lactate that can be used by neurons as an alternative energetic substrate. Since brain metabolism is higher in wake than in sleep, it was hypothesized that glycogen stores are depleted during wake and replenished during sleep. Furthermore, it was proposed that glycogen depletion leads to the progressive increase in adenosine levels during wake, providing a homeostatic signal that reflects the buildup of sleep pressure. However, previous studies that measured glycogen dynamics across the sleep/wake cycle obtained inconsistent results, and only measured glycogen in whole tissue. Since most energy in the brain is used to sustain synaptic activity, here we employed tridimensional electron microscopy to quantify glycogen content in the astrocytic processes surrounding the synapse. We studied axon-spine synapses in the frontal cortex of young mice after ~7 h of sleep, 7–8 h of spontaneous or forced wake, or 4.5 days of sleep restriction. Relative to sleep, all wake conditions increased the number of glycogen granules around the synapses to a similar extent. However, progressively longer periods of wake were associated with progressively smaller glycogen granules, suggesting increased turnover. Despite the increased number of granules, in all wake conditions the estimated amount of glucose within the granules was lower than in sleep, indicating that sleep may favor glucose storage. Finally, chronic sleep restriction moved glycogen granules closer to the synaptic cleft. Thus, both short and long wake lead to increased glycogen turnover around cortical synapses, whereas sleep promotes glycogen accumulation.

Integrated information theory provides a mathematical framework to fully characterize the cause-effect structure of a physical system. Here, we introduce PyPhi, a Python software package that implements this framework for causal analysis and unfolds the full cause-effect structure of discrete dynamical systems of binary elements. The software allows users to easily study these structures, serves as an up-to-date reference implementation of the formalisms of integrated information theory, and has been applied in research on complexity, emergence, and certain biological questions. We first provide an overview of the main algorithm and demonstrate PyPhi's functionality in the course of analyzing an example system, and then describe details of the algorithm's design and implementation. PyPhi can be installed with Python's package manager via the command 'pip install pyphi' on Linux and macOS systems equipped with Python 3.4 or higher. PyPhi is open-source and licensed under the GPLv3; the source code is hosted on GitHub at https://github.com/wmayner/pyphi. Comprehensive and continually-updated documentation is available at https://pyphi.readthedocs.io. The pyphi-users mailing list can be joined at https://groups.google.com/forum/#!forum/pyphi-users. A web-based graphical interface to the software is available at http://integratedinformationtheory.org/calculate.html.

Previous work showed that two types of slow waves are temporally dissociated during the transition to sleep: widespread, large and steep slow waves predominate early in the falling asleep period (type I), while smaller, more circumscribed slow waves become more prevalent later (type II). Here, we studied the possible occurrence of these two types of slow waves in stable non-REM (NREM) sleep and explored potential differences in their regulation. A heuristic approach based on slow wave synchronization efficiency was developed and applied to high-density electroencephalographic (EEG) recordings collected during consolidated NREM sleep to identify the potential type I and type II slow waves. Slow waves with characteristics compatible with those previously described for type I and type II were identified in stable NREM sleep. Importantly, these slow waves underwent opposite changes across the night, with only type II slow waves displaying a clear homeostatic regulation. In addition, we showed that the occurrence of type I slow waves was often followed by larger type II slow waves, whereas the occurrence of type II slow waves was usually followed by smaller type I waves. Finally, type II slow waves were associated with a relative increase in spindle activity, while type I slow waves triggered periods of high-frequency activity. Our results provide evidence for the existence of two distinct slow wave synchronization processes that underlie two different types of slow waves. These slow waves may have different functional roles and mark partially distinct “micro-states” of the sleeping brain.

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by employing a principled, well-defined measure of intrinsic cause-effect power-integrated information (Φ), and showing that, according to this measure, it is possible for a macro level to "beat" the micro level. Simple systems were evaluated for Φ across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro updates. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal micro elements that support their input-output function. We show how black-box elements can have more common inputs and outputs than the corresponding micro elements, revealing the emergence of high-order mechanisms and joint constraints that are not apparent at the micro level. As a consequence, a macro, black-box system can have higher Φ than its micro constituents by having more mechanisms (higher composition) that are more interconnected (higher integration). We also show that, for a given micro system, one can identify local maxima of Φ across several spatiotemporal scales. The framework is demonstrated on a simple biological system, the Boolean network model of the fission-yeast cell-cycle, for which we identify stable local maxima during the course of its simulated biological function. These local maxima correspond to macro levels of organization at which emergent cause-effect properties of physical systems come into focus, and provide a natural vantage point for scientific inquiries.

Current approaches to characterize the complexity of dynamical systems usually rely on state-space trajectories. In this article instead we focus on causal structure, treating discrete dynamical systems as directed causal graphs—systems of elements implementing local update functions. This allows us to characterize the system’s intrinsic cause-effect structure by applying the mathematical and conceptual tools developed within the framework of integrated information theory (IIT). In particular, we assess the number of irreducible mechanisms (concepts) and the total amount of integrated conceptual information Φ specified by a system. We analyze: (i) elementary cellular automata (ECA); and (ii) small, adaptive logic-gate networks (“animats”), similar to ECA in structure but evolving by interacting with an environment. We show that, in general, an integrated cause-effect structure with many concepts and high Φ is likely to have high dynamical complexity. Importantly, while a dynamical analysis describes what is “happening” in a system from the extrinsic perspective of an observer, the analysis of its cause-effect structure reveals what a system “is” from its own intrinsic perspective, exposing its dynamical and evolutionary potential under many different scenarios.

A set of images can be considered as meaningfully different for an observer if they can be distinguished phenomenally from one another. Each phenomenal difference must be supported by some neurophysiological differences. Differentiation analysis aims to quantify neurophysiological differentiation evoked by a given set of stimuli to assess its meaningfulness to the individual observer. As a proof of concept using high-density EEG, we show increased neurophysiological differentiation for a set of natural, meaningfully different images in contrast to another set of artificially generated, meaninglessly different images in nine participants. Stimulus-evoked neurophysiological differentiation (over 257 channels, 800 ms) was systematically greater for meaningful vs. meaningless stimulus categories both at the group level and for individual subjects. Spatial breakdown showed a central-posterior peak of differentiation, consistent with the visual nature of the stimulus sets. Temporal breakdown revealed an early peak of differentiation around 110 ms, prominent in the central-posterior region; and a later, longer-lasting peak at 300–500 ms that was spatially more distributed. The early peak of differentiation was not accompanied by changes in mean ERP amplitude, whereas the later peak was associated with a higher amplitude ERP for meaningful images. An ERP component similar to visual-awareness-negativity occurred during the nadir of differentiation across all image types. Control stimulus sets and further analysis indicate that changes in neurophysiological differentiation between meaningful and meaningless stimulus sets could not be accounted for by spatial properties of the stimuli or by stimulus novelty and predictability.

The activity-regulated cytoskeleton associated protein Arc is strongly and quickly upregulated by neuronal activity, synaptic potentiation and learning. Arc entry in the synapse is followed by the endocytosis of glutamatergic AMPA receptors (AMPARs), and its nuclear accumulation has been shown in vitro to result in a small decline in the transcription of the GluA1 subunit of AMPARs. Since these effects result in a decline in synaptic strength, we asked whether a change in Arc dynamics may temporally correlate with sleep-dependent GluA1 down-regulation. We measured the ratio of nuclear to cytoplasmic Arc expression (Arc Nuc/Cyto) in the cerebral cortex of EGFP-Arc transgenic mice that were awake most of the night and then perfused immediately before lights on (W mice), or were awake most of the night and then allowed to sleep (S mice) or sleep deprived (SD mice) for the first 2 h of the light phase. In primary motor cortex (M1), neurons with high levels of nuclear Arc (High Arc cells) were present in all mice, but in these cells Arc Nuc/Cyto was higher in S mice than in W mice and, importantly, ~15% higher in S mice than in SD mice collected at the same time of day, ruling out circadian effects. Greater Arc Nuc/Cyto with sleep was observed in the superficial layers of M1, but not in the deep layers. In High Arc cells, Arc Nuc/Cyto was also ~15%–30% higher in S mice than in W and SD mice in the superficial layers of primary somatosensory cortex (S1) and cingulate cortex area 1 (Cg1). In High Arc Cells of Cg1, Arc Nuc/Cyto and cytoplasmic levels of GluA1 immunoreactivities in the soma were also negatively correlated, independent of behavioral state. Thus, Arc moves to the nucleus during both sleep and wake, but its nuclear to cytoplasmic ratio increases with sleep in the superficial layers of several cortical areas. It remains to be determined whether the relative increase in nuclear Arc contributes significantly to the overall decline in the strength of excitatory synapses that occurs during sleep. Similarly, it remains to be determined whether the entry of Arc into specific synapses is gated by sleep.

The dynamical evolution of a system of interacting elements can be predicted in terms of its elementary constituents and their interactions, or in terms of the system’s global state transitions. For this reason, systems with equivalent global dynamics are often taken to be equivalent for all relevant purposes. Nevertheless, such systems may still vary in their causal composition—the way mechanisms within the system specify causes and effects over different subsets of system elements. We demonstrate this point based on a set of small discrete dynamical systems with reversible dynamics that cycle through all their possible states. Our analysis elucidates the role of composition within the formal framework of integrated information theory. We show that the global dynamical and information-theoretic capacities of reversible systems can be maximal even though they may differ, quantitatively and qualitatively, in the information that their various subsets specify about each other (intrinsic information). This can be the case even for a system and its time-reversed equivalent. Due to differences in their causal composition, two systems with equivalent global dynamics may still differ in their capacity for autonomy, agency, and phenomenology.

Actual causation is concerned with the question: “What caused what?” Consider a transition between two states within a system of interacting elements, such as an artificial neural network, or a biological brain circuit. Which combination of synapses caused the neuron to fire? Which image features caused the classifier to misinterpret the picture? Even detailed knowledge of the system’s causal network, its elements, their states, connectivity, and dynamics does not automatically provide a straightforward answer to the “what caused what?” question. Counterfactual accounts of actual causation, based on graphical models paired with system interventions, have demonstrated initial success in addressing specific problem cases, in line with intuitive causal judgments. Here, we start from a set of basic requirements for causation (realization, composition, information, integration, and exclusion) and develop a rigorous, quantitative account of actual causation, that is generally applicable to discrete dynamical systems. We present a formal framework to evaluate these causal requirements based on system interventions and partitions, which considers all counterfactuals of a state transition. This framework is used to provide a complete causal account of the transition by identifying and quantifying the strength of all actual causes and effects linking the two consecutive system states. Finally, we examine several exemplary cases and paradoxes of causation and show that they can be illuminated by the proposed framework for quantifying actual causation.

Sleep changes were studied in mice (n = 59) from early adolescence to adulthood (postnatal days P19–111). REM sleep declined steeply in early adolescence, while total sleep remained constant and NREM sleep increased slightly. Four hours of sleep deprivation starting at light onset were performed from ages P26 through adulthood (>P60). Following this acute sleep deprivation all mice slept longer and with more consolidated sleep bouts, while NREM slow wave activity (SWA) showed high interindividual variability in the younger groups, and increased consistently only after P42. Three parameters together explained up to 67% of the variance in SWA rebound in frontal cortex, including weight-adjusted age and increase in alpha power during sleep deprivation, both of which positively correlated with the SWA response. The third, and strongest predictor was the SWA decline during the light phase in baseline: mice with high peak SWA at light onset, resulting in a large SWA decline, were more likely to show no SWA rebound after sleep deprivation, a result that was also confirmed in parietal cortex. During baseline, however, SWA showed the same homeostatic changes in adolescents and adults, declining in the course of sleep and increasing across periods of spontaneous wake. Thus, we hypothesize that, in young adolescent mice, a ceiling effect and not the immaturity of the cellular mechanisms underlying sleep homeostasis may prevent the SWA rebound when wake is extended beyond its physiological duration.

Sleeping brain activity reflects brain anatomy and physiology. The aim of this study was to use high density (256 channel) electroencephalography (EEG) during sleep to characterize topographic changes in sleep EEG power across normal aging, with high spatial resolution. Sleep was evaluated in 92 healthy adults aged 18-65 years old using full polysomnography and high density EEG. After artifact removal, spectral power density was calculated for standard frequency bands for all channels, averaged across the NREM periods of the first 3 sleep cycles. To quantify topographic changes with age, maps were generated of the Pearson's coefficient of the correlation between power and age at each electrode. Significant correlations were determined by statistical non-parametric mapping. Absolute slow wave power declined significantly with increasing age across the entire scalp, whereas declines in theta and sigma power were significant only in frontal regions. Power in fast spindle frequencies declined significantly with increasing age frontally, whereas absolute power of slow spindle frequencies showed no significant change with age. When EEG power was normalized across the scalp, a left centro-parietal region showed significantly less age-related decline in power than the rest of the scalp. This partial preservation was particularly significant in the slow wave and sigma bands. The effect of age on sleep EEG varies substantially by region and frequency band. This non-uniformity should inform the design of future investigations of aging and sleep. This study provides normative data on the effect of age on sleep EEG topography, and provides a basis from which to explore the mechanisms of normal aging as well as neurodegenerative disorders for which age is a risk factor.

STUDY OBJECTIVES:We have recently shown higher parietal-occipital EEG gamma activity during sleep in long-term meditators compared to meditation-naive individuals. This gamma increase was specific for NREM sleep, was present throughout the entire night and correlated with meditation expertise, thus suggesting underlying long-lasting neuroplastic changes induced through prolonged training. The aim of this study was to explore the neuroplastic changes acutely induced by 2 intensive days of different meditation practices in the same group of practitioners. We also repeated baseline recordings in a meditation-naive cohort to account for time effects on sleep EEG activity. DESIGN:High-density EEG recordings of human brain activity were acquired over the course of whole sleep nights following intervention. SETTING:Sound-attenuated sleep research room. PATIENTS OR PARTICIPANTS:Twenty-four long-term meditators and twenty-four meditation-naïve controls. INTERVENTIONS:Two 8-h sessions of either a mindfulness-based meditation or a form of meditation designed to cultivate compassion and loving kindness, hereafter referred to as compassion meditation. MEASUREMENTS AND RESULTS:We found an increase in EEG low-frequency oscillatory activities (1-12 Hz, centered around 7-8 Hz) over prefrontal and left parietal electrodes across whole night NREM cycles. This power increase peaked early in the night and extended during the third cycle to high-frequencies up to the gamma range (25-40 Hz). There was no difference in sleep EEG activity between meditation styles in long-term meditators nor in the meditation naïve group across different time points. Furthermore, the prefrontal-parietal changes were dependent on meditation life experience. CONCLUSIONS:This low-frequency prefrontal-parietal activation likely reflects acute, meditation-related plastic changes occurring during wakefulness, and may underlie a top-down regulation from frontal and anterior parietal areas to the posterior parietal and occipital regions showing chronic, long-lasting plastic changes in long-term meditators.

A meaningful set of stimuli, such as a sequence of frames from a movie, triggers a set of different experiences. By contrast, a meaningless set of stimuli, such as a sequence of 'TV noise' frames, triggers always the same experience--of seeing 'TV noise'--even though the stimuli themselves are as different from each other as the movie frames. We reasoned that the differentiation of cortical responses underlying the subject's experiences, as measured by Lempel-Ziv complexity (incompressibility) of functional MRI images, should reflect the overall meaningfulness of a set of stimuli for the subject, rather than differences among the stimuli. We tested this hypothesis by quantifying the differentiation of brain activity patterns in response to a movie sequence, to the same movie scrambled in time, and to 'TV noise', where the pixels from each movie frame were scrambled in space. While overall cortical activation was strong and widespread in all conditions, the differentiation (Lempel-Ziv complexity) of brain activation patterns was correlated with the meaningfulness of the stimulus set, being highest in the movie condition, intermediate in the scrambled movie condition, and minimal for 'TV noise'. Stimulus set meaningfulness was also associated with higher information integration among cortical regions. These results suggest that the differentiation of neural responses can be used to assess the meaningfulness of a given set of stimuli for a given subject, without the need to identify the features and categories that are relevant to the subject, nor the precise location of selective neural responses.

Natural selection favors the evolution of brains that can capture fitness-relevant features of the environment's causal structure. We investigated the evolution of small, adaptive logic-gate networks ("animats") in task environments where falling blocks of different sizes have to be caught or avoided in a 'Tetris-like' game. Solving these tasks requires the integration of sensor inputs and memory. Evolved networks were evaluated using measures of information integration, including the number of evolved concepts and the total amount of integrated conceptual information. The results show that, over the course of the animats' adaptation, i) the number of concepts grows; ii) integrated conceptual information increases; iii) this increase depends on the complexity of the environment, especially on the requirement for sequential memory. These results suggest that the need to capture the causal structure of a rich environment, given limited sensors and internal mechanisms, is an important driving force for organisms to develop highly integrated networks ("brains") with many concepts, leading to an increase in their internal complexity.

This paper presents Integrated Information Theory (IIT) of consciousness 3.0, which incorporates several advances over previous formulations. IIT starts from phenomenological axioms: information says that each experience is specific--it is what it is by how it differs from alternative experiences; integration says that it is unified--irreducible to non-interdependent components; exclusion says that it has unique borders and a particular spatio-temporal grain. These axioms are formalized into postulates that prescribe how physical mechanisms, such as neurons or logic gates, must be configured to generate experience (phenomenology). The postulates are used to define intrinsic information as "differences that make a difference" within a system, and integrated information as information specified by a whole that cannot be reduced to that specified by its parts. By applying the postulates both at the level of individual mechanisms and at the level of systems of mechanisms, IIT arrives at an identity: an experience is a maximally irreducible conceptual structure (MICS, a constellation of concepts in qualia space), and the set of elements that generates it constitutes a complex. According to IIT, a MICS specifies the quality of an experience and integrated information ΦMax its quantity. From the theory follow several results, including: a system of mechanisms may condense into a major complex and non-overlapping minor complexes; the concepts that specify the quality of an experience are always about the complex itself and relate only indirectly to the external environment; anatomical connectivity influences complexes and associated MICS; a complex can generate a MICS even if its elements are inactive; simple systems can be minimally conscious; complicated systems can be unconscious; there can be true "zombies"--unconscious feed-forward systems that are functionally equivalent to conscious complexes.

Over the past several years meditation practice has gained increasing attention as a non-pharmacological intervention to provide health related benefits, from promoting general wellness to alleviating the symptoms of a variety of medical conditions. However, the effects of meditation training on brain activity still need to be fully characterized. Sleep provides a unique approach to explore the meditation-related plastic changes in brain function. In this study we performed sleep high-density electroencephalographic (hdEEG) recordings in long-term meditators (LTM) of Buddhist meditation practices (approximately 8700 mean hours of life practice) and meditation naive individuals. We found that LTM had increased parietal-occipital EEG gamma power during NREM sleep. This increase was specific for the gamma range (25-40 Hz), was not related to the level of spontaneous arousal during NREM and was positively correlated with the length of lifetime daily meditation practice. Altogether, these findings indicate that meditation practice produces measurable changes in spontaneous brain activity, and suggest that EEG gamma activity during sleep represents a sensitive measure of the long-lasting, plastic effects of meditative training on brain function.

What is the relationship between the complexity and the fitness of evolved organisms, whether natural or artificial? It has been asserted, primarily based on empirical data, that the complexity of plants and animals increases as their fitness within a particular environment increases via evolution by natural selection. We simulate the evolution of the brains of simple organisms living in a planar maze that they have to traverse as rapidly as possible. Their connectome evolves over 10,000s of generations. We evaluate their circuit complexity, using four information-theoretical measures, including one that emphasizes the extent to which any network is an irreducible entity. We find that their minimal complexity increases with their fitness.

Recent EEG studies have shown that implicit learning involving specific cortical circuits results in an enduring local trace manifested as local changes in spectral power. Here we used a well characterized visual sequence learning task and high density-(hd-)EEG recording to determine whether also declarative learning leaves a post-task, local change in the resting state oscillatory activity in the areas involved in the learning process. Thus, we recorded hd-EEG in normal subjects before, during and after the acquisition of the order of a fixed spatial target sequence (VSEQ) and during the presentation of targets in random order (VRAN). We first determined the temporal evolution of spectral changes during VSEQ and compared it to VRAN. We found significant differences in the alpha and theta bands in three main scalp regions, a right occipito-parietal (ROP), an anterior-frontal (AFr), and a right frontal (RFr) area. The changes in frontal theta power during VSEQ were positively correlated with the learning rate. Further, post-learning EEG recordings during resting state revealed a significant increase in alpha power in ROP relative to a pre-learning baseline. We conclude that declarative learning is associated with alpha and theta changes in frontal and posterior regions that occur during the task, and with an increase of alpha power in the occipito-parietal region after the task. These post-task changes may represent a trace of learning and a hallmark of use-dependent plasticity.

In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.

The glutamate transporter GLT-1 is responsible for the largest proportion of total glutamate transport. Recently, it has been demonstrated that ceftriaxone (CEF) robustly increases GLT-1 expression. In addition, physiological studies have shown that GLT-1 up-regulation strongly affects synaptic plasticity, and leads to an impairment of the prepulse inhibition, a simple form of information processing, thus suggesting that GLT-1 over-expression may lead to dysfunctions of large populations of neurons. To test this possibility, we assessed whether CEF affects cortical electrical activity by using chronic electroencephalographic (EEG) recordings in male WKY rats. Spectral analysis showed that 8 days of CEF treatment resulted in a delayed reduction in EEG theta power (7-9 Hz) in both frontal and parietal derivations. This decrease peaked at day 10, i.e., 2 days after the end of treatment, and disappeared by day 16. In addition, we found that the same CEF treatment increased motor activity, especially when EEG changes are more prominent. Taken together, these data indicate that GLT-1 up-regulation, by modulating glutamatergic transmission, impairs the activity of widespread neural circuits. In addition, the increased motor activity and prepulse inhibition alterations previously described suggest that neural circuits involved in sensorimotor control are particularly sensitive to GLT-1 up-regulation.

Sleep must serve an essential, universal function, one that offsets the risk of being disconnected from the environment. The synaptic homeostasis hypothesis (SHY) is an attempt to identify this essential function. Its core claim is that sleep is needed to reestablish synaptic homeostasis, which is challenged by the remarkable plasticity of the brain. In other words, sleep is “the price we pay for plasticity.” In this issue, M. G. Frank reviewed several aspects of the hypothesis and raised several issues. The comments below provide a brief summary of the motivations underlying SHY and clarify that SHY is a hypothesis not about specific mechanisms, but about a universal, essential function of sleep. This function is the preservation of synaptic homeostasis in the face of a systematic bias toward a net increase in synaptic strength—a challenge that is posed by learning during adult wake, and by massive synaptogenesis during development.

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.

According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems. Qualia space (Q) is a space having an axis for each possible state (activity pattern) of a complex. Within Q, each submechanism specifies a point corresponding to a repertoire of system states. Arrows between repertoires in Q define informational relationships. Together, these arrows specify a quale -- a shape that completely and univocally characterizes the quality of a conscious experience. Phi -- the height of this shape -- is the quantity of consciousness associated with the experience. Entanglement measures how irreducible informational relationships are to their component relationships, specifying concepts and modes. Several corollaries follow from these premises. The quale is determined by both the mechanism and state of the system. Thus, two different systems having identical activity patterns may generate different qualia. Conversely, the same quale may be generated by two systems that differ in both activity and connectivity. Both active and inactive elements specify a quale, but elements that are inactivated do not. Also, the activation of an element affects experience by changing the shape of the quale. The subdivision of experience into modalities and submodalities corresponds to subshapes in Q. In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes. Finally, specific qualities, such as the "redness" of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale. Ultimately, the present framework may offer a principled way for translating qualitative properties of experience into mathematics.

A governing assumption about repetitive transcranial magnetic stimulation (rTMS) has been that it interferes with task-related neuronal activity – in effect, by “injecting noise” into the brain – and thereby disrupts behavior. Recent reports of rTMS-produced behavioral enhancement, however, call this assumption into question. We investigated the neurophysiological effects of rTMS delivered during the delay period of a visual working memory task by simultaneously recording brain activity with electroencephalography (EEG). Subjects performed visual working memory for locations or for shapes, and in half the trials a 10-Hz train of rTMS was delivered to the superior parietal lobule or a control brain area. The wide range of individual differences in the effects of rTMS on task accuracy, from improvement to impairment, was predicted by individual differences in the effect of rTMS on power in the alpha-band of the EEG (~ 10 Hz): a decrease in alpha-band power corresponded to improved performance, whereas an increase in alpha-band power corresponded to the opposite. The EEG effect was localized to cortical sources encompassing the frontal eye fields and the intraparietal sulcus, and was specific to task (location, but not object memory) and to rTMS target (superior parietal lobule, not control area). Furthermore, for the same task condition, rTMS-induced changes in cross-frequency phase synchrony between alpha- and gamma-band (> 40 Hz) oscillations predicted changes in behavior. These results suggest that alpha-band oscillations play an active role cognitive processes and do not simply reflect absence of processing. Furthermore, this study shows that the complex effects of rTMS on behavior can result from biasing endogenous patterns of network-level oscillations.