A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks.

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.

Infraslow oscillations in human sleep spindle activity.

BACKGROUND: It has previously been reported that EEG sigma (10-15 Hz) activity during sleep exhibits infraslow oscillations (ISO) with a period of 50 s. However, a detailed analysis of the ISO of individually identified sleep spindles is not available. NEW METHOD: We investigated basic properties of ISO during baseline sleep of 34 healthy young human participants using new and established methods. The analyses focused on fast sleep spindle and sigma activity (13-15 Hz) in NREM stage 2 and slow wave sleep (SWS). To describe ISO in sigma activity we analyzed power of power of the EEG signal. For the study of ISO in sleep spindle activity we applied a new method in which the EEG signal was reduced to a spindle on/off binary square signal. Its spectral properties were contrasted to that of a square signal wherein the same spindles and also the inter spindle intervals were permutated randomly. This approach was validated using surrogate data with imposed ISO modulation. RESULTS: We confirm the existence of ISO in sigma activity albeit with a frequency below the previously reported 0.02 Hz. These ISO are most prominent in the high sigma band and over the centro-parieto-occipital regions. A similar modulation is present in spindle activity. ISO in sleep spindles are most prominent in the centro-parieto-occipital regions, left hemisphere and second half of the night independent of the number of spindles. CONCLUSIONS: The comparison of spectral properties of binary event signals and permutated event signals is effective in detecting slow oscillatory phenomena.

Association of symptoms of insomnia and sleep parameters among kidney transplant recipients.

OBJECTIVE: Insomnia complaints are frequent among kidney transplant (kTx) recipients and are associated with fatigue, depression, lower quality of life and increased morbidity. However, it is not known if subjective insomnia symptoms are associated with objective parameters of sleep architecture. Thus, we analyze the association between sleep macrostructure and EEG activity versus insomnia symptoms among kTx recipients. METHODS: Participants (n1=100) were selected from prevalent adult transplant recipients (n0=1214) followed at a single institution. Insomnia symptoms were assessed by the Athens Insomnia Scale (AIS) and standard overnight polysomnography was performed. In a subgroup of patients (n2=56) sleep microstructure was also analyzed with power spectral analysis. RESULTS: In univariable analysis AIS score was not associated with sleep macrostructure parameters (sleep latency, total sleep time, slow wave sleep, wake after sleep onset), nor with NREM and REM beta or delta activity in sleep microstructure. In multivariable analysis after controlling for covariables AIS score was independently associated with the proportion of slow wave sleep (ß=0.263; CI: 0.026-0.500) and REM beta activity (ß=0.323; CI=0.041-0.606) (p<0.05 for both associations). CONCLUSIONS: Among kTx recipients the severity of insomnia symptoms is independently associated with higher proportion of slow wave sleep and increased beta activity during REM sleep but not with other parameters sleep architecture. The results suggest a potential compensatory sleep protective mechanism and a sign of REM sleep instability associated with insomnia symptoms among this population.

Stochastic graph Voronoi tessellation reveals community structure.

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called Voronoi cohesion which describes the probability for sharing the same Voronoi cell, when randomly choosing g centers in the network. This measure provides information based on the global context (the network in its entirety), a type of information that is not carried by other similarity measures. We explore the mathematical background of this phenomenon and several of its potential applications. A special focus is laid on the possibilities and limitations pertaining to the exploitation of the phenomenon for community detection purposes.

Slow wave sleep and accelerated forgetting.

We investigated whether the benefit of slow wave sleep (SWS) for memory consolidation typically observed in healthy individuals is disrupted in people with accelerated long-term forgetting (ALF) due to epilepsy. SWS is thought to play an active role in declarative memory in healthy individuals and, furthermore, electrographic epileptiform activity is often more prevalent during SWS than during wakefulness or other sleep stages. We studied the relationship between SWS and the benefit of sleep for memory retention using a word-pair associates task. In both the ALF and the healthy control groups, sleep conferred a memory benefit. However, the relationship between the amount of SWS and sleep-related memory benefits differed significantly between the groups. In healthy participants, the amount of SWS correlated positively with sleep-related memory benefits. In stark contrast, the more SWS, the smaller the sleep-related memory benefit in the ALF group. Therefore, contrary to its role in healthy people, SWS-associated brain activity appears to be deleterious for memory in patients with ALF.

Sleep deficits but no metabolic deficits in premanifest Huntington's disease.

OBJECTIVE: Huntington disease (HD) is a fatal autosomal dominant, neurodegenerative condition characterized by progressively worsening motor and nonmotor problems including cognitive and neuropsychiatric disturbances, along with sleep abnormalities and weight loss. However, it is not known whether sleep disturbances and metabolic abnormalities underlying the weight loss are present at a premanifest stage. METHODS: We performed a comprehensive sleep and metabolic study in 38 premanifest gene carrier individuals and 36 age- and sex-matched controls. The study consisted of 2 weeks of actigraphy at home, 2 nights of polysomnography and multiple sleep latency tests in the laboratory, and body composition assessment using dual energy x-ray absorptiometry scanning with energy expenditure measured over 10 days at home by doubly labeled water and for 36 hours in the laboratory by indirect calorimetry along with detailed cognitive and clinical assessments. We performed a principal component analyses across all measures within each studied domain. RESULTS: Compared to controls, premanifest gene carriers had more disrupted sleep, which was best characterized by a fragmented sleep profile. These abnormalities, as well as a theta power (4-7Hz) decrease in rapid eye movement sleep, were associated with disease burden score. Objectively measured sleep problems coincided with the development of cognitive, affective, and subtle motor deficits and were not associated with any metabolic alterations. INTERPRETATION: The results show that among the earliest abnormalities in premanifest HD is sleep disturbances. This raises questions as to where the pathology in HD begins and also whether it could drive some of the early features and even possibly the pathology.

Circadian regulation of slow waves in human sleep: Topographical aspects.

Slow waves (SWs, 0.5-4Hz) in field potentials during sleep reflect synchronized alternations between bursts of action potentials and periods of membrane hyperpolarization of cortical neurons. SWs decline during sleep and this is thought to be related to a reduction of synaptic strength in cortical networks and to be central to sleep's role in maintaining brain function. A central assumption in current concepts of sleep function is that SWs during sleep, and associated recovery processes, are independent of circadian rhythmicity. We tested this hypothesis by quantifying all SWs from 12 EEG derivations in 34 participants in whom 231 sleep periods were scheduled across the circadian cycle in a 10-day forced-desynchrony protocol which allowed estimation of the separate circadian and sleep-dependent modulation of SWs. Circadian rhythmicity significantly modulated the incidence, amplitude, frequency and the slope of the SWs such that the peaks of the circadian rhythms in these slow-wave parameters were located during the biological day. Topographical analyses demonstrated that the sleep-dependent modulation of SW characteristics was most prominent in frontal brain areas whereas the circadian effect was similar to or greater than the sleep-dependent modulation over the central and posterior brain regions. The data demonstrate that circadian rhythmicity directly modulates characteristics of SWs thought to be related to synaptic plasticity and that this modulation depends on topography. These findings have implications for the understanding of local sleep regulation and conditions such as ageing, depression, and neurodegeneration which are associated with changes in SWs, neural plasticity and circadian rhythmicity.