Lempel-Ziv Complexity Measure Research Articles

Possible Neuropathological Mechanisms Underlying the Increased Complexity of Brain Electrical Activity in Schizophrenia: A Computational Study.

Objective: Schizophrenia is a complex neurodevelopmental illness that is associated with different deficits in the cerebral cortex and neural networks, resulting in irregularity of brain waves. Various neuropathological hypotheses have been proposed for this irregularity that we intend to examine in this computational study. Method : We used a mathematical model of a neuronal population based on cellular automata to examine two hypotheses about the neuropathology of schizophrenia: first, reducing neuronal stimulation thresholds to increase neuronal excitability; and second, increasing the percentage of excitatory neurons and decreasing the percentage of inhibitory neurons to increase the excitation to inhibition ratio in the neuronal population. Then, we compare the complexity of the output signals produced by the model in both cases with real healthy resting-state electroencephalogram (EEG) signals using the Lempel-Ziv complexity measure and see if these changes alter (increase or decrease) the complexity of the neuronal population dynamics. Results: By lowering the neuronal stimulation threshold (i.e., the first hypothesis), no significant change in the pattern and amplitude of the network complexity was observed, and the model complexity was very similar to the complexity of real EEG signals (P > 0.05). However, increasing the excitation to inhibition ratio (i.e., the second hypothesis) led to significant changes in the complexity pattern of the designed network (P < 0.05). More interestingly, in this case, the complexity of the output signals of the model increased significantly compared to real healthy EEGs (P = 0.002) and the model output of the unchanged condition (P = 0.028) and the first hypothesis (P = 0.001). Conclusion: Our computational model suggests that imbalances in the excitation to inhibition ratio in the neural network are probably the source of abnormal neuronal firing patterns and thus the cause of increased complexity of brain electrical activity in schizophrenia.

Permutation Lempel-Ziv 복잡성 척도를 적용한 근 피로도 추정

A new approach for quantifying muscle fatigue is presented by analyzing the deterministic complexity in the surface electromyogram(SEMG) using Permutation Lempel-Ziv(PLZ) complexity measure. The PLZ complexity measure provide a metric for the number of distinct deterministic patterns in signals by combining permutation patterns and Lempel-Ziv complexity analysis. For muscle fatigue experiment by using PLZ complexity measure, surface EMG signals from eleven subjects were recorded in biceps brachii muscle with constant isometric 20, 50, and 80%MVC contractions. The PLZ complexity measure is evaluated with the performance of muscle fatigue estimation for the SEMG signals compared to the performance of previous reported LZ complexity measure. This PLZ complexity measure has advantages that is computationally easy to compute and does not require any assumptions about the stationarity of the SEMG signal.

Multiscale Permutation Lempel-Ziv Complexity Measure for Biomedical Signal Analysis: Interpretation and Application to Focal EEG Signals.

This paper analyses the complexity of electroencephalogram (EEG) signals in different temporal scales for the analysis and classification of focal and non-focal EEG signals. Futures from an original multiscale permutation Lempel–Ziv complexity measure (MPLZC) were obtained. MPLZC measure combines a multiscale structure, ordinal analysis, and permutation Lempel–Ziv complexity for quantifying the dynamic changes of an electroencephalogram (EEG). We also show the dependency of MPLZC on several straight-forward signal processing concepts, which appear in biomedical EEG activity via a set of synthetic signals. The main material of the study consists of EEG signals, which were obtained from the Bern-Barcelona EEG database. The signals were divided into two groups: focal EEG signals (n = 100) and non-focal EEG signals (n = 100); statistical analysis was performed by means of non-parametric Mann–Whitney test. The mean value of MPLZC results in the non-focal group are significantly higher than those in the focal group for scales above 1 (p < 0.05). The result indicates that the non-focal EEG signals are more complex. MPLZC feature sets are used for the least squares support vector machine (LS-SVM) classifier to classify into the focal and non-focal EEG signals. Our experimental results confirmed the usefulness of the MPLZC method for distinguishing focal and non-focal EEG signals with a classification accuracy of 86%.

Consistency of local activation parameters at sensor- and source-level in neural signals

Objective. Although magnetoencephalography and electroencephalography (M/EEG) signals at sensor level are robust and reliable, they suffer from different degrees of distortion due to changes in brain tissue conductivities, known as field spread and volume conduction effects. To estimate original neural generators from M/EEG activity acquired at sensor level, diverse source localisation algorithms have been proposed; however, they are not exempt from limitations and usually involve time-consuming procedures. Connectivity and network-based M/EEG analyses have been found to be affected by field spread and volume conduction effects; nevertheless, the influence of the aforementioned effects on widely used local activation parameters has not been assessed yet. The goal of this study is to evaluate the consistency of various local activation parameters when they are computed at sensor- and source-level. Approach. Six spectral (relative power, median frequency, and individual alpha frequency) and non-linear parameters (Lempel-Ziv complexity, sample entropy, and central tendency measure) are computed from M/EEG signals at sensor- and source-level using four source inversion methods: weighted minimum norm estimate (wMNE), standardised low-resolution brain electromagnetic tomography (sLORETA), linear constrained minimum variance (LCMV), and dynamical statistical parametric mapping (dSPM). Main results. Our results show that the spectral and non-linear parameters yield similar results at sensor- and source-level, showing high correlation values between them for all the source inversion methods evaluated and both modalities of signal, EEG and MEG. Furthermore, the correlation values remain high when performing coarse-grained spatial analyses. Significance. To the best of our knowledge, this is the first study analysing how field spread and volume conduction effects impact on local activation parameters computed from resting-state neural activity. Our findings evidence that local activation parameters are robust against field spread and volume conduction effects and provide equivalent information at sensor- and source-level even when performing regional analyses.

The Lempel–Ziv measure based pedigree map to detect and evaluate correlation between aero-engine gas path system variables

There is a great interest in studying complexity of the aero-engine gas path time series. This paper presents a Lempel–Ziv complexity measure for analysis of aero-engine gas path system signals. By applying a binary Lempel–Ziv measure to define the absolute distance between two non-null numerical sequences, the pedigree map of systemic clustering is constructed to provide a metric for the number of distinct deterministic patterns. And then, we propose a ternary Lempel–Ziv measure, improving on the binary Lempel–Ziv measure, and making it more suited for the analysis of aero-engine gas path time series. The results indicate that the maps, demonstrating the relationship between parameters, based on ternary Lempel–Ziv measure are more vivid than the map based on binary Lempel–Ziv measure.

BOLD temporal variability differentiates wakefulness from anesthesia-induced unconsciousness.

Even though a number of findings, based on information content or information integration, are shown to define neural underpinnings characteristic of a conscious experience, the neurophysiological mechanism of consciousness is still poorly understood. Here, we investigated the brain activity and functional connectivity changes that occur in the isoflurane-anesthetized unconscious state in contrast to the awake state in rats (awake and/or anesthetized, n = 68 rats). We examined nine information measures previously shown to distinguish between conscious states: blood oxygen level-dependent (BOLD) variability, functional connectivity strength, modularity, weighted modularity, efficiency, clustering coefficient, small-worldness, and spatial and temporal Lempel-Ziv complexity measure. We also identified modular membership, seed-based network connectivity, and absolute and normalized power spectrums to assess the integrity of the BOLD functional networks between awake and anesthesia. fMRI BOLD variability and related absolute power were the only information measures significantly higher during the awake state compared with isoflurane anesthesia across animals, and with varying levels of anesthesia, after correcting for motion and respiration confounds. Thus, we conclude that, at least under the specific conditions examined here, global measures of information integration/sharing do not properly distinguish the anesthetized state from wakefulness, and heightened overall, global and local, BOLD variability is the most reliable determinant of conscious brain activity relative to isoflurane anesthesia. NEW & NOTEWORTHY Multiple metrics previously suggested to be able to distinguish between states of consciousness were compared, within and across rats in awake and isoflurane anesthesia-induced unconsciousness. All measures tested showed sensitivity to confounds, correcting for motion and for respiration changes due to anesthesia. Resting state local BOLD variability and the related absolute power were the only information measures that robustly differentiated wakefulness states. These results caution against the general applicability of global information measures in identifying levels of consciousness, thus challenging the popular concept that these measures reflect states of consciousness, and also pointing to local signal variability as a more reliable indicator of states of wakefulness.

Increased spontaneous MEG signal diversity for psychoactive doses of ketamine, LSD and psilocybin

What is the level of consciousness of the psychedelic state? Empirically, measures of neural signal diversity such as entropy and Lempel-Ziv (LZ) complexity score higher for wakeful rest than for states with lower conscious level like propofol-induced anesthesia. Here we compute these measures for spontaneous magnetoencephalographic (MEG) signals from humans during altered states of consciousness induced by three psychedelic substances: psilocybin, ketamine and LSD. For all three, we find reliably higher spontaneous signal diversity, even when controlling for spectral changes. This increase is most pronounced for the single-channel LZ complexity measure, and hence for temporal, as opposed to spatial, signal diversity. We also uncover selective correlations between changes in signal diversity and phenomenological reports of the intensity of psychedelic experience. This is the first time that these measures have been applied to the psychedelic state and, crucially, that they have yielded values exceeding those of normal waking consciousness. These findings suggest that the sustained occurrence of psychedelic phenomenology constitutes an elevated level of consciousness - as measured by neural signal diversity.

Cryptanalysis of a family of 1D unimodal maps

In this paper, we proposed a topologically conjugate map, equivalent to the well known logistic map. This constructed map is defined on the integer domain [0, 2 n ) with a view to be used as a random number generator (RNG) based on an integer domain as is the required in classical cryptography. The maps were found to have a one to one correspondence between points in their respective defining intervals defined on an n-bits precision. The dynamics of the proposed map similar with that of the logistic map, in terms of the Lyapunov exponents with the control parameter. This similarity between the curves indicates topological conjugacy between the maps. With a view to be applied in cryptography as a Pseudo-Random number generator (PRNG), the complexity of the constructed map as a source of randomness is determined using both the permutation entropy (PE) and the Lempel-Ziv (LZ-76) complexity measures, and the results are compared with numerical simulations.

Analysis of altered complexity of gait dynamics with aging and Parkinson’s disease using ternary Lempel–Ziv complexity

Abstract Fluctuations in stride interval series show complex dynamical behavior in healthy young adults. Hypothesizing that these stride interval complexity changes would be altered by changes in neurological function associated with aging and certain disease states, we aimed to develop a tool to facilitate clinical judgments to assess the complex dynamical behavior in the stride series in discerning young, elderly, and Parkinson’s disease (PD) classes. This novel approach, which employs a new variant of coarse-graining in conjunction with Lempel–Ziv complexity measure, yields useful, reliable, and predictive results. We also show the presence of nonlinear deterministic structures in the stride time series and appropriateness of the application of our nonlinear approach through surrogate data analysis. The findings show that the fluctuations are more complex/random in elderly and PD classes than those in young class. These findings may add to the growing body of literature supporting the clinical utility of this new approach to stride time series.

Early diagnosis of threatened premature labor by electrohysterographic recordings – The use of digital signal processing

Prevention and early diagnosis of imminent preterm labor are considered to be the most important perinatal challenge nowadays. Significant progress has been observed on postnatal care of premature infants, but without reducing the prevalence of preterm delivery.Our study was focused on comparison of three methods of spectral analysis of electrohysterographic (EHG) signals: fast Fourier transform (FFT), wavelet transform (WT) and autoregressive modeling (AR). Complexity of the electrohysterographic signals was analyzed by using: the approximate entropy (ApEn), Lempel–Ziv complexity measure (L–Z). Additionally, the work evaluated the applicability of EHG in diagnosing imminent premature labor.EHG signals were recorded among 60 patients with threatened preterm labor symptoms between the 24th and 34th week of pregnancy. Patients included to the study had a shortened cervix (less than 20mm) without regular uterine contractions recorded on regular cardiotocography (CTG). The women were divided into two groups: those delivering within 7 days – group A (n=15) and women delivering after 7 days – group B (n=45).The study confirmed differences in bioelectrical activity of uterus between patients delivering prematurely within 7 days and after from the EHG registration for all analyzed methods.

Lempel-Ziv complexity analysis of one dimensional cellular automata.

Lempel-Ziv complexity measure has been used to estimate the entropy density of a string. It is defined as the number of factors in a production factorization of a string. In this contribution, we show that its use can be extended, by using the normalized information distance, to study the spatiotemporal evolution of random initial configurations under cellular automata rules. In particular, the transfer information from time consecutive configurations is studied, as well as the sensitivity to perturbed initial conditions. The behavior of the cellular automata rules can be grouped in different classes, but no single grouping captures the whole nature of the involved rules. The analysis carried out is particularly appropriate for studying the computational processing capabilities of cellular automata rules.

Permutation Lempel–Ziv complexity measure of electroencephalogram in GABAergic anaesthetics

Monitoring the brain state in anaesthesia is crucial for clinical doctors. In this study, we propose a novel nonlinear method, the permutation Lempel–Ziv complexity (PLZC) index, which describes the complexity in the electroencephalographic (EEG) signal to quantify the effect of GABAergic anaesthetics on brain activities.We applied the PLZC to two EEG data sets that were recorded under sevoflurane and propofol anaesthesia. The results are compared with traditional mean value-based Lempel–Ziv complexity (LZC), permutation entropy (PE), composite PE index (CPEI), response entropy (RE), state entropy (SE) and bispectral index (BIS) or SynchFastSlow (SFS, derived from BIS). Pharmacokinetic/pharmacodynamic (PK/PD) modelling and prediction probability () were used to assess the performance of the proposed method for tracking GABAergic anaesthetic concentrations.We found that PLZC correlates closely with the anaesthetic drug effect. When applied in sevoflurane anaesthesia, the coefficient of determination between the PLZC values and the sevoflurane effect site concentrations was (, mean ± standard deviation), and the prediction probability was (). These values were higher than those for the other indices. While in propofol anaesthesia, the value of between PLZC and the effect site concentrations was (), and the was (), which were close to those for CPEI but better than those for the others.PLZC based on electroencephalogram signals can be used as a new index to characterize the depth of anaesthesia. This index outperformed LZC, PE, CPEI, RE, SE, and BIS or SFS in tracking drug concentration changes during GABAergic anaesthetics.PLZC is a potentially superior method for applications in intra-operative monitoring.

A permutation Lempel-Ziv complexity measure for EEG analysis

ObjectiveIn this study we develop a new complexity measure of time series by combining ordinal patterns and Lempel-Ziv complexity (LZC) for quantifying the dynamical changes of EEG. MethodsA neural mass model (NMM) was used to simulate EEG data and test the performance of the permutation Lempel-Ziv complexity (PLZC) in tracking the dynamical changes of signals against different white noise levels. Then, the PLZC was applied to real EEG data to investigate whether it was able to detect the different states of anesthesia and epileptic seizures. The Z-score model, two-way ANOVA and t-test were used to estimate the significance of the results. ResultsPLZC could successfully track the dynamical changes of EEG series generated by the NMM. Compared with the other four classical LZC based methods, the PLZC was most robust against white noise. In real data analysis, PLZC was effective in differentiating the different anesthesia states and sensitive in detecting epileptic seizures. ConclusionsPLZC is simple, robust and effective for quantifying the dynamical changes of EEG. SignificanceWe suggest that PLZC is a potential nonlinear method for characterizing the changes in EEG signal.

Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures

‘Complexity’ has several definitions in diverse fields. These measures are indicators of some aspects of the nature of the signal. Such measures are used to analyse and classify signals and as a signal diagnostics tool to distinguish between periodic, quasiperiodic, chaotic and random signals. Lempel–Ziv (LZ) complexity and approximate entropy (ApEn) are such popular complexity measures that are widely used for characterizing biological signals also. In this paper, we compare the utility of ApEn, LZ complexities and Shannon’s entropy in characterizing data from a nonlinear chaotic map (logistic map). In this work, we show that LZ and ApEn complexity measures can characterize the data complexities correctly for data sequences as short as 20 in length while Shannon’s entropy fails for length less than 50. In the case of noisy sequences with 10% uniform noise, Shannon’s entropy works only for lengths greater than 200 while LZ and ApEn are successful with sequences of lengths greater than 30 and 20, respectively.

Multi-body vibration modelling of ball bearing–rotor system considering single and compound multi-defects

Vibration modelling is a key link to explore the cognitive rules in fault diagnosis. In order to foresee the vibration characteristics accurately, the dynamic contact among joint interfaces and vibration transmission path of ball bearing are well studied. A novel methodology for multi-body vibration modelling of ball bearing–rotor system with bearing inner race–balls–outer race–pedestal is presented. Additionally, the mathematical formulation is derived with consideration of the nonlinear spring at the contact point between ball and raceway. Then, the progressive processes of single and compound multi-defects are described by using bearing practical kinematics and the vibration responses are systematically analysed. Compared with the experimental results, the fault frequency and its harmonic components are clearly observed and achieved better consistency. Moreover, for compound fault, an important observation is that the strength imbalance and mutual restraint of the vibration amplitude due to the vectors superposition of different frequency components. Further, the Lempel–Ziv complexity measure is also employed to investigate the response of signature variations. The results show that the Lempel–Ziv complexity measure used as a quantitative criterion can effectively evaluate the single and compound fault of ball bearings.

On the non-randomness of maximum Lempel Ziv complexity sequences of finite size

Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. We discuss that, for a finite length, maximum Lempel-Ziv sequences can be built from a well defined generating algorithm, which makes them of low Kolmogorov-Chaitin complexity, quite the opposite to randomness. It will be discussed that Lempel-Ziv measure is, in this sense, less general than Kolmogorov-Chaitin complexity, as it can be fooled by an intelligent enough agent. The latter will be shown to be the case for the binary expansion of certain irrational numbers. Maximum Lempel-Ziv sequences induce a normalization that gives good estimates of entropy rate for several sources, while keeping bounded values for all sequence length, making it an alternative to other normalization schemes in use.

A classification system to discriminate epileptic patients using multi-valued coarse-graining Lempel-Ziv complexity

A classification system to discriminate epileptic subjects from healthy subjects is proposed. All the previous research to detect epileptic seizures/patients using Lempel-Ziv complexity measure had used Binary Coarse-Graining (BLZC). In this work, we show that employing multi-valued coarse-graining Lempel-Ziv complexity (MLZC) improves the performance of classification. This finding is confirmed using Receiver Operating Characteristic (ROC) plots. Both the measures yielded excellent results with the MLZC showing improved results with, a sensitivity of 96.6%, specificity of 100%, precision of 100% and an accuracy of 98.3%. The classification system in this paper will be a valuable asset to the clinician in the separation of epileptic patients from the healthy group.

A Lempel–Ziv complexity measure for muscle fatigue estimation

This paper presents a Lempel–Ziv complexity measure for analysis of surface electromyography signals. The Lempel–Ziv measure provides a metric for the number of distinct deterministic patterns and the rate of their creation in signals. We propose a ternary Lempel–Ziv measure, improving upon the binary Lempel–Ziv measure, and making it more suited for the analysis of biological signals. The Lempel–Ziv measure is evaluated with a muscle fatigue experiment in which participants perform static, cyclic, and random contractions. Results show this complexity measure shows a greater correlation to a steadily increasing muscle fatigue level compared to the conventional median frequency. This measure is computationally easy to compute and does not require power spectrum estimation and signal stationarity assumptions.

Complexity analysis of CO concentrations at a traffic site in Delhi

The Lempel–Ziv complexity measure is used to examine the complexity in carbon monoxide concentration emissions over time. Rescaled range analysis and dispersion analysis is also carried out to confirm the findings. For this, time series of carbon monoxide concentrations observed between 2000 and 2009 at a traffic site in Delhi are used to examine separately the entire time series, and the series by years and months. The presence of complexity is observed in carbon monoxide concentrations over the period. The analysis showed the long-range correlations up to 15 months. The Lempel–Ziv complexity of time series over different years however indicates complexity in all the years except 2000, 2001 and 2006, reflecting the probable impact of control measures in Delhi.

Complexity analysis of the cerebrospinal fluid pulse waveform during infusion studies

Nonlinear dynamics has enhanced the diagnostic abilities of some physiological signals. Recent studies have shown that the complexity of the intracranial pressure waveform decreases during periods of intracranial hypertension in paediatric patients with acute brain injury. We wanted to assess changes in the complexity of the cerebrospinal fluid (CSF) pressure signal over the large range covered during the study of CSF circulation with infusion studies. We performed 37 infusion studies in patients with hydrocephalus of various types and origin (median age 71 years; interquartile range 60-77 years). After 5 min of baseline measurement, infusion was started at a rate of 1.5 ml/min until a plateau was reached. Once the infusion finished, CSF pressure was recorded until it returned to baseline. We analysed CSF pressure signals using the Lempel-Ziv (LZ) complexity measure. To characterise more accurately the behaviour of LZ complexity, the study was segmented into four periods: basal, early infusion, plateau and recovery. The LZ complexity of the CSF pressure decreased in the plateau of the infusion study compared to the basal complexity (p=0.0018). This indicates loss of complexity of the CSF pulse waveform with intracranial hypertension. We also noted that the level of complexity begins to increase when the infusion is interrupted and CSF pressure drops towards the initial values. The LZ complexity decreases when CSF pressure reaches the range of intracranial hypertension during infusion studies. This finding provides further evidence of a phenomenon of decomplexification in the pulsatile component of the pressure signal during intracranial hypertension.