LZ Complexity Research Articles

Manifold learning and Lempel-Ziv complexity-based fault severity recognition method for bearing

The health condition of bearings was related to the operation status of mechanical equipment, and there were relatively few methods to recognize the severity of bearing faults. Although the Lempel-Ziv complexity (LZ complexity) has been proven to be effective in recognizing the bearing fault severity, the LZ was affected by noise. And the frequency band selection-based methods were used for noise reduction for LZ, which might cause the loss of frequency band information, and affect the accuracy of LZ. Aiming at this issue, this paper proposed a bearing fault severity recognition method based on manifold learning. Firstly, the original signal was reconstructed to high-dimensional phase space. Then, local tangent space alignment was used to extract effective signals aliased in noise. Finally, the LZ complexity was obtained according to the signal after noise reduction. The proposed method was verified by constructed data and the real experimental dataset of bearing, respectively. The results showed that the proposed method can be effectively used in the fault severity recognition of bearing.

Compression-Complexity Measures for Analysis and Classification of Coronaviruses

Finding a vaccine or specific antiviral treatment for a global pandemic of virus diseases (such as the ongoing COVID-19) requires rapid analysis, annotation and evaluation of metagenomic libraries to enable a quick and efficient screening of nucleotide sequences. Traditional sequence alignment methods are not suitable and there is a need for fast alignment-free techniques for sequence analysis. Information theory and data compression algorithms provide a rich set of mathematical and computational tools to capture essential patterns in biological sequences. In this study, we investigate the use of compression-complexity (Effort-to-Compress or ETC and Lempel-Ziv or LZ complexity) based distance measures for analyzing genomic sequences. The proposed distance measure is used to successfully reproduce the phylogenetic trees for a mammalian dataset consisting of eight species clusters, a set of coronaviruses belonging to group I, group II, group III, and SARS-CoV-1 coronaviruses, and a set of coronaviruses causing COVID-19 (SARS-CoV-2), and those not causing COVID-19. Having demonstrated the usefulness of these compression complexity measures, we employ them for the automatic classification of COVID-19-causing genome sequences using machine learning techniques. Two flavors of SVM (linear and quadratic) along with linear discriminant and fine K Nearest Neighbors classifer are used for classification. Using a data set comprising 1001 coronavirus sequences (causing COVID-19 and those not causing COVID-19), a classification accuracy of 98% is achieved with a sensitivity of 95% and a specificity of 99.8%. This work could be extended further to enable medical practitioners to automatically identify and characterize coronavirus strains and their rapidly growing mutants in a fast and efficient fashion.

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.

How do maternal emotional regulation difficulties modulate the mother-infant behavioral synchrony?

Mother-infant synchrony is one of the most important processes in the development of socio-affective competencies in children. While maternal abilities and psychopathology are related to maladaptive mother-infant synchrony, it is as yet unclear how maternal emotion regulation difficulties contribute to it. Based on a panel of behavioral indicators (i.e., gaze, vocal, and motor), the present study examined mother-infant synchrony at 6months of age in a modified version of Ainsworth's Strange Situation (n=72 dyads). Mother-infant interaction sequences were characterized by indicators of complexity (LZ complexity of joint behavioral sequences) and of synchronization quality (cross-recurrence plot quantification). Results showed that mothers' touch was greater in the reunion condition than in the initial condition. Mothers' motor behaviors were associated with the global levels of infants' behavioral involvement in the reunion condition, unlike the symmetrical influence observed between mothers and infants in the initial condition. Results show that maternal anxiety mediates the relationships between mothers' emotion regulation difficulties and gaze, vocal, and motor synchrony between mothers and infants in the initial and reunion conditions. This study emphasizes the central role of maternal emotion regulation difficulties in the establishment of maladaptive synchrony and in the adjustments of maternal physical contacts with infants.

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market.

The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.

Using Lempel-Ziv complexity as effective classification tool of the sleep-related breathing disorders

Background and objectivePeople suffer from sleep disorders caused by work-related stress, irregular lifestyle or mental health problems. Therefore, development of effective tools to diagnose sleep disorders is important. Recently, to analyze biomedical signals Information Theory is exploited. We propose efficient classification method of sleep anomalies by applying entropy estimating algorithms to encoded ECGs signals coming from patients suffering from Sleep-Related Breathing Disorders (SRBD). MethodsFirst, ECGs were discretized using the encoding method which captures the biosignals variability. It takes into account oscillations of ECG measurements around signals averages. Next, to estimate entropy of encoded signals Lempel–Ziv complexity algorithm (LZ) which measures patterns generation rate was applied. Then, optimal encoding parameters, which allow distinguishing normal versus abnormal events during sleep with high sensitivity and specificity were determined numerically. Simultaneously, subjects’ states were identified using acoustic signal of breathing recorded in the same period during sleep. ResultsRandom sequences show normalized LZ close to 1 while for more regular sequences it is closer to 0. Our calculations show that SRBDs have normalized LZ around 0.32 (on average), while control group has complexity around 0.85. The results obtained to public database are similar, i.e. LZ for SRBDs around 0.48 and for control group 0.7. These show that signals within the control group are more random whereas for the SRBD group ECGs are more deterministic. This finding remained valid for both signals acquired during the whole duration of experiment, and when shorter time intervals were considered. Proposed classifier provided sleep disorders diagnostics with a sensitivity of 93.75 and specificity of 73.00%. To validate our method we have considered also different variants as a training and as testing sets. In all cases, the optimal encoding parameter, sensitivity and specificity values were similar to our results above. ConclusionsOur pilot study suggests that LZ based algorithm could be used as a clinical tool to classify sleep disorders since the LZ complexities for SRBD positives versus healthy individuals show a significant difference. Moreover, normalized LZ complexity changes are related to the snoring level. This study also indicates that LZ technique is able to detect sleep abnormalities in early disorders stage.

Psychometrics of the Violence Nonlinear Dynamics Scale.

The trajectory of daily partner violence generally demonstrates nonlinear dynamics, and this nonlinearity is important to patient outcomes, as it is sometimes a stronger predictor of outcomes than violence frequency or severity. However, measurement of such dynamics is difficult, requiring complete time series data of sufficient length to yield stable measures. The purpose of this study was to develop a pencil-and-paper instrument to estimate violence nonlinearity and assess its psychometrics. Adult women (N = 143) who experienced violence in the previous month were enrolled from 6 primary care clinics. Baseline surveys assessed factors known to correlate with nonlinearity (partner's control strategies, violence appraisal, hope, social support, coping style) and violence dynamics using a 30-item instrument based on traditional characteristics of complex adaptive systems. Participants completed daily assessments of the previous day's violence using interactive voice response via telephone for 8 weeks, with data collection occurring between August 2013 and March 2015. Three different measures of nonlinearity were computed: LZ complexity (algorithmic complexity), approximate entropy (lack of regularity), and Lyapunov exponent (sensitivity to initial conditions). Using factor analysis and reliability measures, the final 10-item Violence Nonlinearity Dynamics Scale (VNDS) was identified. The VNDS was found to have both internal consistency (0.817) and split-half reliability (0.796). In addition, the instrument demonstrated concurrent (correlating with both the combined nonlinearity factor score [r = 0.267] and Grassberger-Procaccia entropy [r = 0.338]) and construct (correlating with 9 of 13 previously identified nonlinearity correlates) validity. The VNDS has both reliability and validity and could facilitate the inclusion of nonlinearity assessment in both intimate partner violence research and clinical work.

Nonlinear analysis of local field potentials and motor cortex EEG in spinocerebellar ataxia 3

This study explores the potential usefulness of EEG for patient diagnosis by analyzing SCA3 and wt mice. Self-made implantable electrodes were constructed and implanted to extract EEG signals from the cerebral motor cortex and the cerebellar areas that are affected by the disease. Nonlinear dynamic analysis and EEG energy were used to distinguish between SCA3 and WT mice, and we found that all four were increased in SCA3 mice. The alpha and theta bands of LZ complexity were significantly higher in SCA3 mice than in the control group. Therefore, it was possible to distinguish between the two groups by the LZ complexity of their alpha and theta bands. Analysis of C0 complexity and approximate entropy showed that the random part in the disease group was larger than in the control group, and that in addition the randomness was increased in SCA3 mice. The spatial learning and memory were analyzed by means of the Morris water maze test (MWM), The results showed that the swimming velocity, distance traveled and latency to reach the platform in SCA3 mice were increased when compared with WT mice during the 4 training days (p < 0.05, 0.01 or 0.001). And the results are conform to the results of EEG signals. In conclusion, EEG signals could be used to identify SCA3 in mice. They may also be clinically useful for the diagnosis of cerebellar ataxia in patients, and for additional studies aimed at gaining a deeper understanding of spinal cerebral ataxia.

Sequence similarity using composition method

Deoxyribo nucleic acid (DNA) has enormous capacity to carry very important information in the form of character strings. Sequence analysis is the process of applying a wide range of methods to DNA sequences for understanding the structure, feature or evolution of these nucleotides strings. The analysis uses mathematical methods to convert these character strings to numerical values, and these numerical values are used to find similarity between the sequences. DNA sequences only contain four nucleotides: A, C, G and T, but in order to find information from these sequences, sequence comparison becomes essential. In this paper, various methods to analyse DNA sequences including usage of entropy, divergence, LZ complexity and the role of hybridisation are explored. A hybrid model based on the composition vector and distance methods is proposed to find dissimilarity between sequences and this hybrid model is tested on sequences of species downloaded from National Center for Biotechnology Information (NCBI).

Chaos, Fractal and Recurrence Quantification Analysis of Surface Electromyography in Muscular Dystrophy

We analyze muscular dystrophy recorded by sEMG and use standard methodologies and nonlinear chaotic methods here including the RQA. We reach sufficient evidence that the sEMG signal contains a large chaotic component. We have estimated the correlation dimension (fractal measure), the largest Lyapunov exponent, the LZ complexity and the %Rec and %Det of the RQA demonstrating that such indexes are able to detect the presence of repetitive hidden patterns in sEMG which, in turn, senses the level of MU synchronization within the muscle. The results give also an interesting methodological indication in the sense that it evidences the manner in which nonlinear methods and RQA must be arranged and applied in clinical routine in order to obtain results of clinical interest. We have studied the muscular dystrophy and evidence that the continuous regime of chaotic transitions that we have in muscular mechanisms may benefit in this pathology by the use of the NPT treatment that we have considered in detail in our previous publications.

Prediction of antimicrobial peptides based on sequence alignment and support vector machine-pairwise algorithm utilizing LZ-complexity.

This study concerns an attempt to establish a new method for predicting antimicrobial peptides (AMPs) which are important to the immune system. Recently, researchers are interested in designing alternative drugs based on AMPs because they have found that a large number of bacterial strains have become resistant to available antibiotics. However, researchers have encountered obstacles in the AMPs designing process as experiments to extract AMPs from protein sequences are costly and require a long set-up time. Therefore, a computational tool for AMPs prediction is needed to resolve this problem. In this study, an integrated algorithm is newly introduced to predict AMPs by integrating sequence alignment and support vector machine- (SVM-) LZ complexity pairwise algorithm. It was observed that, when all sequences in the training set are used, the sensitivity of the proposed algorithm is 95.28% in jackknife test and 87.59% in independent test, while the sensitivity obtained for jackknife test and independent test is 88.74% and 78.70%, respectively, when only the sequences that has less than 70% similarity are used. Applying the proposed algorithm may allow researchers to effectively predict AMPs from unknown protein peptide sequences with higher sensitivity.

Dynamics of violence.

Three behavioural models suggest different dynamic patterns of intimate partner violence (IPV). However, few studies permit assessment of IPV dynamics. The purpose of this study was to estimate the degree of non-linearity in daily violence between partners over a 3-month period, identify their specific dynamic patterns and determine whether measures of violence severity and dynamics are interrelated. From six primary care clinics, we enrolled 200 adult women who experienced violence in the previous month and asked them to complete daily telephone assessments of household environment, marital relationship and violence using Interactive Verbal Response. To assess non-linearity of violence, algorithmic complexity was measured by LZ complexity and lack of regularity was measured by approximate entropy. Lyapunov exponents and correlation dimension saturation were used to approximate dynamic patterns. Of the 9618 daily reports, women reported experiencing abuse on 39% of days, while perpetrating violence themselves on 23% of days. Most (59%) displayed random dynamics, 30% showed chaotic and 12% showed periodic dynamics. All three measures of non-linearity consistently demonstrated non-linear patterns of violence. Using multivariate analysis of variance, neither episode severity for men or women showed significant differences across dynamic types, but chaotic dynamics had the lowest frequencies of violence in men and women while random dynamics had the highest frequencies. Approximate entropy was positively correlated with violence frequency and burden in men and women, but Lyapunov exponent was inversely related to violence. LZ complexity correlated positively with wife-perpetrated violence only. IPV is rarely a predictable, periodic phenomenon; no behavioural model describes the violence dynamics for all violent relationships. Yet, the measures of non-linearity and specific dynamic patterns correlate with different violent features of these relationships.

Comparing RNA Secondary Structures Based on LZ Complexity

Abstract In this paper, we propose a new similarity measure to compare RNA secondary structure. We first transform an RNA secondary structure into three characteristic sequences. Then, based on these characteristic sequences, we calculate their LZ complexity. Finally, we obtain the similarity/dissimilarity matrix based on the LZ complexity, and make a comparison for the secondary structures at the 3′-terminus belonging to nine different species. The proposed method does not require multiple alignments and is easy to operate. This method will also be useful to researchers who are interested in evolutionary analysis.

Phylogenetic analysis of DNA sequences based on the generalized pseudo-amino acid composition

The main work of this paper is to propose a new theory and method, which is based on the idea of the pseudo-amino acid composition, for phylogenetic analysis of DNA primary sequences. In our method, we revise the part of the occurrence frequency of 20 amino acids in the method of the pseudo-amino acid composition by replacing the frequency of 16 dinucleotides. And we select eight LZ complexity factors of eight (0,1) sequences of a DNA primary sequence as PseAA components. Finally, we characterize a DNA sequence with a 24-dimensional vector. We reconstruct the phylogenetic trees of two datasets. The results show that our method is efficient and significant.

A Complexity-based Method to Compare RNA Secondary Structures and its Application

With the rapid emergence of RNA structure databases recently, efficient methods for RNA structure comparison are in demand for function prediction and evolutionary analysis. In this paper, we transform the complex secondary structure into the linear characteristic sequence which contains the information on primary sequence and the base pairing, and introduce the linear characteristic sequences into similarity analysis and phylogenetic analysis by using conditional LZ complexity. The results obtained from the two sets of real data have shown that our proposed method is effectual and feasible.

Comparison of TOPS strings based on LZ complexity

Topology of protein structure (TOPS) cartoons are simplified descriptions of structural topology of proteins in 2D. This is coarse level description of protein structure. The comparison of protein structures is very important for the study of protein functions, and for the analysis of possible evolutionary relationships. In this paper, we use LZ algorithm to compare TOPS strings.

Comparison between Fetal Heart Rate Standard Parameters and Complexity Indexes for the Identification of Severe Intrauterine Growth Restriction

The intrauterine growth restriction (IUGR) is a pathological state: the fetus is at risk of hypoxia and this condition is associated with increased perinatal morbidity and mortality. However, evidence-based guidelines for clinical surveillance are poor and lack reliable indexes. This study introduces new procedures to extract parameters from the fetal heart rate signal in order to identify severe intrauterine growth restricted (IUGR) fetuses Standard parameters (time domain and frequency domain indexes) are compared to a new parameter, the Lempel Ziv complexity, and to two regularity estimators (approximate entropy and sample entropy). The paper analyzes the robustness of the indexes coming from the parameter extraction procedure. The results show that the LZ complexity is a stable parameter and it is able to significantly discriminate the severe IUGR (preterm delivered) from moderate IUGR (at term delivered) and from healthy fetuses.

Interpretation of the Lempel-Ziv Complexity Measure in the Context of Biomedical Signal Analysis

Lempel-Ziv complexity (LZ) and derived LZ algorithms have been extensively used to solve information theoretic problems such as coding and lossless data compression. In recent years, LZ has been widely used in biomedical applications to estimate the complexity of discrete-time signals. Despite its popularity as a complexity measure for biosignal analysis, the question of LZ interpretability and its relationship to other signal parameters and to other metrics has not been previously addressed. We have carried out an investigation aimed at gaining a better understanding of the LZ complexity itself, especially regarding its interpretability as a biomedical signal analysis technique. Our results indicate that LZ is particularly useful as a scalar metric to estimate the bandwidth of random processes and the harmonic variability in quasi-periodic signals.

Similarity analysis of DNA sequences based on the generalized LZ complexity of (0,1)-sequences

Based on the permutation of a binary alphabet, four generalized LZ complexities of a (0,1)-sequence are introduced. Since the logical representation of a DNA primary sequence includes four logical sequences, a DNA primary sequence can be characterized by a 16-D vector whose entries are the complexities corresponding to the logical sequences. The utility of the new quantitative characterization of DNA sequences is illustrated by an examination of the similarity among the full β-globin genes of 11 different species.

A weighted measure for the similarity analysis of DNA sequences

Here we propose a weighted measure for the similarity analysis of DNA sequences. It is based on LZ complexity and (0,1) characteristic sequences of DNA sequences. This weighted measure enables biologists to extract similarity information from biological sequences according to their requirements. For example, by this weighted measure, one can obtain either the full similarity information or a similarity analysis from a given biological aspect. Moreover, the length of DNA sequence is not problematic. The application of the weighted measure to the similarity analysis of beta-globin genes from nine species shows its flexibility.