Entropy-based early detection of critical transitions in spatial vegetation fields.

In semiarid regions, vegetated ecosystems can display abrupt and unexpected changes, i.e., transitions to different states, due to drifting or time-varying parameters, with severe consequences for the ecosystem and the communities depending on it. Despite intensive research, the early identification of an approaching critical point from observations is still an open challenge. Many data analysis techniques have been proposed, but their performance depends on the system and on the characteristics of the observed data (the resolution, the level of noise, the existence of unobserved variables, etc.). Here, we propose an entropy-based approach to identify an upcoming transition in spatiotemporal data. We apply this approach to observational vegetation data and simulations from two models of vegetation dynamics to infer the arrival of an abrupt shift to an arid state. We show that the permutation entropy (PE) computed from the probabilities of two-dimensional ordinal patterns may provide an early warning indicator of an approaching tipping point, as it may display a maximum (or minimum) before decreasing (or increasing) as the transition approaches. Like other spatial early warning indicators, the spatial permutation entropy does not need a time series of the system dynamics, and it is suited for spatially extended systems evolving on long time scales, like vegetation plots. We quantify its performance and show that, depending on the system and data, the performance can be better, similar or worse than the spatial correlation. Hence, we propose the spatial PE as an additional indicator to try to anticipate regime shifts in vegetated ecosystems.

Permutation entropy-derived parameters to estimate the epileptogenic zone network.

OBJECTIVE: Quantification of the epileptogenic zone network (EZN) most frequently implies analysis of seizure onset. However, important information can also be obtained from the postictal period, characterized by prominent changes in the EZN. We used permutation entropy (PE), a measure of signal complexity, to analyze the peri-ictal stereoelectroencephalography (SEEG) signal changes with emphasis on the postictal state. We sought to determine the best PE-derived parameter (PEDP) for identifying the EZN. METHODS: Several PEDPs were computed retrospectively on SEEG-recorded seizures of 86 patients operated on for drug-resistant epilepsy: mean baseline preictal entropy, minimum ictal entropy, maximum postictal entropy, the ratio between the maximum postictal and the minimum ictal entropy, and the ratio between the maximum postictal and the baseline preictal entropy. The performance of each biomarker was assessed by comparing the identified epileptogenic contacts or brain regions against the EZN defined by clinical analysis incorporating the Epileptogenicity Index and the connectivity epileptogenicity index methods (EZNc), using the receiver-operating characteristic and precision-recall. RESULTS: The ratio between the maximum postictal and the minimum ictal entropy (defined as the Permutation Entropy Index [PEI]) proved to be the best-performing PEDP to identify the EZNC . It demonstrated the highest area under the curve (AUC) and F1 score at the contact level (AUC 0.72; F1 0.39) and at the region level (AUC 0.78; F1 0.47). PEI values gradually decreased between the EZN, the propagation network, and the non-involved regions. PEI showed higher performance in patients with slow seizure-onset patterns than in those with fast seizure-onset patterns. The percentage of resected epileptogenic regions defined by PEI was significantly correlated with surgical outcome. SIGNIFICANCE: PEI is a promising tool to improve the delineation of the EZN. PEI combines ease and robustness in a routine clinical setting with high sensitivity for seizures without fast activity at seizure onset.

Data-Driven Structural Health Monitoring: Leveraging Amplitude-Aware Permutation Entropy of Time Series Model Residuals for Nonlinear Damage Diagnosis.

In structural health monitoring (SHM), most current methods and techniques are based on the assumption of linear models and linear damage. However, the damage in real engineering structures is more characterized by nonlinear behavior, including the appearance of cracks and the loosening of bolts. To solve the structural nonlinear damage diagnosis problem more effectively, this study combines the autoregressive (AR) model and amplitude-aware permutation entropy (AAPE) to propose a data-driven damage detection method. First, an AR model is built for the acceleration data from each structure sensor in the baseline state, including determining the model order using a modified iterative method based on the Bayesian information criterion (BIC) and calculating the model coefficients. Subsequently, in the testing phase, the residuals of the AR model are extracted as damage-sensitive features (DSFs), and the AAPE is calculated as a damage classifier to diagnose the nonlinear damage. Numerical simulation of a six-story building model and experimental data from a three-story frame structure at the Los Alamos Laboratory are utilized to illustrate the effectiveness of the proposed methodology. In addition, to demonstrate the advantages of the present method, we analyzed AAPE in comparison with other advanced univariate damage classifiers. The numerical and experimental results demonstrate the proposed method's advantages in detecting and localizing minor damage. Moreover, this method is applicable to distributed sensor monitoring systems.

An in-depth analysis of parameter settings and probability distributions of specific ordinal patterns in the Shannon permutation entropy during different states of consciousness in humans.

As electrical activity in the brain has complex and dynamic properties, the complexity measure permutation entropy (PeEn) has proven itself to reliably distinguish consciousness states recorded by the EEG. However, it has been shown that the focus on specific ordinal patterns instead of all of them produced similar results. Moreover, parameter settings influence the resulting PeEn value. We evaluated the impact of the embedding dimension m and the length of the EEG segment on the resulting PeEn. Moreover, we analysed the probability distributions of monotonous and non-occurring ordinal patterns in different parameter settings. We based our analyses on simulated data as well as on EEG recordings from volunteers, obtained during stable anaesthesia levels at defined, individualised concentrations. The results of the analysis on the simulated data show a dependence of PeEn on different influencing factors such as window length and embedding dimension. With the EEG data, we demonstrated that the probability P of monotonous patterns performs like PeEn in lower embedding dimension (m = 3, AUC = 0.88, [0.7, 1] in both), whereas the probability P of non-occurring patterns outperforms both methods in higher embedding dimensions (m = 5, PeEn: AUC = 0.91, [0.77, 1]; P(non-occurring patterns): AUC = 1, [1, 1]). We showed that the accuracy of PeEn in distinguishing consciousness states changes with different parameter settings. Furthermore, we demonstrated that for the purpose of separating wake from anaesthesia EEG solely pieces of information used for PeEn calculation, i.e., the probability of monotonous patterns or the number of non-occurring patterns may be equally functional.

Separation of responsive and unresponsive patients under clinical conditions: comparison of symbolic transfer entropy and permutation entropy.

Electroencephalogram (EEG)-based monitoring during general anesthesia may help prevent harmful effects of high or low doses of general anesthetics. There is currently no convincing evidence in this regard for the proprietary algorithms of commercially available monitors. The purpose of this study was to investigate whether a more mechanism-based parameter of EEG analysis (symbolic transfer entropy, STE) can separate responsive from unresponsive patients better than a strictly probabilistic parameter (permutation entropy, PE) under clinical conditions. In this prospective single-center study, the EEG of 60 surgical ASA I-III patients was recorded perioperatively. During induction of and emergence from anesthesia, patients were asked to squeeze the investigators' hand every 15s. Time of loss of responsiveness (LoR) during induction and return of responsiveness (RoR) during emergence from anesthesia were registered. PE and STE were calculated at -15s and +30s of LoR and RoR and their ability to separate responsive from unresponsive patients was evaluated using accuracy statistics. 56 patients were included in the final analysis. STE and PE values decreased during anesthesia induction and increased during emergence. Intra-individual consistency was higher during induction than during emergence. Accuracy values during LoR and RoR were 0.71 (0.62-0.79) and 0.60 (0.51-0.69), respectively for STE and 0.74 (0.66-0.82) and 0.62 (0.53-0.71), respectively for PE. For the combination of LoR and RoR, values were 0.65 (0.59-0.71) for STE and 0.68 (0.62-0.74) for PE. The ability to differentiate between the clinical status of (un)responsiveness did not significantly differ between STE and PE at any time. Mechanism-based EEG analysis did not improve differentiation of responsive from unresponsive patients compared to the probabilistic PE.Trial registration: German Clinical Trials Register ID: DRKS00030562, November 4, 2022, retrospectively registered.

Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers.

This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen-Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.

Tsallis Entropy-Based Complexity-IPE Casualty Plane: A Novel Method for Complex Time Series Analysis.

Due to its capacity to unveil the dynamic characteristics of time series data, entropy has attracted growing interest. However, traditional entropy feature extraction methods, such as permutation entropy, fall short in concurrently considering both the absolute amplitude information of signals and the temporal correlation between sample points. Consequently, this limitation leads to inadequate differentiation among different time series and susceptibility to noise interference. In order to augment the discriminative power and noise robustness of entropy features in time series analysis, this paper introduces a novel method called Tsallis entropy-based complexity-improved permutation entropy casualty plane (TC-IPE-CP). TC-IPE-CP adopts a novel symbolization approach that preserves both absolute amplitude information and inter-point correlations within sequences, thereby enhancing feature separability and noise resilience. Additionally, by incorporating Tsallis entropy and weighting the probability distribution with parameter q, it integrates with statistical complexity to establish a feature plane of complexity and entropy, further enriching signal features. Through the integration of multiscale algorithms, a multiscale Tsallis-improved permutation entropy algorithm is also developed. The simulation results indicate that TC-IPE-CP requires a small amount of data, exhibits strong noise resistance, and possesses high separability for signals. When applied to the analysis of heart rate signals, fault diagnosis, and underwater acoustic signal recognition, experimental findings demonstrate that TC-IPE-CP can accurately differentiate between electrocardiographic signals of elderly and young subjects, achieve precise bearing fault diagnosis, and identify four types of underwater targets. Particularly in underwater acoustic signal recognition experiments, TC-IPE-CP achieves a recognition rate of 96.67%, surpassing the well-known multi-scale dispersion entropy and multi-scale permutation entropy by 7.34% and 19.17%, respectively. This suggests that TC-IPE-CP is highly suitable for the analysis of complex time series.

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen-Shannon Distance.

Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen-Shannon distance. The influence that linear and nonlinear temporal correlations have on the discrimination is unveiled. Results obtained lead to significant conclusions that help to achieve an improved distinction between these resting brain states.

Effects of Pharmacological Treatments in Alzheimer's Disease: Permutation Entropy-Based EEG Complexity Study.

Alzheimer's disease (AD) is a neurodegenerative brain disease affecting cognitive and physical functioning. The currently available pharmacological treatments for AD mainly contain cholinesterase inhibitors (AChE-I) and N-methyl-D-aspartic acid (NMDA) receptor antagonists (i.e., memantine). Because brain signals have complex nonlinear dynamics, there has been an increase in interest in researching complexity changes in the time series of brain signals in individuals with AD. In this study, we explore the electroencephalographic (EEG) complexity for making better observation of pharmacological therapy-based treatment effects on AD patients using the permutation entropy (PE) method. We examined EEG sub-band (delta, theta, alpha, beta, and gamma) complexity in de-novo, monotherapy (AChE-I), dual therapy (AChE-I and memantine) receiving AD participants compared with healthy elderly controls. We showed that each frequency band depicts its own complexity profile, which is regionally altered between groups. These alterations were also found to be associated with global cognitive scores. Overall, our findings indicate that entropy measures could be useful to show medication effects in AD.

Graph Multi-Scale Permutation Entropy for Bearing Fault Diagnosis.

Bearing faults are one kind of primary failure in rotatory machines. To avoid economic loss and casualties, it is important to diagnose bearing faults accurately. Vibration-based monitoring technology is widely used to detect bearing faults. Graph signal processing methods promising for the extraction of the fault features of bearings. In this work, graph multi-scale permutation entropy (MPEG) is proposed for bearing fault diagnosis. In the proposed method, the vibration signal is first transformed into a visibility graph. Secondly, a graph coarsening method is used to generate coarse graphs with different reduced sizes. Thirdly, the graph's permutation entropy is calculated to obtain bearing fault features. Finally, a support vector machine (SVM) is applied for fault feature classification. To verify the effectiveness of the proposed method, open-source and laboratory data are used to compare conventional entropies and other graph entropies. Experimental results show that the proposed method has higher accuracy and better robustness and de-noising ability.

Research on Denoising Method for Hydroelectric Unit Vibration Signal Based on ICEEMDAN-PE-SVD.

Vibration monitoring and analysis play a crucial role in the fault diagnosis of hydroelectric units. However, accurate extraction and identification of fault features from vibration signals are challenging because of noise interference. To address this issue, this study proposes a novel denoising method for vibration signals based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), permutation entropy (PE), and singular value decomposition (SVD). The proposed method is applied for the analysis of hydroelectric unit sway monitoring. Firstly, the ICEEMDAN method is employed to process the signal and obtain several intrinsic mode functions (IMFs), and then the PE values of each IMF are calculated. Subsequently, based on a predefined threshold of PE, appropriate IMFs are selected for reconstruction, achieving the first denoising effect. Then, the SVD is applied to the signal after the first denoising effect, resulting in the SVD spectrum. Finally, according to the principle of the SVD spectrum and the variation in the singular value and its energy value, the signal is reconstructed by choosing the appropriate reconstruction order to achieve the secondary noise reduction effect. In the simulation and case analysis, the method is better than the commonly used wavelet threshold, SVD, CEEMDAN-PE, and ICEEMDAN-PE, with a signal-to-noise ratio (SNR) improvement of 6.9870 dB, 4.6789 dB, 8.9871 dB, and 4.3762 dB, respectively, and where the root-mean-square error (RMSE) is reduced by 0.1426, 0.0824, 0.2093 and 0.0756, respectively, meaning that our method has a better denoising effect and provides a new way for denoising the vibration signal of hydropower units.

A Multi-Target Localization and Vital Sign Detection Method Using Ultra-Wide Band Radar.

Life detection technology using ultra-wideband (UWB) radar is a non-contact, active detection technology, which can be used to search for survivors in disaster rescues. The existing multi-target detection method based on UWB radar echo signals has low accuracy and has difficulty extracting breathing and heartbeat information at the same time. Therefore, this paper proposes a new multi-target localization and vital sign detection method using ultra-wide band radar. A target recognition and localization method based on permutation entropy (PE) and K means++ clustering is proposed to determine the number and position of targets in the environment. An adaptive denoising method for vital sign extraction based on ensemble empirical mode decomposition (EEMD) and wavelet analysis (WA) is proposed to reconstruct the breathing and heartbeat signals of human targets. A heartbeat frequency extraction method based on particle swarm optimization (PSO) and stochastic resonance (SR) is proposed to detect the heartbeat frequency of human targets. Experimental results show that the PE-K means++ method can successfully recognize and locate multiple human targets in the environment, and its average relative error is 1.83%. Using the EEMD-WA method can effectively filter the clutter signal, and the average relative error of the reconstructed respiratory signal frequency is 4.27%. The average relative error of heartbeat frequency detected by the PSO-SR method was 6.23%. The multi-target localization and vital sign detection method proposed in this paper can effectively recognize all human targets in the multi-target scene and provide their accurate location and vital signs information. This provides a theoretical basis for the technical system of emergency rescue and technical support for post-disaster rescue.

Carbon price prediction using multiple hybrid machine learning models optimized by genetic algorithm.

Importance of the carbon trading has been escalating expeditiously not only because of the environmentalist purposes to mitigate the adverse effects of climate change but also the increasing diversification benefits of the carbon emission contracts due to the low correlation between the emission, equity, and commodity markets. In accordance with the promptly rising significance of accurate carbon price prediction, this paper develops and compares 48 hybrid machine learning models by using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Variational Mode Decomposition (VMD), Permutation Entropy (PE), and multiple types of Machine Learning (ML) models optimized by Genetic Algorithm (GA). The outcomes of this study present the performances of the implemented models at different levels of mode decomposition and the impact of genetic algorithm optimization by comparing the key performance indicators that the CEEMDAN-VMD-BPNN-GA optimized double decomposition hybrid model outperforms the others with a striking R2 value of 0.993, RMSE of 0.0103, MAE of 0.0097, and MAPE of 1.61%.

Permutation Entropy Analysis to Intracranial Hypertension from a Porcine Model.

Intracranial pressure (ICP) monitoring is commonly used in the follow-up of patients in intensive care units, but only a small part of the information available in the ICP time series is exploited. One of the most important features to guide patient follow-up and treatment is intracranial compliance. We propose using permutation entropy (PE) as a method to extract non-obvious information from the ICP curve. We analyzed the results of a pig experiment with sliding windows of 3600 samples and 1000 displacement samples, and estimated their respective PEs, their associated probability distributions, and the number of missing patterns (NMP). We observed that the behavior of PE is inverse to that of ICP, in addition to the fact that NMP appears as a surrogate for intracranial compliance. In lesion-free periods, PE is usually greater than 0.3, and normalized NMP is less than 90% and p(s1)>p(s720). Any deviation from these values could be a possible warning of altered neurophysiology. In the terminal phases of the lesion, the normalized NMP is higher than 95%, and PE is not sensitive to changes in ICP and p(s720)>p(s1). The results show that it could be used for real-time patient monitoring or as input for a machine learning tool.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis.

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods.

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand information interchange in the networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, we compare the ordinal permutation entropy, a standard complexity measure in the literature, and the permutation entropy of the ordinal transition probability matrix that describes the transitions between the ordinal patterns derived from a time series. We find that the permutation entropy based on the ordinal transition matrix outperforms the rest of the tested measures in discriminating the topological role of networked chaotic Rössler systems. Since the method is based on permutation entropy measures, it can be applied to arbitrary real-world time series exhibiting correlations originating from an existing underlying unknown network structure. In particular, we show the effectiveness of our method using experimental datasets of networks of nonlinear oscillators.

Probing Intrinsic Neural Timescales in EEG with an Information-Theory Inspired Approach: Permutation Entropy Time Delay Estimation (PE-TD).

Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy-time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states.

Research on the Threshold Determination Method of the Duffing Chaotic System Based on Improved Permutation Entropy and Poincaré Mapping.

The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré section quantitative discrimination method, and experimental analyses based on phase diagram segmentation have limitations in accuracy and efficiency. In addition, they require large computational data and complex algorithms while having slow convergence. Improved permutation entropy incorporates signal amplitude information on the basis of permutation entropy and has better noise resistance. According to the characteristics of improved permutation entropy, a threshold determination method for the Duffing chaotic oscillator detection system based on improved permutation entropy (IPE) and Poincaré mapping (PM) is proposed. This new metric is called Poincaré mapping improved permutation entropy (PMIPE). The simulation results and the verification results of real underwater acoustic signals indicate that our proposed method outperforms traditional methods in terms of accuracy, simplicity, and stability.

Remaining Useful Life Prediction of Rolling Bearings Based on Multi-scale Permutation Entropy and ISSA-LSTM.

The performance of bearings plays a pivotal role in determining the dependability and security of rotating machinery. In intricate systems demanding exceptional reliability and safety, the ability to accurately forecast fault occurrences during operation holds profound significance. Such predictions serve as invaluable guides for crafting well-considered reliability strategies and executing maintenance practices aimed at enhancing reliability. In the real operational life of bearings, fault information often gets submerged within the noise. Furthermore, employing Long Short-Term Memory (LSTM) neural networks for time series prediction necessitates the configuration of appropriate parameters. Manual parameter selection is often a time-consuming process and demands substantial prior knowledge. In order to ensure the reliability of bearing operation, this article investigates the application of three advanced techniques-Maximum Correlation Kurtosis Deconvolution (MCKD), Multi-Scale Permutation Entropy (MPE), and Long Short-Term Memory (LSTM) recurrent neural networks-for the prediction of the remaining useful life (RUL) of rolling bearings. The improved sparrow search algorithm (ISSA) is employed for configuring parameters in the Long Short-Term Memory (LSTM) network. Each technique's principles, methodologies, and applications are comprehensively reviewed, offering insights into their respective strengths and limitations. Case studies and experimental evaluations are presented to assess their performance in RUL prediction. Findings reveal that MCKD enhances fault signatures, MPE captures complexity, and LSTM excels in modeling temporal patterns. The root mean square error of the prediction results is 0.007. The fusion of these techniques offers a comprehensive approach to RUL prediction, leveraging their unique attributes for more accurate and reliable predictions.

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy.

BACKGROUND: As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data. METHODS: To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190-220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE). RESULTS: FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1-5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl. CONCLUSION: The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data.