Rapidly detecting disorder in rhythmic biological signals: a spectral entropy measure to identify cardiac arrhythmias

Complex dynamic behavioral transitions in auditory neurons induced by chaotic activity

Chaotic sequences are widely used in secure communication due to their high randomness. Chaotic resonance (CR) refers to the resonant response of a system to weak signals induced by chaotic activity, but its practical application remains limited. This study designs a simplified FitzHugh-Nagumo (FHN) auditory neuron model by simulating the physiological activities of auditory neurons and considering the combined stimulation of chaotic activity and sound signals. It is found that the neuron dynamics depend on both external sound stimuli and chaotic current intensity. Chaotic currents induce spikes in the neuron output sequence through CR, and the spikes become more frequent with increasing current intensity, eventually leading to a chaotic state regardless of the initial state. However, the sensitivity of the initial value of this chaotic sequence shifts to the chaotic current excitation system. The injection of chaotic currents can reduce the system's average Hamiltonian energy under certain conditions. By measuring the complexity of the generated sequences, we find that the addition of chaotic currents can enhance the complexity of the original sequences, and the enhancement ability increases with the intensity. This provides a new approach to enhance the complexity of original chaotic sequences. Moreover, different chaotic currents can induce different chaotic sequences with varying abilities to enhance the complexity of the original sequences. We hope our work can contribute to secure communication.

A Novel Joint Denoising Method for Hydrophone Signal Based on Improved SGMD and WT

Underwater acoustic technology as an important means of exploring the oceans is receiving more attention. Denoising for underwater acoustic information in complex marine environments has become a hot research topic. In order to realize the hydrophone signal denoising, this paper proposes a joint denoising method based on improved symplectic geometry modal decomposition (ISGMD) and wavelet threshold (WT). Firstly, the energy contribution (EC) is introduced into the SGMD as an iterative termination condition, which efficiently improves the denoising capability of SGMD and generates a reasonable number of symplectic geometry components (SGCs). Then spectral clustering (SC) is used to accurately aggregate SGCs into information clusters mixed-clusters, and noise clusters. Spectrum entropy (SE) is used to distinguish clusters quickly. Finally, the mixed clusters achieve the signal denoising by wavelet threshold. The useful information is reconstructed to achieve the original signal denoising. In the simulation experiment, the denoising effect of different denoising algorithms in the time domain and frequency domain is compared, and SNR and RMSE are used as evaluation indexes. The results show that the proposed algorithm has better performance. In the experiment of hydrophone, the denoising ability of the proposed algorithm is also verified.

Adaptive Fast Image Encryption Algorithm Based on Three-Dimensional Chaotic System

This paper introduces a novel three-dimensional chaotic system that exhibits diverse dynamic behaviors as parameters vary, including phase trajectory offset behaviors and expansion-contraction phenomena. This model encompasses a broad chaotic range and proves suitable for integration within image encryption. Building upon this chaotic system, the study devised a fast image encryption algorithm with an adaptive mechanism, capable of autonomously determining optimal encryption strategies to enhance algorithm security. In pursuit of heightened encryption speed, an FPGA-based chaotic sequence generator was developed for the image encryption algorithm, leveraging the proposed chaotic system. Furthermore, a more efficient scrambling algorithm was devised. Experimental results underscore the superior performance of this algorithm in terms of both encryption duration and security.

Multistability Dynamics Analysis and Digital Circuit Implementation of Entanglement-Chaos Symmetrical Memristive System

Aiming at an entangled-chaos system with a memristor, the dynamic analysis and circuit realization are studied. Combining with the quadratic flux-controlled memristor, a memristive chaotic system is constructed, and the multistable behavior of the system when the initial value of the system changes is studied by using the system phase diagram, bifurcation diagram, and Lyapunov exponent spectrum (LE). Spectral entropy (SE), C0, and SampEn are used to describe the complexity of the memristive entanglement-chaos system. Finally, the multistable behavior of the system is realized by the digital circuit chip STM32. The experimental results are consistent with the system analysis and the numerical simulation of the MATLAB software. The experimental results of the circuit provide a foundation for the engineering application of the system.

Calcium Chloride Toxicology for Food Safety Assessment Using Zebrafish (Danio rerio) Embryos

The salt calcium chloride (CaCl₂) is widely used in industry as a food additive; levels for human consumption are regulated by international or governmental agencies. Generally, the food industry relies on toxicity studies conducted in mammals such as mice, rats, and rabbits for determining food safety. However, testing in mammals is time-consuming and expensive. Zebrafish have been used in a range of toxicological analyses and offer advantages with regard to sensitivity, time, and cost. However, information in not available with regard to whether the sensitivity of zebrafish to CaCl₂ is comparable to the concentrations of CaCl₂ used as food additives. The aim of this study was to compare the CaCl₂ tolerance of zebrafish embryos and larvae with concentrations currently approved as food additives. Acute toxicity, embryotoxicity, cardiotoxicity, and neurotoxicity assays were used to determine the threshold toxic concentration of CaCl₂ in zebrafish embryos and larvae. The data showed that doses above 0.4% had toxic effects on development and on the activity of the cardiac and neuronal systems. Furthermore, all embryos exposed to 0.8 and 1.6% of CaCl₂ died after 24 hpf. These findings are consistent with the limits of CaCl₂ concentrations approved by Codex Alimentarius. Therefore, zebrafish embryos could be suitable for screening food additives.

Electro-optic chaotic system based on time delay feature hiding and key space enhancement based on chaotic post-processing

To improve the output performance of the classical all-optical chaotic system and solve the security problems of its key exposure and small key space, a new chaotic system, to the best of our knowledge, based on logistic map post-processing is proposed. In terms of the general output performance of the system, the spectrum of the proposed system is flatter than the classical system. Through a bifurcation diagram and permutation entropy analysis, it is found that the output of the system is extremely complex. In terms of security, the simulation results show that, with a reasonable selection of system parameters, key hiding can be achieved under a large parameter range. Moreover, through the sensitivity analysis of logistic parameters, it can be seen that the introduction of logistic parameters can improve the key space of the system and further improve the security of the system.

A novel conservative system with hidden flows evolved from the simplest memristive circuit

Over the past few decades, the research of dissipative chaotic systems has yielded many achievements in both theory and application. However, attractors in dissipative systems are easily reconstructed by the attacker, which leads to information security problems. Compared with dissipative systems, conservative ones can effectively avoid these reconstructing attacks due to the absence of attractors. Therefore, conservative systems have advantages in chaos-based applications. Currently, there are still relatively few studies on conservative systems. For this purpose, based on the simplest memristor circuit in this paper, a non-Hamiltonian 3D conservative system without equilibria is proposed. The phase volume conservatism is analyzed by calculating the divergence of the system. Furthermore, a Kolmogorov-type transformation suggests that the Hamiltonian energy is not conservative. The most prominent property in the conservative system is that it exhibits quasi-periodic 3D tori with heterogeneous coexisting and different amplitude rescaling trajectories triggered by initial values. In addition, the results of Spectral Entropy analysis and NIST test show that the system can produce pseudo-random numbers with high randomness. To the best of our knowledge, there is no 3D conservative system with such complex dynamics, especially in a memristive conservative system. Finally, the analog circuit of the system is designed and implemented to test its feasibility as well.

Machine Learning Using a Single-Lead ECG to Identify Patients With Atrial Fibrillation-Induced Heart Failure

Aims

Atrial fibrillation (AF) and heart failure often co-exist. Early identification of AF patients at risk for AF-induced heart failure (AF-HF) is desirable to reduce both morbidity and mortality as well as health care costs. We aimed to leverage the characteristics of beat-to-beat-patterns in AF to prospectively discriminate AF patients with and without AF-HF.

Methods

A dataset of 10,234 5-min length RR-interval time series derived from 26 AF-HF patients and 26 control patients was extracted from single-lead Holter-ECGs. A total of 14 features were extracted, and the most informative features were selected. Then, a decision tree classifier with 5-fold cross-validation was trained, validated, and tested on the dataset randomly split. The derived algorithm was then tested on 2,261 5-min segments from six AF-HF and six control patients and validated for various time segments.

Results

The algorithm based on the spectral entropy of the RR-intervals, the mean value of the relative RR-interval, and the root mean square of successive differences of the relative RR-interval yielded an accuracy of 73.5%, specificity of 91.4%, sensitivity of 64.7%, and PPV of 87.0% to correctly stratify segments to AF-HF. Considering the majority vote of the segments of each patient, 10/12 patients (83.33%) were correctly classified.

Conclusion

Beat-to-beat-analysis using a machine learning classifier identifies patients with AF-induced heart failure with clinically relevant diagnostic properties. Application of this algorithm in routine care may improve early identification of patients at risk for AF-induced cardiomyopathy and improve the yield of targeted clinical follow-up.

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

In this paper, a class of fractional-order symmetric hyperchaotic systems is studied based on the Adomian decomposition method. Starting from the definition of Adomian, the nonlinear term of a fractional-order five-dimensional chaotic system is decomposed. At the same time, the dynamic behavior of a fractional-order hyperchaotic system is analyzed by using bifurcation diagrams, Lyapunov exponent spectrum, complexity and attractor phase diagrams. The simulation results show that with the decrease of fractional order q, the complexity of the hyperchaotic system increases. Finally, based on the fractional-order circuit design principle, a circuit diagram of the system is designed, and the circuit is simulated by Multisim. The results are consistent with the numerical simulation results, which show that the system can be realized, which provides a foundation for the engineering applications of fractional-order hyperchaotic systems.

Dynamics of Fractional-Order Digital Manufacturing Supply Chain System and Its Control and Synchronization

Digital manufacturing is widely used in the production of automobiles and aircrafts, and plays a profound role in the whole supply chain. Due to the long memory property of demand, production, and stocks, a fractional-order digital manufacturing supply chain system can describe their dynamics more precisely. In addition, their control and synchronization may have potential applications in the management of real-word supply chain systems to control uncertainties that occur within it. In this paper, a fractional-order digital manufacturing supply chain system is proposed and solved by the Adomian decomposition method (ADM). Dynamical characteristics of this system are studied by using a phase portrait, bifurcation diagram, and a maximum Lyapunov exponent diagram. The complexity of the system is also investigated by means of SE complexity and C0 complexity. It is shown that the complexity results are consistent with the bifurcation diagrams, indicating that the complexity can reflect the dynamical properties of the system. Meanwhile, the importance of the fractional-order derivative in the modeling of the system is shown. Moreover, to further investigate the dynamics of the fractional-order supply chain system, we design the feedback controllers to control the chaotic supply chain system and synchronize two supply chain systems, respectively. Numerical simulations illustrate the effectiveness and applicability of the proposed methods.

A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task

Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

Complexity and Chimera States in a Network of Fractional-Order Laser Systems

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

Resting Heartbeat Complexity Predicts All-Cause and Cardiorespiratory Mortality in Middle- to Older-Aged Adults From the UK Biobank

Background

Spontaneous heart rate fluctuations contain rich information related to health and illness in terms of physiological complexity, an accepted indicator of plasticity and adaptability. However, it is challenging to make inferences on complexity from shorter, more practical epochs of data. Distribution entropy (DistEn) is a recently introduced complexity measure that is designed specifically for shorter duration heartbeat recordings. We hypothesized that reduced DistEn predicted increased mortality in a large population cohort.

Method and Results

The prognostic value of DistEn was examined in 7631 middle‐older–aged UK Biobank participants who had 2‐minute resting ECGs conducted (mean age, 59.5 years; 60.4% women). During a median follow‐up period of 7.8 years, 451 (5.9%) participants died. In Cox proportional hazards models with adjustment for demographics, lifestyle factors, physical activity, cardiovascular risks, and comorbidities, for each 1‐SD decrease in DistEn, the risk increased by 36%, 56%, and 73% for all‐cause, cardiovascular, and respiratory disease–related mortality, respectively. These effect sizes were equivalent to the risk of death from being >5 years older, having been a former smoker, or having diabetes mellitus. Lower DistEn was most predictive of death in those <55 years with a prior myocardial infarction, representing an additional 56% risk for mortality compared with older participants without prior myocardial infarction. These observations remained after controlling for traditional mortality predictors, resting heart rate, and heart rate variability.

Conclusions

Resting heartbeat complexity from short, resting ECGs was independently associated with mortality in middle‐ to older‐aged adults. These risks appear most pronounced in middle‐aged participants with prior MI, and may uniquely contribute to mortality risk screening.

Entropy Profiling for Detection of Fetal Arrhythmias in Short Length Fetal Heart Rate Recordings

The use of fetal heart rate (FHR) recordings for assessing fetal wellbeing is an integral component of obstetric care. Recently, non-invasive fetal electrocardiography (NI-FECG) has demonstrated utility for accurately diagnosing fetal arrhythmias via clinician interpretation. In this work, we introduce the use of data-driven entropy profiling to automatically detect fetal arrhythmias in short length FHR recordings obtained via NI-FECG. Using an open access dataset of 11 normal and 11 arrhythmic fetuses, our method (TotalSampEn) achieves excellent classification performance (AUC = 0.98) for detecting fetal arrhythmias in a short time window (i.e. under 10 minutes). We demonstrate that our method outperforms SampEn (AUC = 0.72) and FuzzyEn (AUC = 0.74) based estimates, proving its effectiveness for this task. The rapid detection provided by our approach may enable efficient triage of concerning FHR recordings for clinician review.

A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller

In the present work, a new nonequilibrium four-dimensional chaotic jerk system is presented. The proposed system includes only one constant term and has coexisting and hidden attractors. Firstly, the dynamical behavior of the system is investigated using bifurcation diagrams and Lyapunov exponents. It is illustrated that this system either possesses symmetric equilibrium points or does not possess an equilibrium. Rich dynamics are found by varying system parameters. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Then, coexisting and hidden chaotic attractors are observed, and basin attraction is plotted. Moreover, using the multiscale C0 algorithm, the complexity of the system is investigated, and a broad area of high complexity is displayed in the parameter planes. In addition, the chaotic behavior of the system is studied by field-programmable gate array implementation. A novel methodology to discretize, simulate, and implement the proposed system is presented, and the successful implementation of the proposed system on FPGA is verified through the simulation outcome. Finally, a robust sliding mode controller is designed to suppress the chaotic behavior of the system. To deal with unexpected disturbances and uncertainties, a disturbance observer is developed along with the designed controller. To show the successful performance of the designed control scheme, numerical simulations are also presented.

Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals

Measuring the complexity of time series provides an important indicator for characteristic analysis of nonlinear systems. The permutation entropy (PE) is widely used, but it still needs to be modified. In this paper, the PE algorithm is improved by introducing the concept of the network, and the network PE (NPE) is proposed. The connections are established based on both the patterns and weights of the reconstructed vectors. The complexity of different chaotic systems is analyzed. As with the PE algorithm, the NPE algorithm-based analysis results are also reliable for chaotic systems. Finally, the NPE is applied to estimate the complexity of EEG signals of normal healthy persons and epileptic patients. It is shown that the normal healthy persons have the largest NPE values, while the EEG signals of epileptic patients are lower during both seizure-free intervals and seizure activity. Hence, NPE could be used as an alternative to PE for the nonlinear characteristics of chaotic systems and EEG signal-based physiological and biomedical analysis.

Development of an alert system for subjects with paroxysmal atrial fibrillation

Background

Knowledge of the onset of atrial fibrillation (AF) episodes in patients with paroxysmal atrial fibrillation (PAF) will enable them to better manage this condition. Current advances in mobile technology allow RR interval data to be obtained in real time. An analysis technique using RR interval data is presented with a view to alert a subject before a PAF episode.

Method

The method is based on a time series of standard deviation and 0.99 quantile values of the spectral entropy, constructed from RR data. The RR data are taken from three time periods. The first time period has no occurrences of AF for 45 min to either side of the time period. The second time period just precedes an AF attack. Both of these are of thirty minutes duration. The third time period of approximately 5 min follows the second, and is when AF occurs.

Results

Twenty-two PAF subjects were studied and in all cases there was a steady increase in the values of these indices as the onset of the AF attack approached.

Conclusion

This method of analysis of RR interval data shows potential use to alert a PAF subject before the onset of an AF episode.

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A method to alert the PAF subject before the onset of paroxysms of AF, based on a time series of standard deviation and 0.99 quantile values of the spectral entropy, obtained from the RR interval data.

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The RR data used in analysis each subject was obtained from three time periods. The first two are of thirty minute duration while the third set is of 5 min duration.

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RR data from the first time period had no occurrences of AF, 45 min on either side of it. The time period of the second set just precedes an AF attack. The third set which follows the second is when AF occurs.

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22 PAF subjects were studied and in all cases there was a steady increase in the values of the standard deviation and 0.99 quantile values of the spectral entropy.

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Such a signature of these indices shows that this analysis technique of RR data could be useful to PAF patients to better manage the onset of AF attacks.