Multi-Scale Permutation Entropy: A Potential Measure for the Impact of Sleep Medication on Brain Dynamics of Patients with Insomnia

Insomnia is a common sleep disorder that is closely associated with the occurrence and deterioration of cardiovascular disease, depression and other diseases. The evaluation of pharmacological treatments for insomnia brings significant clinical implications. In this study, a total of 20 patients with mild insomnia and 75 healthy subjects as controls (HC) were included to explore alterations of electroencephalogram (EEG) complexity associated with insomnia and its pharmacological treatment by using multi-scale permutation entropy (MPE). All participants were recorded for two nights of polysomnography (PSG). The patients with mild insomnia received a placebo on the first night (Placebo) and temazepam on the second night (Temazepam), while the HCs had no sleep-related medication intake for either night. EEG recordings from each night were extracted and analyzed using MPE. The results showed that MPE decreased significantly from pre-lights-off to the period during sleep transition and then to the period after sleep onset, and also during the deepening of sleep stage in the HC group. Furthermore, results from the insomnia subjects showed that MPE values were significantly lower for the Temazepam night compared to MPE values for the Placebo night. Moreover, MPE values for the Temazepam night showed no correlation with age or gender. Our results indicated that EEG complexity, measured by MPE, may be utilized as an alternative approach to measure the impact of sleep medication on brain dynamics.     

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%.     

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.     

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.     

A Diversity Model Based on Dimension Entropy and Its Application to Swarm Intelligence Algorithm

The swarm intelligence algorithm has become an important method to solve optimization problems because of its excellent self-organization, self-adaptation, and self-learning characteristics. However, when a traditional swarm intelligence algorithm faces high and complex multi-peak problems, population diversity is quickly lost, which leads to the premature convergence of the algorithm. In order to solve this problem, dimension entropy is proposed as a measure of population diversity, and a diversity control mechanism is proposed to guide the updating of the swarm intelligence algorithm. It maintains the diversity of the algorithm in the early stage and ensures the convergence of the algorithm in the later stage. Experimental results show that the performance of the improved algorithm is better than that of the original algorithm.     

一种少投影光学层析新算法及其应用

研究少投影数情况下等离子体温度场重建问题。结合光学层析重建算法及等离子体光谱诊断中的谱线绝对强度法进行自由电弧等离子体温度场重建实验。理论上，详细讨论了一种基于最大熵准则及最优化原理的光学层析图像重建新算法。通过计算机数值模拟，考察了该算法对非对称温度场分布的重建效果。详细分析了投影噪声、投影方向数、场分布性质对重建精度的影响，并与代数迭代重建算法结果进行对比．结果表明，该算法以两个正交方向投影数据重建单峰余弦模拟场平均误差仅为0.3％，而代数迭代重建算法为3．81％；该算法以四个均匀角度间隔投影数据重建三峰随机高斯模拟场平均误差为1．77％，而代数迭代重建算法为2．02％。实验中，运用该算法结合谱线绝对强度法重建了自由电弧等离子体的温度分布。     

Modified Hilbert Curve for Rectangles and Cuboids and Its Application in Entropy Coding for Image and Video Compression

In our previous work, by combining the Hilbert scan with the symbol grouping method, efficient run-length-based entropy coding was developed, and high-efficiency image compression algorithms based on the entropy coding were obtained. However, the 2-D Hilbert curves, which are a critical part of the above-mentioned entropy coding, are defined on squares with the side length being the powers of 2, i.e., 2ⁿ, while a subband is normally a rectangle of arbitrary sizes. It is not straightforward to modify the Hilbert curve from squares of side lengths of 2ⁿ to an arbitrary rectangle. In this short article, we provide the details of constructing the modified 2-D Hilbert curve of arbitrary rectangle sizes. Furthermore, we extend the method from a 2-D rectangle to a 3-D cuboid. The 3-D modified Hilbert curves are used in a novel 3-D transform video compression algorithm that employs the run-length-based entropy coding. Additionally, the modified 2-D and 3-D Hilbert curves introduced in this short article could be useful for some unknown applications in the future.     

A Locally Conformal Algorithm for Handling Curved Metallic Surfaces and Its Application

This paper describes a modified locally conformal algorithm for finite-difference time-domain (FDTD) method. Fields in the entire computational domain are computed by a regular FDTD algorithm except those near curved metallic surfaces, where special techniques proposed in this paper are applied. The computation efficiency of a regular FDTD method is maintained while a high space-resolution is obtained by this new algorithm. To validate the reliability of the algorithm, coaxial continuous transverse stub arrays at millimeter wave Ka-band and microwave X-band are tested, and the simulated results show good agreement with the experimental results from an HP-8510B Network Analyzer and the simulation results from software package HFSS.