Signal In Phase Space Research Articles

Twitter Self-Organization to the Edge of a Phase Transition: Discrete-Time Model and Effective Early Warning Signals in Phase Space

Many real-world systems of various origins are capable of self-organization to the edge of a phase transition, characterized by avalanche-like behavior. Therefore, it is important, by observing the behavior of early warning measures for dynamical series generated by systems, to timely see the early warning signals (precursors) of such self-organization and, if necessary, take preventive measures. To date, convincing evidence of self-organization to the edge of a phase transition has been obtained, but no effective precursors for this self-organization have been found. This research explores precursors for the Twitter self-organization based on the analysis of the behavior of measures directly related to the critical slowdown of the network and measures of the phase space reconstructed by the Takens method for the series of the number of network users creating avalanches of retweets in the network, corresponding to the three debates of the 2016 United States Presidential Election. We hydrated the relevant Tweet IDs, which were obtained from the Harvard Dataverse using the Social Feed Manager, to form this series. Preliminarily, we explore the potential of measures for early detection of self-organization of sandpile cellular automata as systems with Twitter-equivalent self-organization mechanisms. The equivalence is justified in the proposed discrete-time model for Twitter self-organization to the edge of a phase transition. It is found that there are more moments of the Twitter self-organization than the moments of time when debates started, and Twitter stays at the edge of a phase transition longer than the debate lasts. The effective measures, as the measures with the lowest number of false early warning signals, among all studied measures and for all studied systems, are dispersion and correlation dimension. Obtained results are practically important in the design and implementation of early warning systems for the systems with similar mechanisms for sandpile cellular automata self-organization to the edge of a phase transition.

Cluster-based phase space density feature in multichannel scalp EEG for seizure prediction by deep learning

The electroencephalogram (EEG) is one of the most common methods for studying epileptic seizures. Seizure detection has been a well-known subject in neuroscience. According to previous research projects, it is more effective to extract features from the EEG to detect seizures rather than analyzing the raw EEG signals. Therefore, a new feature extraction method is suggested in this work.In this paper, new features are proposed to classify different brain states in EEG records of patients with epilepsy disorder. In previous works, some of the proposed features were based on the ellipses’ data density in phase space which is the motivation of this paper. The innovation here is to use clusters with no specific shapes instead of ellipses to extract improved features. A clustering method is performed on EEG signals in phase space. The densities of data in each cluster are considered as features, and these features are given to a classifier as inputs to classify different brain signals.The investigation is performed on the CHB-MIT scalp EEG dataset. In the binary classification scenario, the achieved results include a sensitivity of 94.94%, a specificity of 94.94%, and a FPR of 0.051 per hour. On the other hand, for the multiclass classification, the specificity is 92.33% and the FPR is 0.077 per hour. These performance metrics highlight the effectiveness of the proposed feature extraction method in generating robust features for classifying brain states. The achieved results demonstrate its superiority over the methods used in previous studies. By extracting meaningful and discriminative features from the EEG signals, the classification model can accurately differentiate between different brain states. This suggests that the proposed method holds promise for improving the accuracy and reliability of brain state classification.The proposed technique can assist neuroscientists in easily distinguishing different states of the brain before the seizure onset.

Early Warning Signals in Phase Space: Geometric Resilience Loss Indicators From Multiplex Cumulative Recurrence Networks.

The detection of Early Warning Signals (EWS) of imminent phase transitions, such as sudden changes in symptom severity could be an important innovation in the treatment or prevention of disease or psychopathology. Recurrence-based analyses are known for their ability to detect differences in behavioral modes and order transitions in extremely noisy data. As a proof of principle, the present paper provides an example of a recurrence network based analysis strategy which can be implemented in a clinical setting in which data from an individual is continuously monitored for the purpose of making decisions about diagnosis and intervention. Specifically, it is demonstrated that measures based on the geometry of the phase space can serve as Early Warning Signals of imminent phase transitions. A publicly available multivariate time series is analyzed using so-called cumulative Recurrence Networks (cRN), which are recurrence networks with edges weighted by recurrence time and directed towards previously observed data points. The results are compared to previous analyses of the same data set, benefits, limitations and future directions of the analysis approach are discussed.

Randomized Signal Processing with Continuous Frames

This paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional coefficient space (also called phase space) using a continuous frame, processed in the coefficient space, and synthesized to an output signal. We show how to approximate such methods, termed phase space signal processing methods, using a Monte Carlo method. As opposed to standard discretizations of continuous frames, based on sampling discrete frames from the continuous system, the proposed Monte Carlo method is directly a quadrature approximation of the continuous frame. We show that the Monte Carlo method allows working with highly redundant continuous frames, since the number of samples required for a certain accuracy is proportional to the dimension of the signal space, and not to the dimension of the phase space. Moreover, even though the continuous frame is highly redundant, the Monte Carlo samples are spread uniformly, and hence represent the coefficient space more faithfully than standard frame discretizations.

Application of Neural Network Algorithm Based on Principal Component Image Analysis in Band Expansion of College English Listening.

With the development of information technology, band expansion technology is gradually applied to college English listening teaching. This technology aims to recover broadband speech signals from narrowband speech signals with a limited frequency band. However, due to the limitations of current voice equipment and channel conditions, the existing voice band expansion technology often ignores the high-frequency and low-frequency correlation of the audio, resulting in excessive smoothing of the recovered high-frequency spectrum, too dull subjective hearing, and insufficient expression ability. In order to solve this problem, a neural network model PCA-NN (principal components analysis-neural network) based on principal component image analysis is proposed. Based on the nonlinear characteristics of the audio image signal, the model reduces the dimension of high-dimensional data and realizes the effective recovery of the high-frequency detailed spectrum of audio signal in phase space. The results show that the PCA-NN, i.e., neural network based on principal component analysis, is superior to other audio expansion algorithms in subjective and objective evaluation; in log spectrum distortion evaluation, PCA-NN algorithm obtains smaller LSD. Compared with EHBE, Le, and La, the average LSD decreased by 2.286 dB, 0.51 dB, and 0.15 dB, respectively. The above results show that in the image frequency band expansion of college English listening, the neural network algorithm based on principal component analysis (PCA-NN) can obtain better high-frequency reconstruction accuracy and effectively improve the audio quality.

Research on Multichannel Signals Fault Diagnosis for Bearing via Generalized Non-Convex Tensor Robust Principal Component Analysis and Tensor Singular Value Kurtosis

Tensor decomposition technique has been widely used in multichannel signals processing for its distinct superiority. The early fault feature signal of bearing is weak and easily inundated by ambient noise. In addition, the interference signals generated by other mechanical components also have a serious impact on the result of fault diagnosis. Aiming at the above issues, and built on the methods of generalized non-convex tensor robust principal component analysis (GNCTRPCA) and tensor singular value kurtosis (TSVK), this paper introduces a new fault diagnosis technique for multichannel bearing signals. First, the attractor tensor is formed by reconstructing the acquired multichannel signals in phase space. Second, based on tensor singular value decomposition (TSVD), the tensor robust principal component analysis (TRPCA) can provide a favorable noise reduction performance. However, TRPCA usually lowers the amplitude of useful singular value tubes (SVTs). To tackle this problem, the GNCTRPCA method is proposed to avoid the amplitude reduction. Third, a new TSVK method is introduced to determine the reconstructed order of SVTs, so as to extract the multichannel fault feature signals. Finally, the bearing fault type can be identified by comparing the peak frequencies of the extracted signals with the theoretical fault-related frequencies. Simulation analysis and experiment studies verify the principle and effectiveness of the proposed technique.

Discrimination of multi-class EEG signal in phase space of variability for epileptic seizure detection using error correcting output code (ECOC)

A new approach for detection of epileptic seizure based on multiclass decision tree classier combining with error correcting output codes (ECOC) using ensemble learning is presented in this paper. The dynamical properties in electroencephalogram (EEG) recorded data of electrical character of the brain during seizure is different from a normal behavior of the brain. Based on the electrical characteristics of the brain, the classification of epileptic seizure in EEG signal is performed in two steps: extraction of feature by first-order difference (FOD) whose variability has been used in 95% confidence ellipse area computation in 2D phase space reconstruction (PSR) and Interquartile range (IQR) of Euclidean distance of FOD plot in 3D PSR; and for classification, bagging algorithm of ensemble learning with decision tree as a base classifier and ECOC is used. This shows a great discriminating ability among datasets belonging to five groups (denoted A–E) at different state of the brain. The proposed method shows 100% classification accuracy.

Performance improvement of a phase space detection algorithm for electrocardiogram wave morphology classification

An algorithm based on embedding phase space signal was developed by the authors in previous works. The algorithm detects the characteristic points of the waves of a multilead electroacardiogram (ECG). In the present work, the parameters of this algorithm are optimized to improve its performance. The algorithm uses 2 configurable parameters to obtain the phase spacethe dimension of the phase space and the delayand a threshold to select the points of the ECG. By a proper selection of these parameters, the algorithm obtains all the points in the ECG that are similar to a reference one that was selected by the analyst. Several strategies have been developed and incorporated in the phase space algorithm to obtain the optimal values of these parameters based on the sampling rate and the number of leads in the records. The professional only needs to mark the reference point and the associated wave to it, for example, the start and end of a P wave and its peak. The algorithm obtains every P wave of the ECG record and a classification of their morphology using clustering techniques. Moreover, a simple graphical interface has been developed to ease its use. The algorithm was applied to detect the start, peak, and end of the P waves of a collection of ECG records of 6 minutes. Using this information, the algorithm extracts and classifies the P waves by applying clustering techniques to study their variability. The algorithm can also be used online to detect and classify different types of morphologies in any ECG wave. A future use of this algorithm will be the detection of several extracardiac pathologies in the ECG Holter, for example, sleep apnea. (Less)

Study on phase-space reconstruction of chaotic signal based on wavelet transform

Using the methods of the wavelet transform and the nonlinear dynamics, the b ehavior of chaotic signals in phase space is studied. It is indicated that, in p hase space reconstruction, the wavelet transform of chaotic time series is essen tia lly a projection of strange attractor on the axis of the space that filter vect ors opened, which in correspondance with the method of phase space reconstructio n proposed by Packard et al. The experimental results show that, after d oing wavelet transform, the architecture of attractor trajectory is similar to t he original one, and the nonlinear invariants such as correlation dimension and Kolmogorov entropy are reserved. These results show that wavelet transform is ef fective for studying chaotic signal.

Pharmaceutical fingerprinting in phase space. 1. Construction of phase fingerprints.

The present study proposes a general method for constructing pharmaceutical fingerprints in the analysis of HPLC trace organic impurity patterns. The approach considers signals in phase space and accounts for two different types of noise: additive and perturbative. The first type, additive noise, contributes to distortion of the absolute values of signal peaks. The second type, perturbative noise, contributes to variations of the retention times of signal peaks and distorts the time scale of the trace organic impurity patterns. The ability of the proposed approach to consider both types of noise significantly distinguishes it from existing methods of data analysis that are usually designed to treat only the additive noise. Analysis of the HPLC signals in phase space eliminates the problem of perturbation noise and enables detection and comparison of similar signal segments recorded at different retention times. The current study analyzes the chromatographic trace organic impurity patterns collected from six different manufacturers of L-tryptophan using three HPLC columns. For five manufacturers the variability of data recorded with the same column are in perfect agreement with the proposed model. A significant variance of parameters is detected for one manufacturer, thus indicating a possible change in its product consistency. The analysis in phase space is also used to explain the previously detected variability of HPLC signals across columns. The accompanying paper reports an application of the proposed approach for the pattern recognition of HPLC data.

Pharmaceutical fingerprinting in phase space. 2. Pattern recognition.

The current study introduces an approach for pattern recognition of drug manufacturers according to their HPLC trace impurity data. This method considers signals in phase space and accounts for two different types of noise: additive and perturbative. The pharmaceutical fingerprints are estimated as mean trajectories of HPLC trace impurity data and are used as reference models for recognition of new data by the minimal length classifier. The chromatographic trace organic impurity patterns collected from six different manufacturers of L-tryptophan are analyzed as an example. The prediction ability of the new method tested using three different cross-validation procedures remains about 95% even if the number of available data in the training sets decreases by 5 times. The accuracy of prediction in phase space is superior compared to results calculated using a Window Preprocessing method and artificial neural networks. The difference in performance between new and previous methods becomes more significant under particular conditions that are more adequate for practical application of the method. In addition, the current approach enables simple and comprehensive interpretation of the calculated results.

Quasi-geometrical Paraxial Approach to Fraunhofer Diffraction by Thick Planar Objects Using Phase-space Signal Representations

Abstract Quasi-geometrical techniques for calculating the Fraunhofer diffraction produced by some thick objects are related to phase-space signal representations, such as the Wigner distribution function. In this way, the properties derived from these functions can be applied directly to obtain an adequate display of the corresponding diffraction patterns.