A reconfigurable parallel acceleration platform for evaluation of permutation entropy.

The present thesis explores some approaches to classify time series without prior statistical information using the concept of permutation entropy. Motivated by the results from a previous published and relevant work that set similarity relationships between EEG time series, a reproduction of the proposed approach was performed giving negative results. The failure to reproduce those results led to the conclusion that the approach of building statistics from permutation patterns have to be complemented with another metric in order to be used for classification purposes. The concept of Total Variation Distance (TVD) was then used to develop three algorithms to classify time series in a non-parametric way. At first, the developed algorithms were tested using EEG time series. Even though the results using the developed algorithms were better than previous results, they were not as satisfactory as desired. However, the inherent complexity of brain measurements led to switch to self-generated data to test the algorithms. Using time series coming from different sets of filtered versions of Gaussian white noise the classification was performed. For comparison purposes a parametric classification approach using the Maximum Likelihood Estimation was also used. Results showed that when each set of data came from the same filtering equation the classification using the developed algorithms was optimal reaching 100% success rate in many cases, being as good as the ML approach. On the other hand, when each set of data came from a mixture of different filter equations that generate the time series (reflecting the complex situations we faced when processing EEG data) , results were fairly successful with variations with respect to the ML approach, which was outperformed in some cases but also not surpassed in others. The results obtained pointed the permutation entropy analysis to be an approach in the right direction to efficiently classify time series, however more research needs to be done to adjust the correct metric to get better results.

Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy. Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors.Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy. Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors.

Entropy calculation provides meaningful insight into the dynamics and complexity of temporal signals, playing a crucial role in classification tasks. These measures are able to describe intrinsic characteristics of temporal series, such as regularity, complexity or predictability. Depending on the characteristics of the signal under study, the performance of entropy as a feature for classification may vary, and not any kind of entropy calculation technique may be suitable for that specific signal. Therefore, we aim to increase entropy’s classification accuracy performance, specially in the case of Slope Entropy (SlpEn), by enhancing the information content of the patterns present in the data before calculating the entropy, with downsampling techniques. More specifically, we will be using both uniform downsampling (UDS) and non-uniform downsampling techniques. In the case of non-uniform downsapling, the technique used is known as Trace Segmentation (TS), which is a non-uniform downsampling scheme that is able to enhance the most prominent patterns present in a temporal series while discarding the less relevant ones. SlpEn is a novel method recently proposed in the field of time series entropy estimation that in general outperforms other methods in classification tasks. We will combine it both with TS or UDS. In addition, since both techniques reduce the number of samples that the entropy will be calculated on, it can significantly decrease the computation time. In this work, we apply TS or UDS to the data before calculating SlpEn to assess how downsampling can impact the behaviour of SlpEn in terms of performance and computational cost, experimenting on different kinds of datasets. In addition, we carry out a comparison between SlpEn and one of the most commonly used entropy calculation methods: Permutation Entropy (PE). Results show that both uniform and non-uniform downsampling are able to enhance the performance of both SlpEn and PE when used as the only features in classification tasks, gaining up to 13% and 22% in terms of accuracy, respectively, when using TS and up to 10% and 21% when using UDS. In addition, when downsampling to 50% of the original data, we obtain a speedup around ×2 with individual entropy calculations, while, when incorporating the downsampling algorithms into time count, speedups with UDS are between ×1.2 and ×1.7, depending on the dataset. With TS, these speedups are above ×2, while maintaining accuracy levels similar to those obtained when using the 100% of the original data. Our findings suggest that most temporal series, specially medical ones, have been measured using a sampling frequency above the optimal threshold, thus obtaining unnecessary information for classification tasks, which is then discarded when performing downsampling. Downsampling techniques are potentially beneficial to any kind of entropy calculation technique, not only those used in the paper. It is able to enhance entropy’s performance in classification tasks while reducing its computation time, thus resulting in a win-win situation. We recommend to downsample to percentages between 20% and 45% of the original data to obtain the best results in terms of accuracy in classification tasks.

In this paper, we propose a Shannon-Fisher information plane based on the information entropy to analyze financial stock markets. In order to evaluate the effectiveness of this method, we apply this method to two types of artificial time series: Autoregressive Fractionally Integrated Moving Average models and Chebyshev map model. The results show that with the embedding dimension and the number of possible states of the system increasing, the normalized Shannon entropy increases, and the Fisher information measure (FIM) decreases. When the parameter is not so big, the embedding dimension plays a leading role in determining the FIM. In addition, compared with the classical Shannon-Fisher information through permutation entropy, we conclude that the proposed approach can give us more accurate information on the classification of financial stock markets.

An echo state network (ESN) is an efficient recurrent neural network (RNN) that is widely used in time series prediction tasks due to its simplicity and low training cost. However, the "black-box" nature of reservoirs hinders the development of ESN. Although a large number of studies have concentrated on reservoir interpretability, the perspective of reservoir modeling is relatively single, and the relationship between reservoir richness and reservoir projection capacity has not been effectively established. To tackle this problem, a novel reservoir interpretability framework based on permutation entropy (PE) theory is proposed in this paper. In structure, this framework consists of reservoir state extraction, PE modeling, and PE analysis. Based on these, the instantaneous reservoir states and neuronal time-varying states are extracted, which are followed by phase space reconstruction, sorting, and entropy calculation. Firstly, the obtained instantaneous state entropy (ISE) and global state entropy (GSE) can measure reservoir richness for interpreting good reservoir projection capacity. On the other hand, the multiscale complexity-entropy analysis of global and neuron-level reservoir states is performed to reveal more detailed dynamics. Finally, the relationships between ESN performance and reservoir dynamic are investigated via Pearson correlation, considering different prediction steps and time scales. Experimental evaluations on several benchmarks and real-world datasets demonstrate the effectiveness and superiority of the proposed reservoir interpretability framework.

Compared with amplitude, phase contains more important information. Renyi phase permutation entropy (RPPE), which introduces phase information into Renyi permutation entropy (RPE), is proposed in this paper. Using one-dimension simulation signal, a systematic study of the influence of window length, move step, embedding dimension, time delay and entropy parameter $q$ for RPE and RPPE on the abnormal changes detection are presented and we obtain a set of optimal values of these parameters. Furthermore, two electrocardiogram (ECG) signals are applied to analyze the influence of $q$ for the actual signal and the results show that increasing $q$ can enhance the ability of RPE and RPPE for detecting abnormal change. The analyses of simulation signal and actual signal illustrate that RPPE is more remarkable for detecting the abnormal change than RPE under the same conditions.

Automatic diagnosis of epileptic seizures using entropy-based features and multimodel deep learning approaches

The automated epileptic seizure detection has emerged as an important field in the recent years; this involves analyzing the Electroencephalogram (EEG) signals instead of the traditional visual inspection performed by expert neurologists. In this paper, a model has been introduced that integrates Weighted Permutation Entropy (WPE) as input feature to a Support Vector Machine (SVM) learning model to enhance the sensitivity and precision of the detection process. WPE is a modified statistical parameter of the permutation entropy (PE) that measures the complexity and irregularity of a time series. It incorporates both the mapped ordinal pattern of the time series and the information contained in the amplitude of its sample points. The proposed system utilizes the fact that entropy based measures for the EEG segments during epileptic seizure are lower than in normal EEG. Experiments have been conducted to demonstrate the sensitivity and precision of the proposed model. Results showed that the model can considerably discriminate between EEG brain signal into seizure and no-seizure classes.

The genesis of epileptic seizures is nowadays still mostly unknown. The hypothesis that most of scientist share is that an abnormal synchronization of different groups of neurons seems to trigger a recruitment mechanism that leads the brain to the seizure in order to reset this abnormal condition. If this is the case, a gradual transformation of the characteristics of the EEG can be hypothesized. It is therefore necessary to find a parameter that is able to measure the synchronization level in the EEG and, since the spatial dimension has to be taken into account if we aim to find out how the different areas in the brain recruit each other to develop the seizure, a spatio-temporal analysis of this parameter has to be carried out. In the present paper, a spatio-temporal analysis of EEG synchronization in 24 patients affected by absence seizure is proposed and the results are hereby reported and compared to the results obtained with a group of 40 healthy subjects. The spatio-temporal analysis is based on Permutation Entropy (PE). We found out that, ever since the interictal stages, fronto-temporal areas appear constantly associated to PE levels that are higher compared to the rest of the brain, whereas the parietal/occipital areas appear associated to low-PE. The brain of healthy subjects seems to behave in a different way because we could not see a recurrent behaviour of PE topography.

The genesis of epileptic seizures is nowadays still mostly unknown. The hypothesis that most of scientist share is that an abnormal synchronization of different groups of neurons seems to trigger a recruitment mechanism that leads the brain to the seizure in order to reset this abnormal condition. If this is the case, a gradual transformation of the characteristics of the EEG can be hypothesized. It is therefore necessary to find a parameter that is able to measure the synchronization level in the EEG and, since the spatial dimension has to be taken into account if we aim to find out how the different areas in the brain recruit each other to develop the seizure, a spatio-temporal analysis of this parameter has to be carried out. In the present paper, a spatio-temporal analysis of EEG synchronization in 24 patients affected by absence seizure is proposed and the results are hereby reported and compared to the results obtained with a group of 40 healthy subjects. The spatio-temporal analysis is based on Permutation Entropy (PE). We found out that, ever since the interictal stages, fronto-temporal areas appear constantly associated to PE levels that are higher compared to the rest of the brain, whereas the parietal/occipital areas appear associated to low-PE. The brain of healthy subjects seems to behave in a different way because we could not see a recurrent behaviour of PE topography.

Epileptic seizures are caused by a disturbance in the electrical activity of the brain and classified as many different types of epileptic seizures based on the characteristics of EEG and other parameters. Till now research has been conducted to classify EEG as seizure and non-seizures, but the classification of seizure types has not been explored. Thus, in this paper, we have proposed the 8-class classification problem in order to classify different seizure types using convolutional neural networks (CNN). This research study suggests a CNN based framework for classification of epileptic seizure types that include simple partial, complex partial, focal non-specific, generalized non-specific, absence, tonic, and tonic-clonic, and non-seizures. EEG time series was converted into spectrogram stacks and used as input for CNN. To the best of authors knowledge, ours is the very first study that classified the seizures types using the computational algorithm. The four CNN models, namely AlexNet, VGG16, VGG19, and basic CNN model was applied to study the performance of 8-class classification problem. The proposed study showed a classification accuracy of 84.06%, 79.71%, 76.81%, and 82.14% using AlexNet, VGG16, VGG19 and basic CNN models respectively. The experimental results suggest that the proposed framework could be helpful to the neurology community for recognition of seizures types.

Diversity in brain health is influenced by individual differences in demographics and cognition. However, most studies on brain health and diseases have typically controlled for these factors rather than explored their potential to predict brain signals. Here, we assessed the role of individual differences in demographics (age, sex, and education; n = 1298) and cognition (n = 725) as predictors of different metrics usually used in case-control studies. These included power spectrum and aperiodic (1/f slope, knee, offset) metrics, as well as complexity (fractal dimension estimation, permutation entropy, Wiener entropy, spectral structure variability) and connectivity (graph-theoretic mutual information, conditional mutual information, organizational information) from the source space resting-state EEG activity in a diverse sample from the global south and north populations. Brain-phenotype models were computed using EEG metrics reflecting local activity (power spectrum and aperiodic components) and brain dynamics and interactions (complexity and graph-theoretic measures). Electrophysiological brain dynamics were modulated by individual differences despite the varied methods of data acquisition and assessments across multiple centers, indicating that results were unlikely to be accounted for by methodological discrepancies. Variations in brain signals were mainly influenced by age and cognition, while education and sex exhibited less importance. Power spectrum activity and graph-theoretic measures were the most sensitive in capturing individual differences. Older age, poorer cognition, and being male were associated with reduced alpha power, whereas older age and less education were associated with reduced network integration and segregation. Findings suggest that basic individual differences impact core metrics of brain function that are used in standard case-control studies. Considering individual variability and diversity in global settings would contribute to a more tailored understanding of brain function.

Elliptic curve cryptography (ECC) is widely used for secure communications, because it can provide the same level of security as RSA with a much smaller key size. In constrained environments, it is important to consider efficiency, in terms of execution time and hardware costs. Modular inversion is a key time-consuming calculation used in ECC. Its hardware implementation requires extensive hardware resources, such as lookup tables and registers. We investigate the state-of-the-art modular inversion algorithms, and evaluate the performance and cost of the algorithms and their hardware implementations. We then propose a high-radix modular inversion algorithm aimed at reducing the execution time and hardware costs. We present a detailed radix-8 hardware implementation based on 256-bit primes in Verilog HDL and compare its cost performance to other implementations. Our implementation on the Altera Cyclone V FPGA chip used 1227 ALMs (adaptive logic modules) and 1037 registers. The modular inversion calculation took 3.67 ms. The AT (area–time) factor was 8.30, outperforming the other implementations. We also present an implementation of ECC using the proposed radix-8 modular inversion algorithm. The implementation results also showed that our modular inversion algorithm was more efficient in area–time than the other algorithms.

Objective To investigate the etiology of early-onset Alzheimer disease which caused by presenilin 1 (PSEN1) mutation in one case of early-onset Alzheimer disease patient with initial symptom of epilepsy childhood and his large family. Methods From November 28, 2014 to November 14, 2015, one case of patient with initial symptom of epilepsy from age of 12 years old who was diagnosed as early-onset Alzheimer disease (the proband) in Department of Neurology of Peking University First Hospital and his large family genealogy (Ⅰ-Ⅳ generations)were recruited as research objects. Diagnostic criteria of Alzheimer disease were as follows. ①Age of onset less than 65 years old. ②The clinical examination evidence supported the diagnosis for dementia; ③Cognitive impairment showed in more than two fields. ④The progressive decline of memory and with other cognitive disorders. ⑤Without disturbance of consciousness. ⑥Without other systemic diseases and the memory and cognitive impairment which can be explained by the brain diseases. The proband, a male, 36 years old had seizures from the age of 12-year-old. He visited the hospital to seek for etiological and to study for his abnormal family history. Clinical data and genomic DNA of the proband and his family members were collected. Targeted next-generation sequencing (TGS) was performed to detect the PSEN1 mutation in the proband. All exons and exon-intron boundaries of PSEN1 were checked by polymerase chain reaction (PCR). Sanger sequencing was used to verify the corresponding mutation. The procedure of this study was consistent with ethical standard established by the committee of investigation in human beings of Peking University First Hospital. And it was approved by this committee. Informed consent was obtained from all participants. Results ①The proband (Ⅲ16) presented with seizures when he was 12 years old. After treated by sodium valproate from the age of 15 years old, the seizure was not observed. He had normal psychomotor development. His cranial MRI showed no abnormality. Relapse occurred when he stopped the drug at the age of 33 years old and sodium valproate remained effective. Primary epilepsy was suspected. However, he have presented with memory loss and disorientation since the age of 35 years old. ②His grandmother (Ⅰ2) had psychiatric disorder in her thirties and died at around 40 years old. His father (Ⅱ6), two aunts(Ⅱ4and Ⅱ5)and two uncles(Ⅱ2and Ⅱ3) presented with similar symptoms, progressive memory loss and mental retroversion at the age of about 35 years old, died in their forties, indicating early-onset Alzheimer disease. ③The sequencing results showed that, in exon 5 of PSEN1of the proband, a reported heterozygous mutation (c.346G>A, p. Glu116Lys) was identified. The same heterozygous mutation was found respectively in his son, a son (Ⅲ11,45 years old) and a grandson (Ⅳ11,7 years old) of a paternal aunt, and a daughter (Ⅲ15,29 years old) of another paternal aunt. The son of the paternal aunt who had the same mutation with the proband was 45 years old without any symptoms. Conclusions Clinical and molecular genetic features of the proband′s pedigree were clearly definite. The results confirmed the diagnosis of early-onset Alzheimer disease. It will be helpful for the genetic counseling and the prenatal diagnosis of the next generation of the family. Key words: Alzheimer disease; Presenilin-1; Epilepsy; Memory disorders; Mental retroversion; DNA mutational analysis; Familial genetic disease

We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window embeddings, as seen through the lens of persistent homology. In particular, we show that maximum persistence at the point-cloud level can be used to quantify periodicity at the signal level, prove structural and convergence theorems for the resulting persistence diagrams, and derive estimates for their dependency on window size and embedding dimension. We apply this methodology to quantifying periodicity in synthetic data sets and compare the results with those obtained using state-of-the-art methods in gene expression analysis. We call this new method SW1PerS, which stands for Sliding Windows and 1-Dimensional Persistence Scoring.