Correction to: Observations on NIST SP 800-90B entropy estimators

Abstract. The Lagrangian particle dispersion model FLEXPART was originally designed for calculating long-range and mesoscale dispersion of air pollutants from point sources, such that occurring after an accident in a nuclear power plant. In the meantime, FLEXPART has evolved into a comprehensive tool for atmospheric transport modeling and analysis at different scales. A need for further multiscale modeling and analysis has encouraged new developments in FLEXPART. In this paper, we present a FLEXPART version that works with the Weather Research and Forecasting (WRF) mesoscale meteorological model. We explain how to run this new model and present special options and features that differ from those of the preceding versions. For instance, a novel turbulence scheme for the convective boundary layer has been included that considers both the skewness of turbulence in the vertical velocity as well as the vertical gradient in the air density. To our knowledge, FLEXPART is the first model for which such a scheme has been developed. On a more technical level, FLEXPART-WRF now offers effective parallelization, and details on computational performance are presented here. FLEXPART-WRF output can either be in binary or Network Common Data Form (NetCDF) format, both of which have efficient data compression. In addition, test case data and the source code are provided to the reader as a Supplement. This material and future developments will be accessible at http://www.flexpart.eu.

It is known that heart activity changes during aging. In this paper, we evaluated alterations of heart activity from the complexity point of view. We analyzed the variations of heart rate of patients with congestive heart failure that are categorized into four different age groups, namely 30–39, 50–59, 60–69, and 70–79 years old. For this purpose, we employed three complexity measures that include fractal dimension, sample entropy, and approximate entropy. The results showed that the trend of increment of subjects’ age is reflected in the trend of increment of the complexity of heart rate variability (HRV) since the values of fractal dimension, approximate entropy, and sample entropy increase as subjects get older. The analysis of the complexity of other physiological signals can be further considered to investigate the variations of activity of other organs due to aging.

Multiple entropies performance measure for detection and localization of multi-channel epileptic EEG

The paper considers a number of issues related to the calculation of the local entropy in a sliding window for image processing tasks. A new algorithm for entropy estimation is proposed, which has several times lower computational complexity than the known ones. The algorithm is based on the approximate representation of the histogram in the form of a truncated series expansion over some system of orthogonal basis functions, recursive calculation of the coefficients of this expansion in a sliding window and subsequent recalculation of the coefficients into the entropy estimate. Questions of an orthogonal basis selection for representing the local histogram as a truncated series are considered and the appropriateness of using the Haar basis is shown. A technique of constructing hierarchical approximator, which realizes fast recalculation of histogram decomposition coefficients into entropy value, is described. The theoretical statements of the paper are verified by experiments on the Earth remote sensing images.

Influence of the signal to noise ratio for the estimation of Permutation Entropy

Objective. Parkinson's disease (PD) is a neurodegenerative disorder characterized by a range of motor and non-motor symptoms. Despite extensive research, the neural structure of time distortion, remains unclear. This study aimed to determine the neurobiological origins of time distortion by analyzing dynamic features in PD patients compared to control participants.Approach. We used PD and control electroencephalography (EEG) signals to investigate brain function during time distortion. The EEG signal was recorded during an interval-timing task. Following artifact reduction and EEG signal segmentation, dynamic features were extracted from each frequency band across all the channels. Channels showing significant discrepancies between the two groups were selected by statistical analysis. The features are sent to an Artificial Neural Network (ANN) classifier to evaluate their discriminative potential.Main results.The results indicated lower values of Lyapunov Exponent and Approximate Entropy along with higher value of Fractal dimension in PD which presented higher level of irregularity and randomness, particularly in the CPz, P5, P6, and C5 channels. The ANN classifier achieved 90% accuracy, 89% sensitivity, 87% F1 score, and 95% specificity in a 10-fold cross-validation.Significance.Significantly different channels were concentrated in the central and parietal areas of the brain and were linked to decision-making, maintenance, and retrieval of stored information, and working memory. Moreover, based on dynamic EEG analysis, it seems that disrupted connections between the basal ganglia and posterior parietal cortex in PD appear to compromise frontoparietal network dysfunction, which is associated with impaired temporal processing in patients with PD.

A concussion is a mild traumatic brain injury as a result from a blow to the head. From battlefields to football fields, concussions are unavoidable risks that occur on a daily basis. The goal of this research is to design and test the prototype of a portable concussion assessment device that can offer a quick indication of the state of concussion immediately after the concussion. Approximate Entropy (ApEn) values reflecting the amount of irregularity hiding in center-of-pressure (COP) oscillations will be used to calculate the index. The prototype will adopt a portable design and use the measurements of the load cells located at the four corners of the prototype. The test subject will be asked to stand on the device in normal stance for 30 seconds with their eyes closed. The COP oscillations will then be recorded. Based on the oscillation measurements, the ApEn index will be calculated and quickly displayed to indicate the state of concussion.

Brain waves are proposed as a biometric for verification of the identities of individuals in a small group. The approach is based on a novel two-stage biometric authentication method that minimizes both false accept error (FAE) and false reject error (FRE). These brain waves (or electroencephalogram (EEG) signals) are recorded while the user performs either one or several thought activities. As different individuals have different thought processes, this idea would be appropriate for individual authentication. In this study, autoregressive coefficients, channel spectral powers, inter-hemispheric channel spectral power differences, inter-hemispheric channel linear complexity and non-linear complexity (approximate entropy) values were used as EEG features by the two-stage authentication method with a modified four fold cross validation procedure. The results indicated that perfect accuracy was obtained, i.e. the FRE and FAE were both zero when the proposed method was tested on five subjects using certain thought activities. This initial study has shown that the combination of the two-stage authentication method with EEG features from thought activities has good potential as a biometric as it is highly resistant to fraud. However, this is only a pilot type of study and further extensive research with more subjects would be necessary to establish the suitability of the proposed method for biometric applications.

This paper first analyzes the causes of phonological and lexical changes in English linguistics and discusses the main manifestations of English phonological changes and phonological and lexical changes. Then, it constructs the evaluation model of English linguistics using the dominant correlation method based on the entropy value, approximation ideal, and gray correlation methods. Finally, data on phonological and lexical changes are analyzed about the development of English linguistics in the past sixty years. From the analysis of factors affecting English vocabulary change, the historical factor responsible for vocabulary change is the development of human society, and the factor value currently stands at 0.428. In comparison, the social, psychological, cultural and foreign language factor values reach 0.654, 0.458, 0.512 and 0.461, respectively.

Recently, NIST has published the second draft of SP 800-90B used for entropy estimations of random number generators. It is conducted within the framework of a cryptographic module validation program (CMVP) for the entropy source. The official evaluation criteria such as CMVP should be supported by rigorous and theoretical foundations so as to achieve the credibility and reliability of the evaluation process. For the theoretical background of the entropy estimation, it is assumed in SP 800-90B that the distribution of the entropy source is unknown since we cannot obtain an appropriate hypothesis about the distribution of the noise source which is a component of the entropy source. In this case, the nonparametric statistical method is commonly used. The test suite of SP 800-90B is divided into two major steps. The first step is to determine the track, IID(independent and identically distributed) or Non-IID, and the second step is to estimate the entropy of the given source. The permutation tests and additional chi-square tests are used to test IID assumption for entropy source in the first step, and when all tests in the first step are passed, the given source is determined as IID. Depending on whether the given data is determined as IID or Non-IID, the entropy estimation is conducted using different estimators in the second step. In this paper, we concentrate on the additional chi-square tests and analyze them from the view point of the nonparametric statistical method. We find out several defects of the degrees of freedom in the tests of independence for binary and non-binary data. We correct the degrees of freedom based on our analysis, and it solidifies the theoretical basis of SP 800- 90B. Furthermore, we provide some experimental results with the corrected degrees of freedom which show that the corrected tests are more effective.

In this paper, an efficient and low‐cost cryptographic system for highly secure image encryption is presented. The proposed image encryption structure is implemented based on the key processing (KP) stage, the processing of the input image (PII) stage, and the round function (KPPII‐RF). The key processing stage and the processing of the input image stage are used to increase key sensitivity and plain‐image sensitivity, respectively. The method is independent of the input image and the bit pattern of the main key, and no information is affected by the main key and the original image. In the proposed method, three parameters, the main key, the counter value, and the previously generated ciphertext, are utilized within the encryption process to produce each subsequent ciphertext. Because this method uses the previous ciphertext to generate the next ciphertext, it increases the confusion of the final result and provides better security against differential attacks. The most important innovations of this work include the simultaneous use of various techniques such as shuffling key bits by the key processing unit, shuffling pixels of the original image by the original image processing unit, utilizing a parameter known as a seed as a unique parameter for an image, and employing an appropriate round function to apply complexity to the data. The performance of the proposed structure is evaluated based on different security analyses. The information entropy values of the encrypted images based on the proposed scheme are higher than 7.995, while correlation values are very close to zero. Furthermore, the number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed KPPII‐RF image encryption are higher than 99.5% and 33.3, respectively. The KPPII‐RF image encryption is verified for randomness through 16 NIST benchmark statistical tests from the NIST SP 800‐22 suite. The proposed structure provides an acceptable security level for image encryption.

This study evaluated the amount, and particularly, the structure of variability in postural control accompanying an unstable shoe (US) application. Mediolateral and anterior-posterior center of pressure signals plus electromyographic profiles of the tibialis anterior and gastrocnemius medialis were recorded in 29 asymptomatic men while wearing both US and flat shoes. Statistical analysis included common measures of dispersion as well as sample entropy and largest Lyapunov exponent estimates. Data were compared by two-way repeated-measures analysis of variance. Corresponding main effects of footwear revealed that, in contrast to the flat shoes condition, the US intervention consistently increased center of pressure and electromyographic net fluctuations and rendered the overall system less complex, as reflected by the lower sample entropy and higher Lyapunov exponent values observed throughout. Accordingly, employing US in stance should be functional concerning motor development; however, the greater sensitivity of US users to external perturbations must not be overlooked and warrants further investigation.

Electroencephalography (EEG) is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG) not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (FE), and Permutation Entropy (PE), have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE), Multiscale Permutation Entropy (MPE), and Multiscale Fuzzy Entropy (MFE) are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE) is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD)/event-related synchronization (ERS) phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM) as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields relatively high classification accuracy compared with other entropy-based and classical time–frequency–space feature extraction methods. The t-test is used to prove the correctness of the improved MFE.

To examine the effects of increased cadence and minimalist footwear on lower-limb variability in runners with patellofemoral pain (PFP). Fifteen (12 female, 3 male) runners with PFP ran on an instrumented treadmill with three-dimensional motion capture in three randomly ordered conditions: (i) standard shoe at preferred cadence, (ii) standard shoe +10% cadence, and (iii) minimalist shoe at preferred cadence. Vector coding was used to calculate coordination variability between strides for select lower-limb joint couplings. Approximate entropy was calculated to assess continuous variability for segment kinematic and kinetic data and compared between conditions using repeated-measures ANOVA. One-dimensional statistical parametric mapping repeated-measures ANOVA was performed on the coordination variability data. Cohen's d effect size was calculated for all comparisons. Larger approximate entropy values (i.e., greater variability) were observed for the standard shoe +10% cadence versus the standard shoe at preferred cadence for hip flexion/extension (P < 0.001; d = 1.12), hip adduction/abduction (P < 0.001; d = 0.99) and ankle dorsiflexion/plantarflexion (P < 0.001; d = 1.37) kinematics, and knee flexion/extension moments (P < 0.001; d = 0.93). Greater variability was also observed in the minimalist shoe versus the standard shoe at preferred cadence for hip internal/external rotation moments (P < 0.001; d = 0.76), knee adduction/abduction moments (P < 0.001; d = 0.51), and knee internal/external rotation moments (P < 0.001; d = 1.02). One-dimensional statistical parametric mapping repeated-measures ANOVA revealed no significant differences in coordination variability between running conditions. Greater hip and knee kinematic and kinetic variability observed with either increased cadence or minimalist footwear may be beneficial for those with PFP.

The Effect of Anterior Cruciate Ligament Reconstruction on Stride-to-Stride Variability