Unbiased entropy estimates in stress: a parameter study

On Quantization Errors in Approximate and Sample Entropy

Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal.

Characterization of the Stages of Creative Writing With Mobile EEG Using Generalized Partial Directed Coherence

Two stages of the creative writing process were characterized through mobile scalp electroencephalography (EEG) in a 16-week creative writing workshop. Portable dry EEG systems (four channels: TP09, AF07, AF08, TP10) with synchronized head acceleration, video recordings, and journal entries, recorded mobile brain-body activity of Spanish heritage students. Each student's brain-body activity was recorded as they experienced spaces in Houston, Texas (“Preparation” stage), and while they worked on their creative texts (“Generation” stage). We used Generalized Partial Directed Coherence (gPDC) to compare the functional connectivity among both stages. There was a trend of higher gPDC in the Preparation stage from right temporo-parietal (TP10) to left anterior-frontal (AF07) brain scalp areas within 1–50 Hz, not reaching statistical significance. The opposite directionality was found for the Generation stage, with statistical significant differences (p < 0.05) restricted to the delta band (1–4 Hz). There was statistically higher gPDC observed for the inter-hemispheric connections AF07–AF08 in the delta and theta bands (1–8 Hz), and AF08 to TP09 in the alpha and beta (8–30 Hz) bands. The left anterior-frontal (AF07) recordings showed higher power localized to the gamma band (32–50 Hz) for the Generation stage. An ancillary analysis of Sample Entropy did not show significant difference. The information transfer from anterior-frontal to temporal-parietal areas of the scalp may reflect multisensory interpretation during the Preparation stage, while brain signals originating at temporal-parietal toward frontal locations during the Generation stage may reflect the final decision making process to translate the multisensory experience into a creative text.

On Entropy of Probability Integral Transformed Time Series

The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties-pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series-systolic blood pressure and pulse interval-acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities.

Cardiovascular variability and β-ARs gene expression at two stages of doxorubicin - Induced cardiomyopathy

Using comprehensive analysis of heart rate (HRV) and blood pressure (BPV) short-term variability we estimated the time course of changes of autonomic nervous system remodeling in two stages of doxorubicin-induced cardiomyopathy (DCM). We also investigated the level of gene expression of cardiac β-1 (β-1AR) and β-2 (β-2AR) adrenoceptors. Experiments were performed in adult male Wistar rats equipped with indwelling catheters for BP recording and blood withdrawal. A 15 mg/kg total cumulative dose of doxorubicin was injected i.p. to rats to induce DCM or saline for control (n=18). Rats were assessed for general toxicity, cardiovascular hemodynamic and echocardiography before treatment (n=6), 35 days (DOX35; n=6) and 70 days (DOX70; n=6) post-treatment. HRV was evaluated by spectral analysis, Poincaré plots, sample and approximate entropy. Expression of β-1AR and β-2AR mRNA was evaluated by RT-qPCR. Doxorubicin-treated rats exhibited poor general condition and lower survival than saline-treated rats. In DOX35 rats, there were no echocardiography signs of decompensation, no increase in serum cardiac troponins, but there was an increase of HRV and decrease of HR complexity. In these rats typical microscopic signs of cardiotoxicity were seen along with over-expression of β-1AR mRNA. 70 days post-treatment echocardiography revealed signs of decompensation and serum cardiac troponin T was increased. At this stage BPV decreased. In conclusion, HRV increase matches transient over-expression of cardiac β-1AR mRNA in compensate stage of DCM while decompensate stage of DCM is characterized by a decrease of BPV and no changes in β-1AR and β-2AR gene expression.

Binarized cross-approximate entropy in crowdsensing environment

OBJECTIVES

Personalised monitoring in health applications has been recognised as part of the mobile crowdsensing concept, where subjects equipped with sensors extract information and share them for personal or common benefit. Limited transmission resources impose the use of local analyses methodology, but this approach is incompatible with analytical tools that require stationary and artefact-free data. This paper proposes a computationally efficient binarised cross-approximate entropy, referred to as (X)BinEn, for unsupervised cardiovascular signal processing in environments where energy and processor resources are limited.

METHODS

The proposed method is a descendant of the cross-approximate entropy ((X)ApEn). It operates on binary, differentially encoded data series split into m-sized vectors. The Hamming distance is used as a distance measure, while a search for similarities is performed on the vector sets. The procedure is tested on rats under shaker and restraint stress, and compared to the existing (X)ApEn results.

RESULTS

The number of processing operations is reduced. (X)BinEn captures entropy changes in a similar manner to (X)ApEn. The coding coarseness yields an adverse effect of reduced sensitivity, but it attenuates parameter inconsistency and binary bias. A special case of (X)BinEn is equivalent to Shannon's entropy. A binary conditional entropy for m =1 vectors is embedded into the (X)BinEn procedure.

CONCLUSION

(X)BinEn can be applied to a single time series as an auto-entropy method, or to a pair of time series, as a cross-entropy method. Its low processing requirements makes it suitable for mobile, battery operated, self-attached sensing devices, with limited power and processor resources.

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series.