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.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions—as a function of time series length—present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.

Sensitivity of excess mortality due to the COVID-19 pandemic to the choice of the mortality index, method, reference period, and the time unit of the death series

Estimating excess mortality is challenging. The metric depends on the expected mortality level, which can differ based on given choices, such as the method and the time series length used to estimate the baseline. However, these choices are often arbitrary, and are not subject to any sensitivity analysis. We bring to light the importance of carefully choosing the inputs and methods used to estimate excess mortality. Drawing on data from 26 countries, we investigate how sensitive excess mortality is to the choice of the mortality index, the number of years included in the reference period, the method, and the time unit of the death series. We employ two mortality indices, three reference periods, two data time units, and four methods for estimating the baseline. We show that excess mortality estimates can vary substantially when these factors are changed, and that the largest variations stem from the choice of the mortality index and the method. We also find that the magnitude of the variation in excess mortality can change markedly within countries, resulting in different cross-country rankings. We conclude that the inputs and method used to estimate excess mortality should be chosen carefully based on the specific research question.

New Lossless Compression Algorithms for Transport Images

The article considers the relevance of the development of lossless image compression and transmission algorithms and their application for creating transport video surveillance systems. A brief overview of lossless transport image compression methods is provided. We propose a method for compressing transport plots based on the pyramid-recursive method of splitting the source image into polygons of various shapes and sizes. We consider two new algorithms for implementing the proposed method that are fundamentally different from each other: with a transition to the spectral region and without a transition to the spectral region of the original signal to ensure lossless compression. The results of testing various well-known lossless compression algorithms are analyzed: series length, Huffman, and arithmetic encoding, and compared with the proposed algorithms. It is shown that the proposed algorithms are more efficient in terms of compression ratio (2—3 times) compared to the known ones, while the computational complexity increases approximately by more than 3-4 times.

An integrated state-space model to assess Italian alpine galliforms status from count and bag data

The assessment of wildlife population sizes and their trends is one of the most important research fields in conservation biology, as it is used to identify vulnerability soon enough to implement measures in threatened species, or to set up sustainable harvesting rates in exploited populations. Yet, because field work is expensive, may be difficult in terms of logistics and because some populations of the same species may be monitored by different stakeholders, population status often rely on fragmented and heterogenous information on sub-populations collected through various monitoring programs. In this context, data integration, i.e. the simultaneous analysis of different datasets in a single modelling framework allows to get unbiased and more precise trend estimates than separated analysis that in turn may lead to more adequate management policies. In this study we developed an integrated state-space model to jointly model populations growth rates from individual counts and hunting bags data for three hunted species of mountain Galliformes in Italy. We examined population trends at various spatial scales and disentangled the potential effect of game management plans from biological factors. The integration of counts and bags succeeded in improving growth rate parameter precision and in reducing proxy-specific bias by increasing the sample size and extending data series length. On a 19-year basis, all three species exhibited negative mean growth rates. We did not find strong regional patterns for Rock ptarmigan and Rock partridge, as a likely consequence of prevailing effects of local environmental conditions on population growth rate. Black grouse eastern populations exhibited lower growth rate than western populations. Our paper demonstrates that an integrated model of different index of population size of game species can provide more accurate values than separate analysis, we advocate to consider such an approach for other wildlife monitoring cases for which data is scarce.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

The GPS velocity field of the Aegean. New observations, contribution of the earthquakes, crustal blocks model

Summary We calculate and analyse the coordinate time series of 282 permanent GPS stations located in Greece and 47 in surrounding countries. The studied period is 2000–2020. The average GPS time series length is 6.5 years. The formal velocity uncertainties are rescaled to be consistent with the velocity scatters measured at 110 pairs of stations separated by less 15 km. We remove the effect of the crustal earthquakes of Mw ≥ 5.3. We quantify and model the postseismic deformations. Two relaxation times are usually needed, one short of some weeks, one long of one year or more. For the large Mw = 6.9 events of Samothraki 2014 and Methoni 2008, the postseismic deformation equals or exceeds the coseismic one. We detect at three stations a deformation transient in May 2018 that may correspond to a slow earthquake beneath Zakynthos and north-west Peloponnese, with equivalent magnitude 5.8. The density and accuracy of the velocities make it possible to better quantify several characteristics of the deformation in the Aegean, in particular: (a) the transition from the Anatolian domain, located in the south-east, to the European domain through the western end of the North Anatolian fault; (b) the north-south extension in the western Aegean; (c) the east-west extension of the western Peloponnese; (d) the clockwise rotation of the Pindos; (e) the north-south extension in central Macedonia. Large parts of the central Aegean, eastern Peloponnese and western Crete form a wide stable domain with internal deformation below 2 nstrain yr−1. We build a kinematic model comprising ten crustal blocks corresponding to areas where the velocities present homogeneous gradients. The block boundaries are set to fit with known localized deformation zones, e.g. the rift of Corinth, the North Anatolian fault, the Katouna fault. When the velocities steps are clear but not localized, e.g. through the Peloponnese, the boundary line is arbitrary and represents the transition zone. The model fits the velocities with a root mean square deviation of ± 0.9 mm yr−1. At the boundaries between blocks we compare the predicted and observed deformations. We find shear rates of 7.4 and 9.0 mm yr−1 along the Movri and Katouna faults, 14.9 and 8.7 mm yr−1 along the North Anatolian fault near Lemnos and near Skopelos respectively, extension of 7.6, 1.5 and 12.6 mm yr−1 across the Gulf of Patras, the Trichonis Lake and the Ambracian Gulf. The compression across western Epirus is 3.7 mm yr−1. There is a dextral transtensional movement of 4.5 mm yr−1 between the Amorgos and Astypalea islands. Only the Ionian Islands region shows evidence of coupling along the subduction interface.

An evaluation of rainfall regime changes in Italy over the last decades from literature

<p>The growing attention to modifications in climate in several societal sectors has led to an increasing number of studies and research on the topic of climate change and especially on changes in precipitation. The analysis presented here draws a “state of the art” of changes in the Italian precipitation regime through the review of the most relevant published studies, in peer-review journals. The aim of the study is to summarize a large quantity of information derived from specific studies, in a unique analysis and to highlight the main patterns of rainfall changes in Italy in the last decades. The results of 54 selected studies are discussed through the introduction of a weight factor, which considers the importance of each study according to its geographical area, stations density, and time series length, and provides a quantitative evaluation of the review. To offer a coherent climatic classification of the review findings, Italy is subdivided in three main macro areas and studies are also subdivided in 3 groups according to the Time-Series Length: Short TSL, less than 65 years; Long TSL, until 100 years; and centennial TSL, over 100 years. The analysis is focused on the Total Precipitation (TP) and the number of Wet Days (WDs) indices at the annual and seasonal scale. Looking at the overall results of the review, most of the studies agree about a decrease at the annual scale of the Wet Days index throughout the Italian territory for short and centennial TSL. The reduction of precipitation is confirmed by the Total Precipitation index that at the annual scale reflects this tendency except for the Northern Italy. This feature also emerges from the seasonal analysis, with some heterogeneity in the results due to difference in the number of studies used in the various areas, suggesting that there is an underlying climatic pattern driving trends toward a reduction in wet days and rainfall over the Italian territory.</p>