Analogies and Relations between Non-Additive Entropy Formulas and Gintropy.

We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented.

Comparison of four performance models in quantifying the inequality of leaf and fruit size distribution.

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t-tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution.

Socio-economic factors determine maternal and neonatal outcomes in women with peripartum cardiomyopathy: A study of the ESC EORP PPCM registry.

BACKGROUND: Peripartum cardiomyopathy (PPCM) is a global disease with substantial morbidity and mortality. The aim of this study was to analyze to what extent socioeconomic factors were associated with maternal and neonatal outcomes. METHODS: In 2011, >100 national and affiliated member cardiac societies of the European Society of Cardiology (ESC) were contacted to contribute to a global PPCM registry, under the auspices of the ESC EORP Programme. We investigated the characteristics and outcomes of women with PPCM and their babies according to individual and country-level sociodemographic factors (Gini index coefficient [GINI index], health expenditure [HE] and human developmental index [HDI]). RESULTS: 739 women from 49 countries (Europe [33%], Africa [29%], Asia-Pacific [15%], Middle East [22%]) were enrolled. Low HDI was associated with greater left ventricular (LV) dilatation at time of diagnosis. However, baseline LV ejection fraction did not differ according to sociodemographic factors. Countries with low HE prescribed guideline-directed heart failure therapy less frequently. Six-month mortality was higher in countries with low HE; and LV non-recovery in those with low HDI, low HE and lower levels of education. Maternal outcome (death, re-hospitalization, or persistent LV dysfunction) was independently associated with income. Neonatal death was significantly more common in countries with low HE and low HDI, but was not influenced by maternal income or education attainment. CONCLUSIONS: Maternal and neonatal outcomes depend on country-specific socioeconomic characteristics. Attempts should therefore be made to allocate adequate resources to health and education, to improve maternal and fetal outcomes in PPCM.

Securing Smart Healthcare Cyber-Physical Systems against Blackhole and Greyhole Attacks Using a Blockchain-Enabled Gini Index Framework.

The increasing reliance on cyber-physical systems (CPSs) in critical domains such as healthcare, smart grids, and intelligent transportation systems necessitates robust security measures to protect against cyber threats. Among these threats, blackhole and greyhole attacks pose significant risks to the availability and integrity of CPSs. The current detection and mitigation approaches often struggle to accurately differentiate between legitimate and malicious behavior, leading to ineffective protection. This paper introduces Gini-index and blockchain-based Blackhole/Greyhole RPL (GBG-RPL), a novel technique designed for efficient detection and mitigation of blackhole and greyhole attacks in smart health monitoring CPSs. GBG-RPL leverages the analytical prowess of the Gini index and the security advantages of blockchain technology to protect these systems against sophisticated threats. This research not only focuses on identifying anomalous activities but also proposes a resilient framework that ensures the integrity and reliability of the monitored data. GBG-RPL achieves notable improvements as compared to another state-of-the-art technique referred to as BCPS-RPL, including a 7.18% reduction in packet loss ratio, an 11.97% enhancement in residual energy utilization, and a 19.27% decrease in energy consumption. Its security features are also very effective, boasting a 10.65% improvement in attack-detection rate and an 18.88% faster average attack-detection time. GBG-RPL optimizes network management by exhibiting a 21.65% reduction in message overhead and a 28.34% decrease in end-to-end delay, thus showing its potential for enhanced reliability, efficiency, and security.

Inequality Measure of Leaf Area Distribution for a Drought-Tolerant Landscape Plant.

Measuring the inequality of leaf area distribution per plant (ILAD) can provide a useful tool for quantifying the influences of intra- and interspecific competition, foraging behavior of herbivores, and environmental stress on plants' above-ground architectural structures and survival strategies. Despite its importance, there has been limited research on this issue. This paper aims to fill this gap by comparing four inequality indices to measure ILAD, using indices for quantifying household income that are commonly used in economics, including the Gini index (which is based on the Lorenz curve), the coefficient of variation, the Theil index, and the mean log deviation index. We measured the area of all leaves for 240 individual plants of the species Shibataea chinensis Nakai, a drought-tolerant landscape plant found in southern China. A three-parameter performance equation was fitted to observations of the cumulative proportion of leaf area vs. the cumulative proportion of leaves per plant to calculate the Gini index for each individual specimen of S. chinensis. The performance equation was demonstrated to be valid in describing the rotated and right shifted Lorenz curve, given that >96% of root-mean-square error values were smaller than 0.004 for 240 individual plants. By examining the correlation between any of the six possible pairs of indices among the Gini index, the coefficient of variation, the Theil index, and the mean log deviation index, the data show that these indices are closely related and can be used interchangeably to quantify ILAD.

Identify travel and health factors influencing well-being of the older adults-a case study in China.

Objective: With the increase in aging populations worldwide, the travel well-being of the elders has gained attention. The objective of this study is to examine the nonlinear relationships between the well-being of the older people in China and factors associated with travel and health. Method: Based on the data collected in China, combined embedded feature selection and decision tree built by Gini index were utilized to screen for influential factors and to determine the importance of the features selected. Tamhane's T2 was used to study the differences in the important factors among older people with different levels of travel well-being. Results: This study found that the travel well-being of older adults depends mainly on accessibility to public places, such as schools and medical facilities, and the availability of bus services. Out of expectation, the most important influential factor of travel well-being of older people is the distance from home to high school. This is related to the traditional Chinese concept of education. In addition, it was found that the body mass index is more important than self-perceived health as an influence factor of travel well-being of the elders in China. Social skills are important factors too. Conclusion: This study investigated various health-related and travel-related factors and their impacts on the travel well-being of older adults Chinese with the overall goal to improve the quality of life of the elders in China. The findings may provide a theoretical basis for the implementation of various transportation management and urban planning and design -related policies to improve the travel well-being of older adults in China.

Using machine learning to identify patient characteristics to predict mortality of in-patients with COVID-19 in south Florida.

Introduction: The SARS-CoV-2 (COVID-19) pandemic has created substantial health and economic burdens in the US and worldwide. As new variants continuously emerge, predicting critical clinical events in the context of relevant individual risks is a promising option for reducing the overall burden of COVID-19. This study aims to train an AI-driven decision support system that helps build a model to understand the most important features that predict the "mortality" of patients hospitalized with COVID-19. Methods: We conducted a retrospective analysis of "5,371" patients hospitalized for COVID-19-related symptoms from the South Florida Memorial Health Care System between March 14th, 2020, and January 16th, 2021. A data set comprising patients' sociodemographic characteristics, pre-existing health information, and medication was analyzed. We trained Random Forest classifier to predict "mortality" for patients hospitalized with COVID-19. Results: Based on the interpretability of the model, age emerged as the primary predictor of "mortality", followed by diarrhea, diabetes, hypertension, BMI, early stages of kidney disease, smoking status, sex, pneumonia, and race in descending order of importance. Notably, individuals aged over 65 years (referred to as "older adults"), males, Whites, Hispanics, and current smokers were identified as being at higher risk of death. Additionally, BMI, specifically in the overweight and obese categories, significantly predicted "mortality". These findings indicated that the model effectively learned from various categories, such as patients' sociodemographic characteristics, pre-hospital comorbidities, and medications, with a predominant focus on characterizing pre-hospital comorbidities. Consequently, the model demonstrated the ability to predict "mortality" with transparency and reliability. Conclusion: AI can potentially provide healthcare workers with the ability to stratify patients and streamline optimal care solutions when time is of the essence and resources are limited. This work sets the platform for future work that forecasts patient responses to treatments at various levels of disease severity and assesses health disparities and patient conditions that promote improved health care in a broader context. This study contributed to one of the first predictive analyses applying AI/ML techniques to COVID-19 data using a vast sample from South Florida.

Distribution of Primary Healthcare Centers Between 2017 and 2021 Across Saudi Arabia.

BACKGROUND AND AIM: Access to adequate healthcare systems is seen as a fundamental human right. Therefore, healthcare services must be distributed and accessible in the most efficient way possible to those who need them the most. Primary healthcare centers are the backbone of any healthcare system as they provide essential healthcare services to the general population. Inequalities in the distribution of primary healthcare centers can lead to disparities in healthcare access and outcomes. This study aimed to assess the equity of primary healthcare centers distribution, we analyzed and evaluated the allocation of primary healthcare centers in Saudi Arabia from 2017 to 2021. METHOD: This cross-sectional study utilized data from the Health Statistical Yearbook published by the Ministry of Health, Saudi Arabia, during the period of 2017-2021. The number of primary healthcare centers per 10,000 population was calculated for the 20 health regions. We used the Gini index to measure inequality in the distribution of primary healthcare centers. The Pearson coefficient was calculated to assess the correlation between the number of primary healthcare centers and the population in each health region. RESULT:  The overall ratio of primary healthcare centers to population decreased from 0.72 to 0.62 between 2017 and 2021. The Gini index showed relative equality in the distribution of primary healthcare centers from 2017 to 2021 with values between 0.2 and 0.3. There was a positive correlation between the population and the primary healthcare centers in Jeddah, Tabouk, and the Northern Region. However, in Riyadh, Makkah, Taif, Madinah, Qaseem, Eastern Region, Al-Ahsa, Aseer, Hail, Jazan, Najran, Al-Baha, and Al-Jouf, the correlation was found to be negative. CONCLUSION:  From 2017 to 2021, primary healthcare facilities are distributed fairly throughout 20 health regions of Saudi Arabia. However, there are still some disparities between provinces, and efforts must be made to ensure that primary healthcare centers are distributed equitably across the country to improve healthcare access and outcomes for all.

Physiological Signal Analysis and Stress Classification from VR Simulations Using Decision Tree Methods.

Stress is induced in response to any mental, physical or emotional change associated with our daily experiences. While short term stress can be quite beneficial, prolonged stress is detrimental to the heart, muscle tissues and immune system. In order to be proactive against these symptoms, it is important to assess the impact of stress due to various activities, which is initially determined through the change in the sympathetic (SNS) and parasympathetic (PNS) nervous systems. After acquiring physiological data wirelessly through captive electrocardiogram (ECG), galvanic skin response (GSR) and respiration (RESP) sensors, 21 time, frequency, nonlinear, GSR and respiration features were manually extracted from 15 subjects ensuing a baseline phase, virtual reality (VR) roller coaster simulation, color Stroop task and VR Bubble Bloom game. This paper presents a comprehensive physiological analysis of stress from an experiment involving a VR video game Bubble Bloom to manage stress levels. A personalized classification and regression tree (CART) model was developed using a novel Gini index algorithm in order to effectively classify binary classes of stress. A novel K-means feature was derived from 11 other features and used as an input in the Decision Tree (DT) algorithm, strong learners Ensemble Gradient Boosting (EGB) and Extreme Gradient Boosting (XGBoost (XGB)) embedded in a pipeline to classify 5 classes of stress. Results obtained indicate that heart rate (HR), approximate entropy (ApEN), low frequency and high frequency ratio (LF/HF), low frequency (LF), standard deviation (SD1), GSR and RESP all reduced and high frequency (HF) increased following the VR Bubble Bloom game phase. The personalized CART model was able to classify binary stress with 87.75% accuracy. It proved to be more effective than other related studies. EGB was able to classify binary stress with 100% accuracy, which outperformed every other related study. XGBoost and DT were able to classify five classes of stress with 72.22% using the novel K-means feature. This feature produced less error and better model performance in comparison to using all the features. Results substantiate that our proposed methods were more effective for stress classification than most related studies.

Modified Gini Index Detector for Cooperative Spectrum Sensing over Line-of-Sight Channels.

Recently, the Gini index detector (GID) has been proposed as an alternative for data-fusion cooperative spectrum sensing, being mostly suitable for channels with line-of-sight or dominant multi-path components. The GID is quite robust against time-varying noise and signal powers, has the constant false-alarm rate property, can outperform many the state-of-the-art robust detectors, and is one of the simplest detectors developed so far. The modified GID (mGID) is devised in this article. It inherits the attractive attributes of the GID, yet with a computational cost far below the GID. Specifically, the time complexity of the mGID obeys approximately the same run-time growth rate of the GID, but has a constant factor approximately 23.4 times smaller. Equivalently, the mGID takes approximately 4% of the computation time spent to calculate the GID test statistic, which brings a huge reduction in the latency of the spectrum sensing process. Moreover, this latency reduction comes with no performance loss with respect to the GID.

Stillbirths attributable to open fires and their geographic disparities in non-Western countries.

Due to global warming, an increased number of open fires is becoming a major contributor to PM2.5 pollution and thus a threat to public health. However, the burden of stillbirths attributable to fire-sourced PM2.5 is unknown. In low- and middle-income countries (LMICs), there is a co-occurrence of high baseline stillbirth rates and frequent firestorms, which may lead to a geographic disparity. Across 54 LMICs, we conducted a self-matched case-control study, making stillbirths comparable to the corresponding livebirths in terms of time-invariant characteristics (e.g., genetics) and duration of gestational exposure. We established a joint-exposure-response function (JERF) by simultaneously associating stillbirth with fire- and non-fire-sourced PM2.5 concentrations, which were estimated by fusing multi-source data, such as chemical transport model simulations and satellite observations. During 2000-2014, 35,590 pregnancies were selected from multiple Demographic and Health Surveys. In each mother, a case of stillbirth was compared to her livebirth(s) based on gestational exposure to fire-sourced PM2.5. We further applied the JERF to assess stillbirths attributable to fire-sourced PM2.5 in 136 non-Western countries. The disparity was evaluated using the Gini index. The risk of stillbirth increased by 17.4% (95% confidence interval [CI]: 1.6-35.7%) per 10 µg/m3 increase in fire-sourced PM2.5. In 2014, referring to a minimum-risk exposure level of 10 µg/m3, total and fire-sourced PM2.5 contributed to 922,860 (95% CI: 578,451-1,183,720) and 49,951 (95% CI: 3,634-92,629) stillbirths, of which 10% were clustered within the 6.4% and 0.6% highest-exposure pregnancies, respectively. The Gini index of stillbirths attributable to fire-sourced PM2.5 was 0.65, much higher than for total PM2.5 (0.28). Protecting pregnant women against PM2.5 exposure during wildfires is critical to avoid stillbirths, as the burden of fire-associated stillbirths leads to a geographic disparity in maternal health.

Impact of the COVID-19 Pandemic on the Socioeconomic Inequalities in Mortality in Spanish Provinces.

BACKGROUND: Although many studies have assessed the socioeconomic inequalities caused by COVID-19 in several health outcomes, there are numerous issues that have been poorly addressed. For instance, have socioeconomic inequalities in mortality from COVID-19 increased? What impact has the pandemic had on inequalities in specific causes of mortality other than COVID-19? Are the inequalities in COVID-19 mortality different from other causes? In this paper we have attempted to answer these questions for the case of Spain. METHODS: We used a mixed longitudinal ecological design in which we observed mortality from 2005 to 2020 in the 54 provinces into which Spain is divided. We considered mortality from all causes, not excluding, and excluding mortality from COVID-19; and cause-specific mortality. We were interested in analysing the trend of the outcome variables according to inequality, controlling for both observed and unobserved confounders. RESULTS: Our main finding was that the increased risk of dying in 2020 was greater in the Spanish provinces with greater inequality. In addition, we have found that: (i) the pandemic has exacerbated socioeconomic inequalities in mortality, (ii) COVID-19 has led to gender differences in the variations in risk of dying (higher in the case of women) and (iii) only in cardiovascular diseases and Alzheimer did the increased risk of dying differ between the most and least unequal provinces. The increase in the risk of dying was different by gender (greater in women) for cardiovascular diseases and cancer. CONCLUSION: Our results can be used to help health authorities know where and in which population groups future pandemics will have the greatest impact and, therefore, be able to take appropriate measures to prevent such effects.

Sandpile Universality in Social Inequality: Gini and Kolkata Measures.

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the 'wealth' owned by (1-k) fraction of the 'people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around g=k≈0.87, starting from the point of perfect equality, where g=0 and k=0.5) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law (k=0.80), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

Comparison of health inequalities according to socioeconomic status: findings from the fourth Korean working condition survey (a cross-sectional study).

Introduction: this study aims to examine health inequalities among Korean workers by sex, age, education, monthly income, occupation, and employment type and identify groups of workers who may be neglected in the process of resolving health inequalities. Methods: we used data from the Fourth Korean Working Condition Survey conducted by the Korea Occupational Safety and Health Research Institute and compared the number of health symptoms among various groups using the t-test and one-way analysis of variance to determine their health status. We also calculated the Gini index of the number of health symptoms of each group and plotted the Lorenz curve to illustrate health inequalities. Results: we found that the number of health symptoms was higher in groups with lower socioeconomic status (e.g., female, blue-collar workers, older, low education, low monthly income, and self-employed workers). However, the Gini index and Lorenz curve with respect to socioeconomic status indicated that health inequalities were higher among white-collar and permanent workers vis-à-vis blue-collar and self-employed workers, respectively. Further, it was found that health inequalities were higher among males than females with respect to the same occupational groups and employment types. Conclusion: general health policies are often targeted at the socially and economically vulnerable group, but according to the results of this study, it can be considered that there may be subjects who are vulnerable to health problems even in groups that are not socioeconomically vulnerable.

Competitiveness, country economic inequality and adolescent well-being: Analysis of 60 countries.

INTRODUCTION: Competitiveness might impact on adolescent well-being considering the social salience distinct from the other age groups. However, there is only sizable research on competitiveness and well-being. Also, most previous studies did not distinguish between individual-level and country-level competitiveness and lacked consideration of contextual effects such as country inequality. METHODS: Using cross-sectional data from the Program for International Student Assessment (PISA), we analyzed individual- and country-level competitiveness and its interaction with country inequality in relation to well-being (life satisfaction and purpose of life) in approximately 350,000 adolescents from 60 countries. Competitiveness and well-being were assessed via questionnaires. The Gini index retrieved from the World Bank was used for country inequality. A multilevel model was applied. RESULTS: Individual-level competitiveness was positively associated with both life satisfaction (ß = 0.087, 95%CI = 0.084 to 0.091) and purpose of life (ß = 0.214, 95%CI = 0.211 to 0.217), while country-level competitiveness was not. Although adolescents in the least unequal countries were satisfied with life the most and those in the most unequal countries reported the strongest purpose of life, there observed a nonlinear effect modification as a stronger association in middle unequal countries (p for interaction <0.05) compared to both less and more unequal countries. DISCUSSION: Individual-level competitiveness was positively associated with life satisfaction and purpose of life. The stronger association between competitiveness and well-being in middle unequal countries suggested that encouraging adolescents to compete within their activities or competition may work to mitigate the impact of country inequality.

Global pattern and determinants of coronavirus disease 2019 (COVID-19) vaccine coverage and progression: a global ecological study.

Background: Understanding and minimizing existing global coronavirus disease 2019 (COVID-19) vaccination disparities is critical to global population health and eliminating health inequities. The study aims to investigate the disparities of vaccination coverage and progression and the associated economic and educational determinants to inform global COVID-19 vaccination strategies. Methods: COVID-19 vaccination coverage data from 206 countries used in the study were derived from "Our World in Data" website. After obtaining the vaccination coverage indicators, we fitted the progression indicators for vaccination. Correlation and multiple linear regression analysis were used to examine the effects of gross domestic product (GDP) per capita, Gini index, education, and their interactions on the coverage and progression of the COVID-19 vaccination. Results: The coverage of COVID-19 vaccination ranged from less than 30 doses to more than 150 doses per hundred people, from less than 15% to more than 75% for proportion of people vaccinated, from less than 15% to more than 60% for proportion of people fully vaccinated. Similarly, the progression of vaccination ranged from less than 0.1 to more than 0.6 for progression of total number of doses, from less than 0.1 to more than 0.3 for progression of proportion of people vaccinated, and from less than 0.1 to more than 0.4 for progression of proportion of people fully vaccinated. GDP per capita and education were positively associated with the coverage and progression, while Gini index was negatively associated with the coverage and progression. Negative interaction between GDP per capita and education was also observed for coverage (ß = -0.012 to -0.011, P < 0.05) and progression (ß = -0.012 to -0.011, P < 0.05). Conclusions: Substantial geographic disparities existed for the coverage and progression of COVID-19 vaccination. Economy and education are two important factors contributing to the disparities. Different countries may adopt varied strategies to promote the national distribution and vaccination of COVID-19 vaccines.

Convergence of Income Inequality in OECD Countries Since 1870: A Multi-Method Approach with Structural Changes.

This paper aims to examine convergence of income inequality in 21 OECD countries using several empirical techniques. In particular, we have used a new panel stationarity test, which allows for structural changes and cross-sectional dependence to examine the stochastic convergence of income inequality. We also employed a time series approach, residual augmented least squares-Lagrange multiplier unit root test. The empirical results show evidence for absolute, conditional, and sigma convergence. The conditional convergence test results suggest that countries are converging, but conditional on the two structural factors-economic and population growth. The stochastic convergence test results indicate the existence of convergence at the country-specific level. The results further confirm the existence of convergent clubs among OECD countries.

Comparing Payments to Surgeons From Drug and Medical Device Corporations Reveals Inequalities Between Genders and Specialties.

INTRODUCTION: Maintaining trust in the patient-doctor relationship requires transparency in the details of the financial relationships between physicians and drug and medical device corporations. These details are publicly available through the Open Payments database, and patients are encouraged to ask surgeons to interpret their implications. The purpose of this study was to better equip surgeons in responding to these inquiries and to compare the distribution of these payments by gender and specialty. METHODS: The 2021 Open Payments dataset was searched for all payments to surgeons from the 14 different specialties recognized by the American College of Surgeons. The total payments per surgeon were compared by calculating the mean and median payments. The Gini index, a measure of income inequality, was also calculated for each specialty. RESULTS: There were 96 724 surgeons who received over $755 million in payments from drug and medical device companies. There were 72 245 (74.7%) men and 24 479 (25.3%) women. The total amount of payments to men was $712 million (94.2%) and for women it was $44 million (5.8%). The overall Gini index was .9508. The specialty with the highest Gini index was pediatric surgery (.9844) and the lowest was cardiothoracic surgery (.8656). DISCUSSION: Male surgeons received disproportionately higher payments from drug and device corporations than female surgeons. Surgeons should be aware of their own standing within the Open Payments database in order to respond appropriately to patient inquiries.

Periodicity measure of cyclo-stationary impulses based on low sparsity of Gini index and its application to bearing diagnosis.

A key problem in the fault diagnosis of rolling element bearings is the extraction of features of repetitive transients from vibration signals. The accurate evaluation of maximizing spectral sparsity under complex interference conditions for measuring the periodicity of transients is typically difficult to implement. Accordingly, a novel periodicity measurement approach was designed for time waveforms. According to the Robin Hood criteria, the Gini index of a sinusoidal signal has a stable low sparsity. The periodic modulation of cyclo-stationary impulses can be represented by several sinusoidal harmonics based on envelope autocorrelation and bandpass filtering. Thus, this low sparsity of Gini index can be used to evaluate the periodic strength of modulation components. Finally, a sequential feature evaluation method is developed to extract periodic impulses accurately. The proposed method is tested on simulation and bearing fault datasets and compared with the state-of-art methods so to assess its effectiveness.