Estimated Mean Values Research Articles

Distribution and Anisotropy of the Energy Transfer Rate in the Solar Wind Turbulence

The distribution of the energy transfer rate is critical for the interpretation of the intermittent energy cascade in the solar wind turbulence. However, the true observational distribution of the energy transfer rate in the solar wind and its anisotropy remain unknown. Here, we use a 7 day interval measured by Wind in the fast solar wind and investigate the distribution and anisotropy of the energy transfer rate based on the log-Poisson model. We find that the probability density distribution consists of two parts. The majority part locates at smaller values and is consistent with the log-normal distribution. The estimated mean value and standard deviation of the logarithmic energy transfer rate for the majority are both smaller in the direction parallel to the local mean magnetic field than in the perpendicular direction. The mean value displays a power-law shape with respect to the scale, with flatter index in the parallel direction and steeper index in the perpendicular direction. The minority part locates at larger values and expands as the scale decreases, indicating the growing intermittency toward smaller scales. The flatness for parallel logarithmic energy transfer rate is larger than that for perpendicular. And it rises as the scale decreases for all directions, demonstrating the relatively longer tail of the distribution with decreasing scale. Our results provide new insight to help interpret the intermittent energy cascade process in the solar wind turbulence.

Estimates for Smooth Weyl Sums on Major Arcs

Abstract We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.

Comparison of Caregiver and General Population Preferences for Dependency-Related Health States.

We assess whether the preferences regarding dependency-related health states as stated by informal caregivers are aligned with those expressed by the general population. The preferences of a sample of 139 Spanish informal caregivers of dependent patients are compared with those obtained via a sample of 312 persons, also from the Spanish general population. We assess 24 dependency states extracted from the DEP-6D using the time trade-off method. Descriptive statistics and regression methods are used to explore differences between the two samples. Mean difference tests establish that, for all but one of the 24 states, there are no significant differences between the samples. The estimated mean values ranged from - 0.64 to 0.60 for the caregiver sample and from - 0.60 to 0.65 for the general population sample, with a correlation of 0.96. On average, the classification of states as better or worse than dead matched in both samples (except for one state). Regression models also show that sample type does not have a significant average impact. After we introduce interaction effects, only the most severe level of two dimensions, cognitive problems and housework, result in significant differences-with the caregiver sample reporting higher values for the former, and lower values for the latter. Caregivers and the general population exhibit quite similar preferences concerning dependency-related health states. This suggests that the results of cost-utility analyses, and the resource allocation decisions based on them, would likewise not be significantly affected by the preferences used to generate the weighting algorithm.

Quantum-enhanced mean value estimation via adaptive measurement

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.

CORTEX experiments, Part III: Experimental determination of the zero power transfer function of AKR-2 with reliable uncertainties

The transfer function is an important characteristic quantity of a nuclear reactor, since it contains the kinetic parameters. It expresses the response of a nuclear reactor to a disturbance of a certain frequency. If it is determined experimentally, it can be used to draw conclusions about the kinetic parameters. This article presents results of measurements of the zero power transfer function of the AKR-2 reactor at TU Dresden together with new data analysis methods. These measurements are compared to the theoretical zero power transfer function with kinetic parameters obtained via Monte Carlo simulations with MCNP and Serpent. To this end, advanced data analysis techniques based on a bootstrapping algorithms are employed. These techniques suppress the signal outside multiples of the fundamental frequency and additionally allow to obtain the full probability distribution of a peak in the frequency domain. This allowed for a reliable estimation of the mean value and uncertainty estimates of measured data of the zero power transfer function and the quantification of deviations between the experiments and the computations. It also made it possible to determine the phase of the zero power transfer function of AKR-2 for the first time. The experiments and computations are in agreement within the estimated uncertainties.

Enhancing Tumor Localization in Brain MRI Images Using a Scalable Systematic Vector Algorithm for Result-Oriented Accuracy

This paper introduces a novel foundational architecture incorporating two primary algorithms. The Partially Enhanced Linear Mean Analysis Algorithm for significant vectorization and the Vertically Enhanced Tensor-Load Interface Algorithm for structural vectorization. These algorithms are meticulously designed to optimize the extraction of valuable information from complex data sets, enabling efficient and insightful historical data analysis. The performance of these algorithms has been rigorously compared with existing significant vectorization and structural methods, demonstrating superior accuracy in mean value estimation. Simulated results provide robust evidence of the high-dimensional capability and throughput of the proposed architecture. Incorporating tools such as Microsoft Excel for data organization, MATLAB for advanced computational analysis, and Python for algorithmic implementation and automation further enhances the framework’s efficiency and precision. Imminent work on this architecture could expand its applicability into multi-functional systems, potentially integrating a multi-role tape framework. Such an expansion would be particularly beneficial for identifying brain tumors with greater accuracy and precision, contributing significantly to medical diagnostics. The proposed system represents a promising advancement in applying computational tools for complex data analysis and structural vectorization.

Underweight in young Japanese women over time: a longitudinal retrospective study of the change in body mass index from ages 6 to 20 years

Background The high prevalence of underweight in young women has become a serious health problem in Japan. When and how young women reach a low body mass index (BMI) has not been clarified. Aim To clarify the characteristics of BMI standard deviation scores (BMI SDS) trajectory of young Japanese women with underweight. Subjects and methods A total of 601 Japanese female university students aged 20 years were classified into underweight and healthy weight groups. Their school health check-up data were available from the ages of 6 to 20 years. We evaluated the estimated mean values of BMI SDS at each age and differences in BMI SDS (ΔBMI SDS) from 6 years to each age using a mixed-effects model and compared between the two groups at each age. Results In the underweight group, the BMI SDS at every age (−1.67 to −0.91) and the ΔBMI SDS after 16 years of age (−0.76 to −0.38) were significantly lower than those in the healthy weight group (−0.41 to −0.13, −0.07 to 0.04), respectively. Conclusion Young Japanese women with underweight have at least two characteristics of BMI SDS trajectory: being constitutionally underweight and shifting their weight status from baseline towards underweight in their late teens.

Azov sea fishes stock assessment by swept area method through bootstrap

Recently driven changes in habitat conditions in the Azov Sea make classic applications of swept area method inconsistent. Swept area stock assessment method modification for stock estimation of aquatic biological resources through nonparametric bootstrap is presented. New approach is tested against classic calculated results of swept area method for next fish species: Azov anchovy, tulka, turbot and Black-Azov sea shad according to data collected during 2022. Results comparison of classic and modified through bootstrap stock assessment methods leads no significant deviations in mean value estimation. Maximum difference between mean estimates of stock size was 3,75%. Confidential intervals width difference between reviewed methods, in general, was not significant. Most valuable difference in confidential intervals was detected in BCa approach against classic method with quantile approach (due to methodological features of BCa in bias correction procedure). The new stock assessment approach for swept area method though bootstrap permit to calculate statistically valid estimates, their confidential intervals and perform input data validation. The absence of significant differences in the results by the classical and proposed methods indicates the further applicable possibility of classic method even in normality violation in source samples. The normality requirements in methodology of classic approach, probably, is redundant.

Second trimester maternal serum progesterone and estradiol concentrations with live and demised fetuses: Secondary analysis results from a randomized controlled trial

AbstractObjectiveTo provide data on maternal levels of estradiol and progesterone in the second trimester of pregnancy with a live foetus and those complicated by a spontaneous foetal demise.MethodsWithin a randomised trial to assess efficacy of mifepristone in termination following foetal demise from 14 to 28 weeks of gestation, we measured progesterone and estradiol levels in trial patients and in women undergoing termination with a live foetus. Women admitted to King Edward Memorial Hospital (Western Australia) from 2013 to 2016 were considered for eligibility and enroled. Scatter plots with 95% confidence intervals were generated for hormone levels by gestation. Generalised linear models were used to estimate mean values of estradiol and progesterone, accounting for maternal age, gestation and parity.ResultsOverall, women with a foetal demise had lower estradiol levels compared to women with a live foetus, (mean difference of 10 460 pmol/L). With a live foetus, higher levels of estradiol were observed with increasing gestations: with a mean of 17 010 pmol/L at 14 ≤ 17 weeks, 31 180 pmol/L at 23–28 weeks and similarly progesterone with a mean of 113 nmol/L at 14 ≤ 17 weeks and 183 nmol/L at 23–28 weeks. Progesterone levels in women with foetal demise were 37 nmol/L higher than women in the live foetus group. In all women, each unit increase in parity was associated with a decrease of 10nmol/l of progesterone (95% confidence interval: 4–16, p = 0.001).ConclusionsEstradiol and progesterone levels in the second trimester vary between pregnant women with a live and demised foetus.

Bias-free estimation of the covariance function and the power spectral density from data with missing samples including extended data gaps

Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Transmission characteristics and inactivated vaccine effectiveness against transmission of the SARS-CoV-2 Omicron BA.2 variant in Shenzhen, China.

We conducted a retrospective cohort study to evaluate the transmission risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron BA.2 variant and the effectiveness of inactivated COVID-19 vaccine boosters in Shenzhen during a BA.2 outbreak period from 1 February to 21 April 2022. A total of 1,248 individuals were infected with the BA.2 variant, and 7,855 close contacts were carefully investigated. The risk factors for the high secondary attack rate of SARS-CoV-2 infection were household contacts [adjusted odds ratio (aOR): 1.748; 95% confidence interval (CI): 1.448, 2.110], younger individuals aged 0-17 years (aOR: 2.730; 95% CI: 2.118, 3.518), older persons aged ≥60 years (aOR: 1.342; 95% CI: 1.135, 1.588), women (aOR: 1.442; 95% CI: 1.210, 1.718), and the subjects exposed to the post-onset index cases (aOR: 8.546; 95% CI: 6.610, 11.050), respectively. Compared with the unvaccinated and partially vaccinated individuals, a relatively low risk of secondary attack was found for the individuals who received booster vaccination (aOR: 0.871; 95% CI: 0.761, 0.997). Moreover, a high transmission risk was found for the index cases aged ≥60 years (aOR: 1.359; 95% CI: 1.132, 1.632), whereas a relatively low transmission risk was observed for the index cases who received full vaccination (aOR: 0.642; 95% CI: 0.490, 0.841) and booster vaccination (aOR: 0.676; 95% CI: 0.594, 0.770). Compared with full vaccination, booster vaccination of inactivated COVID-19 vaccine showed an effectiveness of 24.0% (95% CI: 7.0%, 37.9%) against BA.2 transmission for the adults ≥18 years and 93.7% (95% CI: 72.4%, 98.6%) for the adults ≥60 years, whereas the effectiveness was 51.0% (95% CI: 21.9%, 69.3%) for the individuals of 14 days to 179 days after booster vaccination and 51.2% (95% CI: 37.5%, 61.9%) for the non-household contacts. The estimated mean values of the generation interval, serial interval, incubation period, latent period, and viral shedding period were 2.7 days, 3.2 days, 2.4 days, 2.1 days, and 17.9 days, respectively. In summary, our results confirmed that the main transmission route of Omicron BA.2 subvariant was household contact, and booster vaccination of the inactivated vaccines was relatively effective against BA.2 subvariant transmission in older people.

Selection and cultivation of seaweed Kappaphycus alvarezii using a long line system (outdoor)

In outdoor cultivation at Amal Beach, three seeding mass selections were reared for 30 days for each cycle. Each variety had a different DGR %/day (Daily Growth Rate %/day) value at the end of the growing season on G1-G2-G3 ranging from 3.62-5.90 %/day, which were still categorized as good, and G3 var.Lampung had the highest DGR value. Carrageenan yield values in this study, G1 to G3, ranged from 23.16% to 45.87%, where the G3 G2 G1 treatment. The best thallus samples (20% were selected for each generation) resulted in carrageenan yield sample population in each variety, where var.Lampung var.Tarakan var.Kupang. The biplot analysis shows that the DGR variable vector coincides with the IAA, Phosphate, Gibberellin, and Ammonia vectors. Ammonia stepwise regression analysis (sigα) affects DGR with an Ammonia coefficient value of 4.89; meaning that for each increase in the Ammonia value by one unit, the estimated mean value of DGR will increase by 4.89. Thus, the application of the mass based on the results of this study was able to increase the DGR value Kappaphycus alvarezii, which in turn produce the highest yield of carrageenan with K. alvarezii var.Lampung G3 was the best seed candidate to be developed at the seaweed cultivation site in Tarakan City.Keywords:AlgaePhytohormonesCarrageenanNitrogenViscosity

Coupled hydrogeophysical inversion of an artificial infiltration experiment monitored with ground-penetrating radar: synthetic demonstration

Abstract. In this study, we investigate the use of ground-penetrating radar (GPR) time-lapse monitoring of artificial soil infiltration experiments. The aim is to evaluate this protocol in the context of estimating the hydrodynamic unsaturated soil parameter values and their associated uncertainties. The originality of this work is to suggest a statistical parameter estimation approach using Markov chain Monte Carlo (MCMC) methods to have direct estimates of the parameter uncertainties. Using the GPR time data from the moving wetting front only does not provide reliable results. Thus, we propose to use additional information from other types of reflectors to optimize the quality of the parameter estimation. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity Ks, the saturated and residual water contents θs and θr, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the MCMC method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the GPR data to the hydrodynamic soil parameters are different between moving and fixed reflectors, whereas fixed reflectors at various depths have similar sensitivities. Ks has a similar and strong influence on the data of both types of reflectors. Concerning the other parameters, for the wetting front, only θs and α have an influence, and only at long time steps since the total variance is zero at the very beginning of the experiment. On the other hand, for the fixed reflectors, the total variance is not zero at the very start and the parameters θs, θr, α and n can have an influence from the very beginning of the infiltration. Results of parameter estimation show that the use of calibration data from the moving or fixed reflectors alone does not enable a good identification of all soil parameters. With the moving reflector, the error between the estimated mean value and the exact target value for θr and α is 9 % and 45 %, respectively, and less than 3 % for the other parameters. The best reduction of the size of the parameter distribution is obtained for n, with a posterior distribution 9 times smaller than the prior one. For the others, this reduction ratio varies between 1 and 5. For the fixed reflectors, the estimated mean values are far from the target values for α, θr and n, representing for a reflector located at 120 cm 15 %, 27 %, and 121 %, respectively. On the other hand, when both data are combined, all soil parameters can be well estimated with narrow confidence intervals. For instance, when using both data from the moving wetting front and a fixed reflector located at 120 cm for calibration, the estimated mean values of the errors of all parameters are less than 5 %. Moreover, all parameter distributions are well reduced, with a maximum reduction for Ks, leading to a posterior distribution being 46 times smaller than the prior one, and the worst but still satisfactory being for θr for which the posterior distribution is 8 times smaller than the prior one. The methodology was applied to fine, medium, and coarse sands with very good results, particularly for the finest soil. The thickness of the unsaturated zone was also tested (0.5, 1, and 2 m) and a better estimation of the hydrodynamic parameters is obtained when the water table is deeper. In addition, the height of water applied in the infiltrometry test influences the speed of the test without affecting the performance of the proposed method.

Analysis of the radiological dose and hazards assessment around swampy agricultural soil in Keffi, Nasarawa State, Nigeria

The present study analyzes radiological dose and hazard around the swampy agricultural soil in Keffi Local Government Area of Nasarawa State, using determined activity concentration (AC) of 238U, 232Th and 40K obtained from swampy agricultural soil samples, systematically collected from Ten (10) sampled points. Samples collected were further analyzed using a sodium iodide detector for activity concentrations of 238U, 232Th and 40K. The average AC of 238U, 232Th and 40K were 26.73±4.64, 9.77±2.57 and 1115.52 ±67.43 Bq/kg, respectively. The gamma absorbed dose rate (Dabs) ranges from 6.37E-01 to 2.33E+01 nGy/hr with a mean value of 6.10E+00 nGy/hr. The annual effective dose equivalent (AEDE) ranges from 8.12E-03 to 2.97E-01 mSv/yr with an estimated mean value of 7.77E-02 mSv/yr. The annual gonadal dose equivalent ranges from 4.48E-02 to 1.72E+01 mSv/yr with a mean value of 4.49E-01 mSv/yr. The calculated radium equivalent activity ranges from 1.44E+01 to 4.49E+02 Bq/kg with a mean value of 1.18E+02 Bq/kg, which falls below the recommended standard value of 3.7E+02 Bq/kg. The external and internal hazard index ranges from 3.89E-02 to 1.21E+00 mSv/yr with a mean value of 3.20E-01 mSv/yr, and 3.90E-02 to 1.41E+00 mSv/yr with a mean value of 3.70E-01 mSv/yr. The gamma hazard index ranges from 5.24E-02 to 1.84E+00 mSv/yr with a mean value of 4.83E-01 mSv/yr. The activity utilization index ranges from 8.65E-02 to 1.34E+00 mSv/yr with a mean value of 3.82E-01 mSv/yr, excess life cancer risk (ELCR) for both adult and child was found to be 1.94E-01 and 2.72E-01, respectively, higher than the recommended world average value of 0.29E-03. The high value of ELCR implies that residents around the study area have a high chance of developing cancer over a lifetime. Hence periodic radiological dose and hazard analysis is recommended to keep the exposure as low as reasonably achievable.

Small-sample confidence interval estimation of the common mean value of a multivariate normal distribution

We derive two new interval estimators for the common mean of a multivariate normal distribution, the general-t confidence interval, and an integrated-likelihood-ratio (ILR) confidence interval. Our numerical evaluations, Monte Carlo simulations, and two real-data-example results suggest that for many realistic multivariate covariance matrices, our general-t interval yields more precise confidence intervals than the conditional-t or ILR confidence intervals when the sample size is small relative to the number of parameters to be estimated. We also prove that for a general class of covariance structures, the general-t interval yields narrower expected lengths than the conditional-t interval proposed by Halperin (1961) for all samples of size two or more. Additionally, via a Monte Carlo simulation, we demonstrate that for a fixed sample size, a confidence interval studied in Krishnamoorthy and Lu (2005) consisting of the shortest of the computed univariate marginal-t intervals yields sub-nominal coverage that becomes increasingly sub-nominal as the multivariate data dimension increases.

Establishment and Characterization of the First Chinese National Standard for Nucleic Acid Amplification Technology Assays for Hepatitis E Virus Nucleic Acid Detection.

The detection of hepatitis E virus (HEV) RNA is the gold standard for HEV infection diagnosis. In order to address the quality control requirements for HEV RNA detection kits within China, we aimed to establish the first Chinese national standard for HEV RNA detection through a collaborative study. The candidate standard was quantified using digital PCR (dPCR). A total of five laboratories were invited to determine the estimated mean value of this national standard relative to the World Health Organization International Standard (WHO IS). Additionally, four commercial kits were used to assess the applicability of the candidate standard. The stability was determined by freeze-thaw cycles and storage at 37 °C, 25 °C and 4 °C. The estimated mean value of this national standard relative to the WHO IS was 5.67 log10 IU/mL. Two out of the four commercial kits can detect as low as the estimated limit of detection (LOD). The degradation rates of samples in the stability study ranged from 4% to 19%. In conclusion, we have established the first Chinese national standard for HEV nucleic acid detection against WHO IS, which can be employed to evaluate the quality of HEV RNA detection kits.

AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS

AbstractThis paper gives an explicit version of Selberg’s mean-value estimate for the prime number theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to short-interval results for primes and for Goldbach numbers. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32\,277\log ^2 y]$ for at least half the $y\in [x,2x]$ for all $x\geq 2$ , and at least one Goldbach number in $(x,x+9696 \log ^2 x]$ for all $x\geq 2$ .

A Design and Analytical Strategy for Monitoring Disease Positivity and Biomarker Levels in Accessible Closed Populations.

In this paper, we advocate and expand upon a previously described monitoring strategy for efficient and robust estimation of disease prevalence and case numbers within closed and enumerated populations such as schools, workplaces, or retirement communities. The proposed design relies largely on voluntary testing, which is notoriously biased (e.g., in the case of coronavirus disease 2019) due to nonrepresentative sampling. The approach yields unbiased and comparatively precise estimates with no assumptions about factors underlying selection of individuals for voluntary testing, building on the strength of what can be a small random sampling component. This component enables the use of a recently proposed "anchor stream" estimator, a well-calibrated alternative to classical capture-recapture (CRC) estimators based on 2 data streams. We show that this estimator is equivalent to a direct standardization based on "capture," that is, selection (or not) by the voluntary testing program, made possible by means of a key parameter identified by design. This equivalency simultaneously allows for novel 2-stream CRC-like estimation of general mean values (e.g., means of continuous variables like antibody levels or biomarkers). For inference, we propose adaptations of Bayesian credible intervals when estimating case counts and bootstrapping when estimating means of continuous variables. We use simulations to demonstrate significant precision benefits relative to random sampling alone.

Fixed-time adaptive tracking control of two moving targets for a class of non-linear multi-agent systems

In this research paper, the fixed-time adaptive tracking of two moving targets for a class of unknown non-linear multi-agent systems based on a distributed competition approach is studied. Each agent simultaneously participates in two competitions based on the k-Winner Take All (k-WTA) approach to obtain its allocation status. Using a mean value estimator, the agent can calculate its allocation status only by its neighbor's information. Since an agent can only track one target, an extended tracking error is introduced, where if the agent wins one of the competitions, it will track the assigned target, and if the agent wins both competitions, by selecting one of the targets, track the selected target. Also, the agent which is not win any competitions, return to a specified point. Then, using neural networks and adaptive techniques, an adaptive fixed-time controller is introduced for the agents to track the target based on the allocation status or to return to the specified point. Analysis of the stability of the closed-loop system through the Lyapunov theorem is investigated. Finally, a simulation study to show the efficiency of the theoretical results is presented.

Temporal Evolution of PM2.5 Levels and COVID-19 Mortality in Europe for the 2020–2022 Period

Air pollution has a strong impact on human health, from respiratory and severe pulmonary diseases to heart attack and cancer. During the 3 years of the COVID-19 pandemic, several peaks of mortality occurred, which could be related to particulate matter (PM) pollution events. The possible effects of PM (PM10 and PM2.5, with diameters less than 10 and 2.5 µm, respectively) on COVID-19 mortality have now been established. To better understand this relationship at the European level for the period 2020–2022, data from 16 representative locations in Europe (81 million people) with PM2.5 levels (µg·m−3) ranging from low to high values were analyzed using statistical methods. The analysis confirms a temporal relation between the peaks of PM2.5 exposure and COVID-19 mortality. The best correlation was obtained considering the history of exposure to PM2.5 pollution during a 2-month integration time coupled with a one-week delay for the COVID-19 mortality. Although the trend of COVID-19 mortality vs. PM2.5 levels varies among locations, the global trend was similar, giving an estimated mean value of a 40 ± 20% mortality increase per µg·m−3 PM2.5 increase. The stronger the positive (negative) gradient of the PM peak, the stronger the positive (negative) gradient of the COVID-19 mortality. These results indicate that a succession of PM pollution peaks could be more dangerous than permanent exposure to moderate pollution levels. Finally, PM number concentrations should be used in the future rather than the PM2.5 mass concentrations (µg·m−3), with the consideration of PM composition to better evaluate the effect of submicron particles on human health, particularly for other respiratory diseases. These results must be considered in the management of future pandemics.