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We develop an expression for the Li-Keiper coefficients λn in terms of k-blocks partitions, to begin with, for low values of n. The k-blocks partitions are given in terms of our cluster functions φn and the main point of this work lies in the emergence of an alternating sequence of values converging toward values of λn near the true values, i.e., increasing the index k of the blocks one obtains an increasing range of positivity of the Li-Keiper coefficients. With the contribution of k = 1 and k = 2 blocks, positivity of the λn is reached already until n = 26-27. The treatment is given here until k = 4 blocks up to n = 30. λn are all found to be positive.

To obtain a thorough knowledge of PM2. 5 chemical composition and its impact on aerosol optical properties across China, existing field studies conducted after the year 2000 are reviewed and summarized in terms of geographical, interannual and seasonal distributions. Annual PM2. 5 was up to 6 times the National Ambient Air Quality Standards (NAAQS) in some megacities in northern China. Annual PM2. 5 was higher in northern than southern cities, and higher in inland than coastal cities. In a few cities with data longer than a decade, PM2. 5 showed a slight decrease only in the second half of the past decade, while carbonaceous aerosols decreased, sulfate (SO42−) and ammonium (NH4+) remained at high levels, and nitrate (NO3−) increased. The highest seasonal averages of PM2. 5 and its major chemical components were typically observed in the cold seasons. Annual average contributions of secondary inorganic aerosols to PM2. 5 ranged from 25 to 48 %, and those of carbonaceous aerosols ranged from 23 to 47 %, both with higher contributions in southern regions due to the frequent dust events in northern China. Source apportionment analysis identified secondary inorganic aerosols, coal combustion and traffic emission as the top three source factors contributing to PM2. 5 mass in most Chinese cities, and the sum of these three source factors explained 44 to 82 % of PM2. 5 mass on annual average across China. Biomass emission in most cities, industrial emission in industrial cities, dust emission in northern cities and ship emission in coastal cities are other major source factors, each of which contributed 7–27 % to PM2. 5 mass in applicable cities. The geographical pattern of scattering coefficient (bsp) was similar to that of PM2. 5, and that of aerosol absorption coefficient (bap) was determined by elemental carbon (EC) mass concentration and its coating. bsp in ambient condition of relative humidity (RH)  =  80 % can be amplified by about 1.8 times that under dry conditions. Secondary inorganic aerosols accounted for about 60 % of aerosol extinction coefficient (bext) at RH greater than 70 %. The mass scattering efficiency (MSE) of PM2. 5 ranged from 3.0 to 5.0 m2 g−1 for aerosols produced from anthropogenic emissions and from 0.7 to 1.0 m2 g−1 for natural dust aerosols. The mass absorption efficiency (MAE) of EC ranged from 6.5 to 12.4 m2 g−1 in urban environments, but the MAE of water-soluble organic carbon was only 0.05 to 0.11 m2 g−1. Historical emission control policies in China and their effectiveness were discussed based on available chemically resolved PM2. 5 data, which provides the much needed knowledge for guiding future studies and emissions policies.

The global annual death toll due to drowning is of the order of 10 5 . Rescue and search operations in urban rivers show a low rate of success. Operational computational drift models have been developed for marine environments but not for the case of river drowning. In the latter case, no scale separation occurs between the body and flow length scales. To model them, three hydrodynamic force coefficients of representative bodies, such as drag, side and lift coefficients, are needed. So far, their value was not characterized for the typical positioning of the body of a drowning victim. In this work, we used full-scale laboratory experiments to identify the range of value of these hydrodynamic coefficients based on 249 tests conducted in a wind tunnel. Observations in the air can be transferred to water environment thanks to flow similarity. For the typical body positioning of a drowning victim, the drag coefficient was found to vary in the range 0.5–1.2. Changing the yaw angle of the body, induces variations in the drag coefficient by about 50%. Considering loose clothes instead of tight clothes leads to an increase in the drag coefficient by about 30%, whereas adding a backpack has a limited influence (less than 5%). With the available experimental setup, it has been difficult to detect distinctive patterns and trends for the side and lift coefficients. This study is part of a multidisciplinary effort for developing scientific knowledge and technologies contributing to a reduction of drowning-induced fatalities in rivers.

Dynamic viscosity coefficient is an important dynamic property of rocks. Its accurate determination is the prerequisite for exploring the dynamic viscosity of rocks. To investigate the evolution of the dynamic viscosity coefficient of deep rocks under high water pressure and high-stress conditions, a series of impact experiments are first conducted on red sandstone using a self-developed dynamic test system. Then, the analytical expression of the dynamic viscosity coefficient of rocks is derived from the amplitude attenuation coefficient based on the Maxwell model. The test results demonstrate that the amplitude attenuation coefficient varies with harmonic frequency and frequency peaks fall in a range of 8–9 kHz. Within this frequency range, the energy consumption of stress wave caused by crack expansion in rock is most pronounced. A frequency range of 8–9 kHz is suggested to calculate the dynamic viscosity coefficient. The validation of the suggested method for determining the dynamic viscosity coefficient is verified by comparing the relative errors between the predicted and tested values of dynamic strain. The results demonstrate that the suggested method is feasible. Then, the effects of water pressure and axial static stress on the dynamic viscosity coefficient of the red sandstone are discussed. As the water pressure rises, the dynamic viscosity coefficient tends to increase first and then decrease, while it monotonically decreases with increasing axial static stress. Finally, the mechanism of dynamic viscosity coefficient changing along with water pressure and axial stress is revealed from the view of wave impedance. These insights provide a theoretical foundation for the prevention of water inrush in deep rock engineering.Article HighlightsThe method for determining the dynamic viscosity coefficient under high water pressure and high-stress conditions is suggested.The effects of water pressure and axial static stress on the dynamic viscosity coefficient of the red sandstone is analyzed based on experimental and analytical results.The impact mechanisms of water pressure and axial static stress on the dynamic viscosity coefficient are revealed based on the evolution of wave impedance.

A large space still exists for improving the measurements used in orthopaedics and sports medicine, especially as we face rapid technological progress in devices used for diagnostic or patient monitoring purposes. For a specific measure to be valuable and applicable in clinical practice, its reliability must be established. Reliability refers to the extent to which measurements can be replicated, and three types of reliability can be distinguished: inter-rater, intra-rater, and test–retest. The present article aims to provide insights into reliability as one of the most important and relevant properties of measurement tools. It covers essential knowledge about the methods used in orthopaedics and sports medicine for reliability studies. From design to interpretation, this article guides readers through the reliability study process. It addresses crucial issues such as the number of raters needed, sample size calculation, and breaks between particular trials. Different statistical methods and tests are presented for determining reliability depending on the type of gathered data, with particular attention to the commonly used intraclass correlation coefficient.

Background To evaluate binary classifications and their confusion matrices, scientific researchers can employ several statistical rates, accordingly to the goal of the experiment they are investigating. Despite being a crucial issue in machine learning, no widespread consensus has been reached on a unified elective chosen measure yet. Accuracy and F 1 score computed on confusion matrices have been (and still are) among the most popular adopted metrics in binary classification tasks. However, these statistical measures can dangerously show overoptimistic inflated results, especially on imbalanced datasets. Results The Matthews correlation coefficient (MCC), instead, is a more reliable statistical rate which produces a high score only if the prediction obtained good results in all of the four confusion matrix categories (true positives, false negatives, true negatives, and false positives), proportionally both to the size of positive elements and the size of negative elements in the dataset. Conclusions In this article, we show how MCC produces a more informative and truthful score in evaluating binary classifications than accuracy and F 1 score, by first explaining the mathematical properties, and then the asset of MCC in six synthetic use cases and in a real genomics scenario. We believe that the Matthews correlation coefficient should be preferred to accuracy and F 1 score in evaluating binary classification tasks by all scientific communities.

We show that Cohen's Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behaviour, i.e. a worse classifier gets higher Kappa score, differing qualitatively from that of MCC. The debate about the incoherence in the behaviour of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies an scenario in which the contradictory behaviour among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rise, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.

Evaluating binary classifications is a pivotal task in statistics and machine learning, because it can influence decisions in multiple areas, including for example prognosis or therapies of patients in critical conditions. The scientific community has not agreed on a general-purpose statistical indicator for evaluating two-class confusion matrices (having true positives, true negatives, false positives, and false negatives) yet, even if advantages of the Matthews correlation coefficient (MCC) over accuracy and F 1 score have already been shown.In this manuscript, we reaffirm that MCC is a robust metric that summarizes the classifier performance in a single value, if positive and negative cases are of equal importance. We compare MCC to other metrics which value positive and negative cases equally: balanced accuracy (BA), bookmaker informedness (BM), and markedness (MK). We explain the mathematical relationships between MCC and these indicators, then show some use cases and a bioinformatics scenario where these metrics disagree and where MCC generates a more informative response.Additionally, we describe three exceptions where BM can be more appropriate: analyzing classifications where dataset prevalence is unrepresentative, comparing classifiers on different datasets, and assessing the random guessing level of a classifier. Except in these cases, we believe that MCC is the most informative among the single metrics discussed, and suggest it as standard measure for scientists of all fields. A Matthews correlation coefficient close to +1, in fact, means having high values for all the other confusion matrix metrics. The same cannot be said for balanced accuracy, markedness, bookmaker informedness, accuracy and F 1 score.

Binary classification is a common task for which machine learning and computational statistics are used, and the area under the receiver operating characteristic curve (ROC AUC) has become the common standard metric to evaluate binary classifications in most scientific fields. The ROC curve has true positive rate  (also called sensitivity or recall ) on the y axis and false positive rate on the x axis, and the ROC AUC can range from 0 (worst result) to 1 (perfect result). The ROC AUC, however, has several flaws and drawbacks. This score is generated including predictions that obtained insufficient sensitivity and specificity, and moreover it does not say anything about positive predictive value  (also known as precision ) nor negative predictive value (NPV) obtained by the classifier, therefore potentially generating inflated overoptimistic results. Since it is common to include ROC AUC alone without precision and negative predictive value, a researcher might erroneously conclude that their classification was successful. Furthermore, a given point in the ROC space does not identify a single confusion matrix nor a group of matrices sharing the same MCC value. Indeed, a given (sensitivity, specificity) pair can cover a broad MCC range, which casts doubts on the reliability of ROC AUC as a performance measure. In contrast, the Matthews correlation coefficient (MCC) generates a high score in its [ - 1 ; + 1 ] interval only if the classifier scored a high value for all the four basic rates of the confusion matrix: sensitivity, specificity, precision, and negative predictive value. A high MCC (for example, MCC = 0.9), moreover, always corresponds to a high ROC AUC, and not vice versa. In this short study, we explain why the Matthews correlation coefficient should replace the ROC AUC as standard statistic in all the scientific studies involving a binary classification, in all scientific fields.

To obtain a thorough knowledge of PM2.5 chemical composition and its impact on aerosol optical properties across China, existing field studies conducted after the year 2000 are reviewed and summarized in terms of geographical, interannual and seasonal distributions. Annual PM2.5 was up to 6 times the National Ambient Air Quality Standards (NAAQS) in some megacities in northern China. Annual PM2.5 was higher in northern than southern cities, and higher in inland than coastal cities. In a few cities with data longer than a decade, PM2.5 showed a slight decrease only in the second half of the past decade, while carbonaceous aerosols decreased, sulfate (SO42-) and ammonium (NH4+) remained at high levels, and nitrate (NO3-) increased. The highest seasonal averages of PM2.5 and its major chemical components were typically observed in the cold seasons. Annual average contributions of secondary inorganic aerosols to PM2.5 ranged from 25 to 48 %, and those of carbonaceous aerosols ranged from 23 to 47 %, both with higher contributions in southern regions due to the frequent dust events in northern China. Source apportionment analysis identified secondary inorganic aerosols, coal combustion and traffic emission as the top three source factors contributing to PM2.5 mass in most Chinese cities, and the sum of these three source factors explained 44 to 82 % of PM2.5 mass on annual average across China. Biomass emission in most cities, industrial emission in industrial cities, dust emission in northern cities and ship emission in coastal cities are other major source factors, each of which contributed 7–27 % to PM2.5 mass in applicable cities.The geographical pattern of scattering coefficient (bsp) was similar to that of PM2.5, and that of aerosol absorption coefficient (bap) was determined by elemental carbon (EC) mass concentration and its coating. bsp in ambient condition of relative humidity (RH) = 80 % can be amplified by about 1.8 times that under dry conditions. Secondary inorganic aerosols accounted for about 60 % of aerosol extinction coefficient (bext) at RH greater than 70 %. The mass scattering efficiency (MSE) of PM2.5 ranged from 3.0 to 5.0 m2 g-1 for aerosols produced from anthropogenic emissions and from 0.7 to 1.0 m2 g-1 for natural dust aerosols. The mass absorption efficiency (MAE) of EC ranged from 6.5 to 12.4 m2 g-1 in urban environments, but the MAE of water-soluble organic carbon was only 0.05 to 0.11 m2 g-1. Historical emission control policies in China and their effectiveness were discussed based on available chemically resolved PM2.5 data, which provides the much needed knowledge for guiding future studies and emissions policies.