Theil Slope Estimate

The present study investigates the behavior of action potential conduction velocity (CV) on each repetition of three isokinetic test sets, focusing on the repetition of peak torque. Results are compared for linear regression slope among the isokinetic sets regarding the rest intervals of one and two minutes. The surface electromyographic signals were recorded from the vastus lateralis muscle during the exercises of maximal concentric repetitions of dominant knee extension at 60°/s. Results show that the slope of CV linear regression increases inside a repetition. However, when observed along the whole set, or between consecutive sets, the CV slope has a decreasing tendency which is higher for shorter rest intervals. This behavior suggests CV slope as good muscle fatigue indicator during isokinetic tests.

Abstract. Long-term PM2.5 data are essential for the atmospheric environment, human health, and climate change. PM2.5 measurements are sparsely distributed and of short duration. In this study, daily PM2.5 concentrations are estimated using a machine learning method for the period from 1959 to 2022 in the Northern Hemisphere based on near-surface atmospheric visibility. They are extracted from the Integrated Surface Database (ISD). Daily continuous monitored PM2.5 concentration is set as the target, and near-surface atmospheric visibility and other related variables are used as the inputs. A total of 80 % of the samples of each site are the training set, and 20 % are the testing set. The training result shows that the slope of linear regression with a 95 % confidence interval (CI) between the estimated PM2.5 concentration and the monitored PM2.5 concentration is 0.955 [0.955, 0.955], the coefficient of determination (R2) is 0.95, the root mean square error (RMSE) is 7.2 µg m−3, and the mean absolute error (MAE) is 3.2 µg m−3. The test result shows that the slope within a 95 % CI between the predicted PM2.5 concentration and the monitored PM2.5 concentration is 0.864 [0.863, 0.865], the R2 is 0.79, the RMSE is 14.8 µg m−3, and the MAE is 7.6 µg m−3. Compared with a global PM2.5 concentration dataset derived from a satellite aerosol optical depth product with 1 km resolution, the slopes of linear regression on the daily (monthly) scale are 0.817 (0.854) from 2000 to 2021, 0.758 (0.821) from 2000 to 2010, and 0.867 (0.879) from 2011 to 2022, indicating the accuracy of the model and the consistency of the estimated PM2.5 concentration on the temporal scale. The interannual trends and spatial patterns of PM2.5 concentration on the regional scale from 1959 to 2022 are analyzed using a generalized additive mixed model (GAMM), suitable for situations with an uneven spatial distribution of monitoring sites. The trend is the slope of the Theil–Sen estimator. In Canada, the trend is −0.10 µg m−3 per decade, and the PM2.5 concentration exhibits an east–high to west–low pattern. In the United States, the trend is −0.40 µg m−3 per decade, and PM2.5 concentration decreases significantly after 1992, with a trend of −1.39 µg m−3 per decade. The areas of high PM2.5 concentration are in the east and west, and the areas of low PM2.5 concentration are in the central and northern regions. In Europe, the trend is −1.55 µg m−3 per decade. High-concentration areas are distributed in eastern Europe, and the low-concentration areas are in northern and western Europe. In China, the trend is 2.09 µg m−3 per decade. High- concentration areas are distributed in northern China, and the low-concentration areas are distributed in southern China. The trend is 2.65 µg m−3 per decade up to 2011 and −22.23 µg m−3 per decade since 2012. In India, the trend is 0.92 µg m−3 per decade. The concentration exhibits a north–high to south–low pattern, with high-concentration areas distributed in northern India, such as the Ganges Plain and Thar Desert, and the low-concentration area in the Deccan Plateau. The trend is 1.41 µg m−3 per decade up to 2013 and −23.36 µg m−3 per decade from 2014. The variation in regional PM2.5 concentrations is closely related to the implementation of air quality laws and regulations. The daily site-scale PM2.5 concentration dataset from 1959 to 2022 in the Northern Hemisphere is available at the National Tibetan Plateau/Third Pole Environment Data Center (https://doi.org/10.11888/Atmos.tpdc.301127) (Hao et al., 2024).

Data evaluation is a crucial step when it comes to the determination of accurate and precise isotope ratios computed from transient signals measured by multi-collector–inductively coupled plasma mass spectrometry (MC-ICPMS) coupled to, for example, laser ablation (LA). In the present study, the applicability of different data evaluation strategies (i.e. ‘point-by-point’, ‘integration’ and ‘linear regression slope’ method) for the computation of 235U/238U isotope ratios measured in single particles by LA-MC-ICPMS was investigated. The analyzed uranium oxide particles (i.e. 9073-01-B, CRM U010 and NUSIMEP-7 test samples), having sizes down to the sub-micrometre range, are certified with respect to their 235U/238U isotopic signature, which enabled evaluation of the applied strategies with respect to precision and accuracy. The different strategies were also compared with respect to their expanded uncertainties. Even though the ‘point-by-point’ method proved to be superior, the other methods are advantageous, as they take weighted signal intensities into account. For the first time, the use of a ‘finite mixture model’ is presented for the determination of an unknown number of different U isotopic compositions of single particles present on the same planchet. The model uses an algorithm that determines the number of isotopic signatures by attributing individual data points to computed clusters. The 235U/238U isotope ratios are then determined by means of the slopes of linear regressions estimated for each cluster. The model was successfully applied for the accurate determination of different 235U/238U isotope ratios of particles deposited on the NUSIMEP-7 test samples.Electronic supplementary materialThe online version of this article (doi:10.1007/s00216-012-6674-3) contains supplementary material, which is available to authorized users.

Influence of disease severity in the efficacy response of Parkinson's disease patients with motor fluctuations: Post-hoc analysis from combined BIPARK-I and II

The fact that Pearson's correlation coefficient and effect size are perspective functions of covariance parameters demonstrates that how covariance is defined is one of the most important issues in data analysis. We suggest that covariance analysis for pairwise numeric, categorical, and mixed numeric-categorical data types are mathematically distinct problems. This is because of the disparate algebraic properties and systematic effects associated with numeric and categorical quantities. We examine the weighted least squares (WLS) formulation of linear regression and obtain definitions for heteroscedastic covariance and variance. Covariance and variance as functions of centered variable vectors are instrumental quantities. Then it is essential that the instrumental effects cancel when dividing covariance by the variance to estimate the slope in linear regression. The tensor product form of the covariance demonstrates that the composite properties of variable vectors are intrinsic to covariate data analysis. The solution of the inverse problem for linear regression takes the form of a relation between slope and covariance parameters, and requires the specification of an error model for the data; otherwise, the inverse problem is ill-posed. We propose that, in current practice, the term “effect size” is ambiguous because it does not distinguish between the different algebraic components of the inverse problem in a case-control data analysis. Then, it is necessary to identify the analogs of WLS covariance for case-control data and to distinguish between covariance and functional parameters in effect size analysis. The development of effect size methodology for studies of complex systems is complicated by the fact that the functional inverse problem is ill-posed.

An earlier study by one of the authors reported significant differences of up to 21% in linear regression slopes between six Kipp & Zonen large-aperture scintillometers. In this note, the consistency of this increasingly popular instrument for measuring sensible heat fluxes at the km scale was quantified by comparing measurements from four Scintec boundary-layer scintillometers and one large-aperture scintillometer over nearly identical transects. The Kipp & Zonen instrument’s sensible heat fluxes were more than 20% larger than those from the Scintec instruments, while the difference in regression slopes amongst the Scintec instruments was 3% or less.

Purpose The QT interval on an ECG is influenced by heart rate, requiring correction formulas for adjusted QT (QTc) values. In daily clinical practice, Bazett's formula is the most commonly used, while the FDA recommends Fridericia's formula for drug development. Other commonly used formulas include Framingham and Hodges. This study compared the accuracy of these four frequently used formulas in correcting the QT interval for heart rate. Methods We retrospectively assessed ECGs from 22.063 medically assessed healthy individuals who participated in phase 1 trials between 1997 and 2023. Pearson correlation coefficient (r) between QTc and heart rate (HR) and the linear regression slope (b) were calculated for each formula and the influence of age, sex and body mass index. Results The study analyzed 16,170 males and 5,893 females (mean age: 34.9 ± 15.3 years) to assess QTc-heart rate (HR) correlations. The Fridericia formula showed the strongest reliability, with the lowest correlation (r = 0.018) and a nearly horizontal regression slope (b = 0.04). The Hodges (r = –0.182, b = 0.39) and Framingham (r = 0.200, b = 0.43) formulas followed. The Bazett formula performed worst (r = 0.483, b = 1.12). Fridericia remained the most accurate across subgroups except in low BMI groups and differed significantly from other formulas in both sexes (P < 0.05). Conclusion In apparently healthy individuals, the Fridericia formula is the most reliable method for correcting the QT interval for heart rate, and we recommend its use in studies involving heathy subjects.Comparison of measured QT intervals

This study was designed to compare neuromuscular response between boys and men during sustained maximal voluntary contraction (MVC). Fifteen boys (YB, 10.5 +/- 0.9 yr) and 12 men (AM, 21.5 +/- 4.5 yr) participated in the experiment. Arm's cross sectional area (CSA) and maximal force (F(max)) of elbow flexor were measured before subjects performed a 30-s sustained MVC. Mean power frequency (MPF) and muscle fiber conduction velocity (MFCV) were calculated from myoelectric signals of the biceps brachii. F(max)/CSA, MPF, and MFCV changes were expressed by slopes of linear regressions. Maximal MPF (I-MPF) and MFCV (I-MFCV) were derived from the intercept of each regression. AM had significantly greater F(max)/CSA (P < 0.05), I-MPF (P < 0.05), and I-MFCV (P < 0.01) than YB. F(max)/CSA (P < 0.001), MPF (P < 0.001), and MFCV (P < 0.01) declined significantly more for AM than YB. MPF/MFCV ratio increased, i.e., MPF decreased more than MFCV, for both groups but this was significantly (P < 0.001) more pronounced for AM. Taken together, those results suggest that more fatigable Type II motor units are involved in men, resulting in greater lactic acid and ions accumulations during fatigue. This difference in muscle's metabolic and ionic state could be responsible for a greater reflex-induced decrease of motor units firing rates in men compared with boys. This firing rate decrease could be explained using the "muscular wisdom" hypothesis and would express a nervous command adaptation to sustain a maximal contraction.

Author Posting. © National Shellfisheries Association, 2008. This article is posted here by permission of National Shellfisheries Association for personal use, not for redistribution. The definitive version was published in Journal of Shellfish Research 27 (2008): 169-175, doi:10.2983/0730-8000(2008)27[169:HVMHCP]2.0.CO;2.

A new approach was demonstrated for the isotope ratio measurement in different elemental species of Hg using transient signal obtained by chromatography coupled with multicollector-inductively coupled plasma mass spectrometry (MC-ICPMS). The method based on the slope of linear regression by transient intensities of different isotopes shows improved accuracy and reproducibility (0.2-0.5 per thousand as 2 standard deviation (SD)). Internal precision (RSD) of the method is very close to the theoretical value given by the counting statistic and is better by a factor of 6 in comparison with previous conventional methods of calculation. We demonstrated that internal RSD (uncertainty) depends on regression coefficients of the linear function (R(2)). The typical internal precision of isotopic ratio measurements (0.003-0.02%) was achieved for delta(202)Hg when injecting as low as 90 pg of Hg species. With the new methodology, it is possible to (i) measure the isotopic composition when a sample and a bracketing standard have significantly different concentrations, (ii) measure the isotopic composition of different species in samples versus single species in a bracketing standard, and (iii) measure the isotopic ratios for low abundant isotopes. We demonstrated application of this method for different environmental samples and processes.

Monitoring of structures and defining the severity of damages that occur under loading are essential in practical applications of civil infrastructure. In this article, we analyze failure using a smart aggregate sensor–based approach. The signals captured by smart aggregate sensors mounted on the structure under loading are de-noised using wavelet de-noising technique to prevent misdirection of the event interpretation of what is happening in the material. The performance of different mother wavelets on the de-noising process was investigated and analyzed. The objective is to identify the optimal mother wavelet for assessing and potentially reducing the effects of existing noise on signal properties for structural damage detection. In addition, we propose two innovative damage indices, entropy-based dispersion and entropy-based beta, for diagnostic purposes. The proposed entropy-based dispersion damage index is based on the modified wavelet packet tree and root mean square deviation, whereas the entropy-based beta damage index is based on the modified wavelet packet tree and slope of linear regression (beta). In both damage indices, the modified wavelet packet tree uses entropy as a high-level feature. Theoretical and experimental analyses are derived by computing indices on smart aggregate–based sensor data for concrete and reinforced-concrete beams. Validity assessment of the proposed indices was addressed through a comparative analysis with root mean square deviation damage index (benchmark) and the loading history. The proposed indices recognized the cracks faster than other measures and well before major cracking incurs in the structure. This article is expected to be beneficial for smart aggregate–based structural health monitoring applications particularly when damages occurred under loading.

Decreased temporary turnover of bacterial communities along soil depth gradient during a 35-year grazing exclusion period in a semiarid grassland

For its application in cancer therapy, targeted drug delivery, radiofrequency ablation, and magnetic resonance imaging, the dynamics of electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been elucidated numerically. The impact of second-order hydrodynamic-slip, nanoparticle radius, first-order thermal-slip, inter-particle spacing and non-uniform heat source are also accounted. The modeled flow equations are transmuted into a nonlinear system of first-order ODEs (with the aid of apposite similarity variables) which are then resolved numerically utilizing the bvp5c scheme. The thermal field augments with an increase and a decrease in the inter-particle spacing and radius of gold-nanoparticles, respectively. However, a reverse trend is noted for the velocity profile when the radius and inter-particle spacing of gold-nanoparticles are altered. The trend and magnitude of the change in the drag rate and heat transfer rate under the influence of effectual parameters have been demonstrated statistically using slope of linear regression. It is noticed that per unit increase in the volume fraction of gold nanoparticles augments the heat transfer rate by 81.71% and reduces the surface drag by 163.51%. Further, per unit increase in the inter-particle spacing of gold nanoparticles augments the drag coefficient by 85.92% whereas per unit increase in the radius of gold nanoparticles reduces the skin friction coefficient by 49.71%.

The relationship between growth respiration and nitrogen content in rice organs was investigated. Top and root CO2 exchange rates were continuously measured for 5-6 days under different nutrient concentrations by lowering the light intensity with each passing day. There were significant positive correlations between the growth respiration rate in the top (Rgt) and dry matter increase in the top, and between the growth respiration rate in the root (Rgt) and dry matter increase in the root. Though, there were significant positive correlations between Rgt and leaf area expansion, and leaf dry matter increase, no significant relationship was found between Rgt and dry matter in leaf sheath. The growth respiration rate in each plant part was closely related to the dry matter increase and nitrogen increase. The nitrogen content of the leaf blade was higher than that of the leaf sheath. This suggests that growth respiration in the top is utilized more for the growth of leaf blade than that of leaf sheath. Moreover, the ranges of growth coefficient in the whole plant, top and root were from 0.56 to 1.26, 0.44 to 1.11, and 0.60 to 1.11 g g-1, respectively, under different nutrient conditions. The growth coefficient of each part increased as the result of nitrogen content in new biomass. The growth coefficient in the root was higher than that in the top when compared at the same value of the ratio of the increase in nitrogen. The slope of linear regression in the root was higher than that in the top. In this paper, it was determined quantitatively the relationship between nitrogen increase and growth coefficient in rice organs.

Rate of force development and relaxation scaling factors are highly sensitive to detect upper extremity motor impairments in multiple sclerosis