Bi-exponential modelling of $$W^{^{\prime}}$$ reconstitution kinetics in trained cyclists

Purpose The aim of this study was to investigate the individual $$W^{^{\prime}}$$ W ′ reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe $$W^{^{\prime}}$$ W ′ reconstitution. Methods Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; $$\dot{V}{\text{O}}_{2\max }$$ V ˙ O 2 max 58.6 ± 7.1 mL kg min−1) completed three incremental ramps (20 W min−1) to the limit of tolerance with varying recovery durations (15–360 s) on 5–9 occasions. $$W^{^{\prime}}$$ W ′ reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R2 and bias-corrected Akaike information criterion (AICc). Results A bi-exponential model outperformed the mono-exponential model of $$W^{^{\prime}}$$ W ′ reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR2 = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)FC = 21.5 s; τSC = 388 s. Following the second recovery, W′ reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τSC to 716 s with τFC unchanged. Individual bi-exponential models also fit well (adjR2 = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)FC = 22.0 ± 11.8 s; (τ)SC = 377 ± 100 s; second recovery: (τ)FC = 16.3.0 ± 6.6 s; (τ)SC = 549 ± 226 s). Conclusions W′ reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W′ reconstitution confined to an increase in the time constant of the slow component.

Adult body size measurement redundancies in Osmia lignaria and Megachile rotundata (Hymenoptera: Megachilidae)

Metrics to assess relative adult bee body size have included both mass and morphometrics, but these metrics may not equally or reliably estimate body size for all bee species and in all situations, due to bee age, diet, and/or environment. Understanding the relationships between different metrics and possible redundancies in the information they afford is important but not always known. Body size measurements provide valuable data for interpreting research outcomes for managed solitary bees, including Osmia lignaria Say and Megachile rotundata F. (Hymenoptera: Megachilidae). Applied studies of these important and readily available U.S. crop pollinators focus on refining commercial management practices, and basic empirical studies in various scientific disciplines (from genomics to ecology) employ them as model systems to study solitary bees. To examine common metrics of body size, we measured head capsule width (HCW), intertegular distance (ITD), and fresh and dry weights of newly emerged adults of both species. Using linear and exponential models, we determined relationships between these body size metrics. For M. rotundata, linear models best described relationships between ITD and all other metrics, and between HCW and fresh and dry weights. For O. lignaria, linear models best fit relationships between all metrics except for fresh weight with both ITD and HCW, which were fitted better with exponential models. For both species, model fits were strongest when males and females were pooled. Depending on the study question, knowing that only one metric may reliably measure body size can simplify evaluations of O. lignaria and M. rotundata responses to artificial or environmental variables.

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.

Modeling of Phosphorus Nutrition to Obtain Maximum Yield, High P Use Efficiency and Low P-Loss Risk for Wheat Grown in Sandy Calcareous Soils

Fertilization with high levels of phosphorus increases the risk of environmental pollution. Identification of critical values of P in soil (SOP) and in plant tissues (PiP) is essential for achieving the maximum wheat yield without P loss. The critical value is the value of P which gives the optimum yield; the response of crop yield to P fertilization above this value is not predictable or nil. Here, a 4-year field experiment was conducted to identify the SOP and PiP for achieving maximum yield of bread wheat using 11 rates of P fertilization (0, 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150 kg P2O5 ha−1). The linear–linear and Mitscherlich exponential models were employed to estimate the PiP and SOP. The degree of phosphorus saturation (DPS) was used to assess the potential environmental risk; furthermore, phosphorus use efficiency (PUE) was also calculated under the studied fertilization levels. Phosphorus in soil and wheat plant was affected by the application rates and growing seasons. Increasing P fertilization rates led to gradual increases in soil and plant P. The SOP ranged between 21 and 32 mg kg−1, while the PiP ranged between 6.40 and 7.49 g kg−1. The critical values of P calculated from the Mitscherlich exponential models were 20% higher than those calculated from the linear–linear models. Adding levels of P fertilization ≥90 kg P2O5 ha−1 leads to higher potentials of P runoff and leaching, in addition, PUE decreased sharply under high P fertilization levels. The response of wheat yield to P fertilization in sandy calcareous soil is predictable below Olsen P values of 21 mg kg−1. Identification of critical P values for wheat production is of great importance to help policy makers improve P use efficiency and attain optimum wheat yield under eco-friendly environmental conditions by eliminating the accumulation of excess P fertilizers in soil and water.

Wormhole Solutions in Symmetric Teleparallel Gravity with Noncommutative Geometry

This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model f(Q)=Q−α1−e−Q, where Q is the non-metricity and α is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.

Comparing critical speed modelling approaches and exploring relationships with match-play variables in elite male youth soccer players

Background: A novel bi-exponential method has emerged to estimate critical speed (CS) and D-prime (D′) from a 3-min all- out test (3MT). Objectives: To compare CS analysis methods to determine whether parameter estimations were interchangeable. Reference values and relationships with key soccer match- play variables were explored. Methods: Thirteen elite male youth (14-15 years old) players completed a 30 m shuttle run 3MT to estimate CS, D′, rate of speed decline time constant, maximal speed (Smax), time to Smax (tmax), and fatigue index (FI), using the traditional method and bi-exponential model on average (Bi-ExpAverage) and max speed settings (Bi-ExpMax-Speed). High-speed running (HSR) and sprinting distances and counts, and the number of accelerations were collected from two matches. Magnitude- based inferences (p < 0.05) with smallest worthwhile change of 0.2 effect sizes were used to analyse differences. Pearson’s and Spearman’s correlation coefficients were used to measure associations between CS model variables and match-play parameters. Results: There were significant differences between the traditional method and both bi-exponential models for CS and D′, as well as between the bi-exponential models for all variables except tmax. Using the Bi-ExpAverage model, strong correlations (r = 0.70-0.73; p < 0.05) were observed for D′ and FI with the number of standardised and individualised HSRs, respectively. With the Bi-ExpMax-Speed model, there were strong correlations (r/ρ = 0.64-0.68; p < 0.05) between D′ and the number of standardised HSRs and sprints, and the number of individualised sprints. Conclusion: There is a lack of interchangeability between analysis methods. It appears that D′ and FI from the bi- exponential models could be associated with high-intensity actions in soccer match-play.

Diffusion-weighted MRI for predicting pathologic response to neoadjuvant chemotherapy in breast cancer: evaluation with mono-, bi-, and stretched-exponential models

Background To investigate the performance of diffusion-weighted (DW) MRI with mono-, bi- and stretched-exponential models in predicting pathologic complete response (pCR) to neoadjuvant chemotherapy (NACT) for breast cancer, and further outline a predictive model of pCR combining DW MRI parameters, contrast-enhanced (CE) MRI findings, and/or clinical-pathologic variables. Methods In this retrospective study, 144 women who underwent NACT and subsequently received surgery for invasive breast cancer were included. Breast MRI including multi-b-value DW imaging was performed before (pre-treatment), after two cycles (mid-treatment), and after all four cycles (post-treatment) of NACT. Quantitative DW imaging parameters were computed according to the mono-exponential (apparent diffusion coefficient [ADC]), bi-exponential (pseudodiffusion coefficient and perfusion fraction), and stretched-exponential (distributed diffusion coefficient and intravoxel heterogeneity index) models. Tumor size and relative enhancement ratio of the tumor were measured on contrast-enhanced MRI at each time point. Pre-treatment parameters and changes in parameters at mid- and post-treatment relative to baseline were compared between pCR and non-pCR groups. Receiver operating characteristic analysis and multivariate regression analysis were performed. Results Of the 144 patients, 54 (37.5%) achieved pCR after NACT. Overall, among all DW and CE MRI measures, flow-insensitive ADC change (ΔADC200,1000) at mid-treatment showed the highest diagnostic performance for predicting pCR, with an area under the receiver operating characteristic curve (AUC) of 0.831 (95% confidence interval [CI]: 0.747, 0.915; P < 0.001). The model combining pre-treatment estrogen receptor and human epidermal growth factor receptor 2 statuses and mid-treatment ΔADC200,1000 improved the AUC to 0.905 (95% CI: 0.843, 0.966; P < 0.001). Conclusion Mono-exponential flow-insensitive ADC change at mid-treatment was a predictor of pCR after NACT in breast cancer.