Simple Quadratic Model Research Articles

Flavonoid Oxidation Potentials and Antioxidant Activities-Theoretical Models Based on Oxidation Mechanisms and Related Changes in Electronic Structure.

Herein, I will review our efforts to develop a comprehensive and robust model for the estimation of the first oxidation potential, Ep1, and antioxidant activity, AA, of flavonoids that would, besides enabling fast and cheap prediction of Ep1 and AA for a flavonoid of interest, help us explain the relationship between Ep1, AA and electronic structure. The model development went forward with enlarging the set of flavonoids and, that way, we had to learn how to deal with the structural peculiarities of some of the 35 flavonoids from the final calibration set, for which the Ep1 measurements were all made in our laboratory. The developed models were simple quadratic models based either on atomic spin densities or differences in the atomic charges of the species involved in any of the three main oxidation mechanisms. The best model takes into account all three mechanisms of oxidation, single electron transfer-proton transfer (SET-PT), sequential proton loss electron transfer (SPLET) and hydrogen atom transfer (HAT), yielding excellent statistics (R2 = 0.970, S.E. = 0.043).

Relação entre índices espectrais e parâmetros de qualidade da forrageira tifton 85

ABSTRACT Computer vision systems can be an alternative to traditional methods of analyzing the quality of forage crops, allowing the instantaneous, non-destructive monitoring of the crop, with cost reduction. This study aimed to evaluate the quality parameters of Tifton 85 (Cynodon spp.) using digital images, relating spectral indices to the quality parameters of this forage. In the experimental area, four levels of nitrogen fertilization were applied and the analyses were made at different times after the standardization cut (14, 28, 42, and 56 days). The quality parameters evaluated were mineral matter, crude protein, and neutral detergent fiber. From images obtained in the visible (RGB) and near-infrared (RGNIR) spectral regions, spectral indices were generated. Principal component analysis was applied to summarize the information obtained by spectral indices into a single principal component (PCI). PCI associated with spectral indices was related to forage quality parameters for each cutting time using simple quadratic regression models. The relationships between mineral matter and spectral indices were variable over time. Crude protein and neutral detergent fiber showed the highest relationships with the spectral indices obtained by RGNIR images already at the initial times. Thus, although the RGB images have shown satisfactory results to obtain information about the quality of Tifton 85, the NIR band tends to increase the reliability of the relationships at early times.

Predicting Total Back Squat Repetitions from Repetition Velocity and Velocity Loss.

The purpose of this investigation was to determine if average concentric velocity (ACV) of a single repetition at 70% of one-repetition maximum (1RM), ACV of the first repetition of a set to failure at 70% of 1RM, or the velocity loss during the set could predict the number of repetitions performed in the back squat. Fifty-six resistance-trained individuals participated in the study (male = 41, age = 23 ± 3 yrs, 1RM = 162.0 ± 40.0 kg; female = 15, age = 21 ± 2 yrs, 1RM = 81.5 ± 12.5 kg). After 1RM testing, participants performed single repetition sets with 70% of 1RM and a set to failure with 70% of 1RM. ACV was recorded on all repetitions. Regression model comparisons were performed, and Akaike Information Criteria (AIC) and Standard Error of the Estimate (SEE) were calculated to determine the best model. Neither single repetition ACV at 70% of 1RM (R2 = 0.004, p = 0.637) nor velocity loss (R2 = 0.011, p = 0.445) were predictive of total repetitions performed in the set to failure. The simple quadratic model using the first repetition of the set to failure () was identified as the best and most parsimonious model (R2 = 0.259, F = 9.247, p < 0.001) due to the lowest AIC value (311.086). A SEE of 2.21 repetitions was identified with this model. This average error of ~2 repetitions warrants only cautious utilization of this method to predict total repetitions an individual can perform in a set, with additional autoregulatory or individualization strategies being necessary to finalize the training prescription.

Formula omitted] quantum corrected scalar field inflation

String theory enjoys an elevated role among quantum gravity theories, since it seems to be the most consistent UV completion of general relativity and the Standard Model. However, it is hard to verify the existence of this underlying theory on terrestrial accelerators. One way to probe string theory is to study its imprints on the low-energy effective inflationary Lagrangian, which are quantified in terms of high energy correction terms. It is highly likely, thus, to find higher order curvature terms combined with string moduli, that is scalar fields, since both these types of interactions and matter fields appear in string theory. In this work we aim to stress the probability that the inflationary dynamics are controlled by the synergy of scalar fields and higher order curvature terms. Specifically, we shall consider a well motivated quantum corrected canonical scalar field theory, with the quantum corrections being of the R2 type. The reason for choosing minimally coupled scalar theory is basically because if scalar fields are evaluated in their vacuum configuration, they will either be minimally coupled or conformally coupled. Here we choose the former case, and the whole study shall be performed in the string frame (Jordan frame), in contrast to similar studies in the literature where the Einstein frame two scalar theory is considered. We derive the field equations of the quantum-corrected theory at leading order and we present the form the slow-roll indices obtain for the quantum corrected theory. We exemplify our theoretical framework by using the quadratic inflation model, and as we show, the R2 quantum corrected quadratic inflation model produces a viable inflationary phenomenology, in contrast with the simple quadratic inflation model.

Allometric equations to estimate the leaf area of Psychotria colorata (Willd. Ex Schult.) Müll.Arg.

Estimating leaf area using non-destructive methods from regression equations has become a more efficient, quick, and accurate way. Thus, this study aimed to propose an equation that significantly estimates the leaf area of Psychotria colorata (Rubiaceae) through linear leaf dimensions. For this purpose, 200 leaves of different shapes were collected, and length (L), width (W), product of length by width (L.W), and real leaf area (LA) of each leaf blade were determined. Then, equations were adjusted for predicting leaf area using simple linear, linear (0.0), quadratic, cubic, power, and exponential regression models. The proposed equation was selected according to the coefficient of determination (R²), Willmott's agreement index (d), Akaike's information criterion (AIC), mean absolute error (MAE), mean squared error (RMSE) and BIAS index. It was noted that the equations adjusted using L.W met the best criteria for estimating leaf area, but the equation LA = 0.59 * L.W from linear regression without intercept was the most suitable. This equation predicts that 59% of leaf area is explained by L.W. Concluding, the leaf area of P. colorata can be estimated using an allometric equation that uses linear leaf blade dimensions.

From low-cost sensors to high-quality data: A summary of challenges and best practices for effectively calibrating low-cost particulate matter mass sensors

Low-cost sensors for particulate matter mass (PM) enable spatially dense, high temporal resolution measurements of air quality that traditional reference monitoring cannot. Low-cost PM sensors are especially beneficial in low and middle-income countries where few, if any, reference grade measurements exist and in areas where the concentration fields of air pollutants have significant spatial gradients. Unfortunately, low-cost PM sensors also come with a number of challenges that must be addressed if their data products are to be used for anything more than a qualitative characterization of air quality. The various PM sensors used in low-cost monitors are all subject to biases and calibration dependencies, corrections for which range from relatively straightforward (e.g. meteorology, age of sensor) to complex (e.g. aerosol source, composition, refractive index). The methods for correcting and calibrating these biases and dependencies that have been used in the literature likewise range from simple linear and quadratic models to complex machine learning algorithms. Here we review the needs and challenges when trying to get high-quality data from low-cost sensors. We also present a set of best practices to follow to obtain high-quality data from these low-cost sensors.

On the estimation of the depth of maximum of extensive air showers using the steepness parameter of the lateral distribution of Cherenkov radiation

Using Monte Carlo simulation of extensive air showers, we showed that the maximum depth of showers, Xmax can be estimated using P=Q(100)∕Q(200), the ratio of Cherenkov photon densities at 100 and 200 meters from the shower core, which is known as the steepness parameter of the lateral distribution of Cherenkov radiation on the ground. A simple quadratic model has been fitted to a set of data from simulated extensive air showers, relating the steepness parameter and the shower maximum depth. Then the model has been tested on another set of simulated showers. The average difference between the actual maximum depth of the simulated showers and the maximum depth obtained from the lateral distribution of Cherenkov light is about 9 g/cm2. In addition, possibility of a more direct estimation of the mass of the initial particle from P has been investigated. An exponential relation between these two quantities has been fitted. Applying the model to another set of showers, we found that the average difference between the estimated and the actual mass of primary particles is less than 0.5 atomic mass unit.

Feasibility of heart girth models in estimating live weight of fat-long-tailed sheep.

Fat deposition in the brisket of Ethiopian fat‐long‐tailed sheep may interfere with the correlation between heart girth (HG) and live weight (LW), bringing into question the accuracy of HG models for LW prediction that are currently in use. This study assessed the accuracy of published HG‐based prediction models of the live weight of Ethiopian sheep breeds. Furthermore, the study identified accurate and robust models that predict the LW of the sheep using HG. Live weight and HG of 1,020 sheep from Bonga, Adilo and Horro breeds were measured. First, data collected from the study was used to gauge the preciseness of previously published prediction models of each breed. Second, the data of individual breeds were divided into a calibration set for model construction and a validation set for model validation. Live weight was regressed on HG to construct simple linear, Box‐Cox, quadratic and allometric prediction models. Prediction error of published models was >20%. Models constructed for each breed did not differ in R2. However, only simple linear models with transformed LW (Adilo: Log10(LW) = 0.408 + 0.015*HG, Bonga: Log10(LW) = −36.6 + 0.882*HG, Horro: LW0.5 = −1.26 + 0.085*HG) had homogenous residuals and prediction error of ≤ 10%. Heart girth models currently used to predict LW of Adilo, Bonga and Horro sheep of Ethiopia are not sufficiently accurate as they have PE higher than 10%. Prediction models generated by the current study could replace the published models for an accurate estimation of LW of the three breeds for husbandry, marketing and veterinary purposes.

Pedestrian Traffic Signal Data Accurately Estimates Pedestrian Crossing Volumes

Existing methods of pedestrian travel monitoring are generally inefficient for collecting pedestrian data in many locations over long time periods. In this study, we demonstrate the validity of using a novel and relatively ubiquitous big data source—pedestrian data from high-resolution traffic signal controller logs—as a way of estimating pedestrian crossing volumes. Every time a person presses a pedestrian push button or a pedestrian call is registered at a signal, this information can be logged and archived. To validate these pedestrian signal data against observed pedestrian counts, we recorded over 10,000 h of video at 90 signalized intersections in Utah, and counted around 175,000 people walking. For each hour and crossing, we compared these observed counts to measures of pedestrian activity calculated from traffic signal data, using a set of five simple piecewise linear and quadratic regression models. Overall, our results show that traffic signal data can be successfully used to estimate pedestrian crossing volumes with good accuracy: model-predicted volumes were strongly correlated (0.84) with observed volumes and had a low mean absolute error (3.0). We also demonstrate how our models can be used to estimate annual average daily pedestrian volumes at signalized intersections and identify high pedestrian volume locations. Transportation agencies can use pedestrian signal data to help improve pedestrian travel monitoring, multimodal transportation planning, traffic safety analyses, and health impact assessments.

Predicting Supercritical Extraction of St. John’s Wort by Simple Quadratic Polynomial Model and Adaptive Neuro-Fuzzy Inference System- Firefly Algorithm

In this study, the applicability of the adaptive neuro-fuzzy inference system (ANFIS) and response surface methodology (RSM) was evaluated to forecasting the supercritical extraction of St. John’s Wort. In this case, the ANFIS model was optimized by the firefly algorithm (FFA) to develop the performance of the model. The accuracy of the models was investigated by comparing the result of the models with experimental data. The precision of the RSM model has been investigated using statistical analysis (P-value<0.05, F-value=148.13, R2=0,99 R2 Adjusted=0.98, R2 Predicted =0.96). The data transfer power was proved by the Box-Cox plot. Also, the polynomial model shows that it is much simpler and easier than other complex models. The results show, the ANFIS-FFA with R2=0.99, RMSE=1.79 and AARD%=2.79 have a high capability of predicting the St. John’s Wort extraction amount

A simple model for the total number of SARS-CoV-2 infections on a national level.

This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R2 = 0.992) fit the current data best for 25 (89%) countries as determined by R2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.

Using a trust region method with nonmonotone technique to solve unrestricted optimization problem

In this work, we combine adaptive trust region method TRM with nonmonotone strategy to introduce a new algorithm to solve systems of unconstrained optimization problems depending on the simple quadratic model. The subproblems will be solving easier with the new approximation of the Hessian function. This technique does not need large capacity and is characterized by ease of application. We established the algorithm convergence with standard assumptions. The numerical results compered the performance of the new approach with three famous algorithms in terms of the time consumed to find the solution in addition to the number of iterations and the number of functions evaluations. From these results we can show that the new method is the best among the traditional algorithms.

Empirical formulation for small circular electron fields

An empirical model for small circular electron fields was developed. This can be of great help in the treatment planning process for small circular electron fields. A complete dosimetric analysis of the circular fields defined by electron cutouts diameters (2 cm–9 cm) was done for nominal electron energies ranging between 6 MeV and 20 MeV using a 3D water phantom and a pin-point ion chamber. Properties studied included depth dose, in-air inverse-square fall-off, and beam profiles. The Varian Clianc 2100 C accelerator was modelled, benchmarked and Monte Carlo simulations were performed using the EGSnrc/BEAMnrc code for the small circular cutouts. A simple exponential model was found to accurately predict the very important therapeutic depth (90% of Dmax) for the small circular field size within an accuracy of better than 2 mm in most cases. The model has only two parameters (d90 and ‘b’). Also, the penumbra widths (90% of the off-axis profiles) of these small circular electron fields were studied and least square fitted to a simple quadratic model. Full dosimetric profiles of these small circular electron fields were further studied using the benchmarked Monte Carlo simulations. This study presents a simple model to predict the very important therapeutic depth (90% of Dmax) and a recipe to develop such an electron treatment model for any linear accelerator system. Such predictions can be extremely valuable and time saving prior to treatment planning involving not only small circular shaped electron fields but also irregularly shaped electron fields.

Modelling of relation between synthesis parameters and average crystallite size of Yb2O3 nanoparticles using Box-Behnken design

A straightforward wet chemical method has been applied for the fabrication of Yb2O3 nanoparticles (NPs) from ytterbium nitrate solution by using ammonium carbonate as precipitation agent. Effects of precursor molarity (0.1, 0.15 and 0.2 M), calcination temperature (800, 900 and 1000 °C) and time (2, 4 and 6 h) on average crystallite size (CS) of the NPs were statistically investigated by using Box-Behnken design. A simple and effective quadratic model was proposed for controlling the CS. The CS values were calculated by using Williamson Hall method (W-H) from X-Ray Diffraction (XRD) broadening data and found to be ranging between 13 and 26 nm. Agglomerated NPs morphologies and particle sizes were revealed by Field Emission Gun-Scanning Electron Microscopy (FEG-SEM). Fourier Transform Infrared (FTIR) spectrophotometry confirmed that as-received Yb2(CO3)3xH2O powders were successfully transformed into Yb2O3 NPs with calcination. High-Resolution Transmission Electron Microscopy (HRTEM) results verified the average CS values. ANOVA analyses revealed that linear and squared terms of the production parameters were significantly related to the CS whereas interaction terms were insignificant with the confidence level of 95% (R2 = 92.67%, R2-adj = 87.17%). The calcination temperature had the highest impact on the average CS followed by the time and precursor molarity. Increasing calcination parameters resulted in bigger crystallites whereas increasing precursor molarity exhibited a critical supersaturation value (0.15 M) from which the average CS was decreased.

Measuring human alertness from histogram of response time to audio-visual stimuli

ABSTRACTResponse time test is one of the widely used metrics to measure/validate human alertness. Response time metrics like Mean reaction time (RT) and Mean of 1/RT suffer from lower range and resolution in case of shorter versions of Response time tasks (<10 min). However, small be the fixed test duration, knowledge of it affects the test performance as the subjects might ration their effort over the test period. Therefore, in this article, we fix the number of stimuli (unknown to the participants) instead of test duration and propose a new reaction time metric – called Peak-to- Spread Ratio () – obtained from histogram of response time to audio-video-stimuli (AVS). Experimental results on data collected from 65 subjects confirms that the proposed has better resolution and sensitivity than Mean RT and Mean of 1/RT. We also propose an alertness level index based on a simple quadratic model trained with a set of values to predict the awake hours of a test subject. Experimental results on 25 subjects emphasize that the proposed alertness level index exhibit higher effect-size and correlation with human alertness level over other related states of the art.

Radiation-Related Risk of Cancers of the Upper Digestive Tract among Japanese Atomic Bomb Survivors.

As a follow-up to the comprehensive work on solid cancer incidence in the Life Span Study (LSS) cohort of atomic bomb survivors between 1958 and 1998, we report here on updated radiation risk estimates for upper digestive tract cancers. In this study, we added 11 years of follow-up (1958-2009), used improved radiation dose estimates, considered effects of smoking and alcohol consumption and performed dose-response analyses by anatomical sub-site. In examining 52 years'worth of data, we ascertained the occurrence of 394 oral cavity/pharyngeal cancers, 486 esophageal cancers and 5,661 stomach cancers among 105,444 subjects. The radiation risk for oral cavity/pharyngeal cancer, other than salivary gland, was elevated but not significantly so. In contrast, salivary gland cancer exhibited a strong linear dose response with excess relative risk (ERR) of 2.54 per Gy [95% confidence interval (CI): 0.69 to 6.1]. Radiation risk decreased considerably with increasing age at time of exposure (-66% per decade, 95% CI: -88% to -32%). The dose response for esophageal cancer was statistically significant under a simple linear, linear-quadratic and quadratic model. Both linear-quadratic and quadratic models described the data better than a simple linear model and, of the two, the quadratic model showed a marginally better fit based on the Akaike Information Criteria. Sex difference in linear ERRs was not statistically significant; however, when the dose-response shape was allowed to vary by sex, statistically significant curvature was found among males, with no evidence of quadratic departure from linearity among females. The risk for stomach cancer increased significantly with dose and there was little evidence for quadratic departure from linearity among either males or females. The sex-averaged ERR at age 70 was 0.33 per Gy (95% CI: 0.20 to 0.47). The ERR decreased significantly (-1.93 power of attained age, 95% CI: -2.94 to -0.82) with increasing attained age, but not with age at exposure, and was higher in females than males (P = 0.02). Our results are largely consistent with the results of prior LSS analyses. Salivary gland, esophageal and stomach cancers continue to show significant increases in risk with radiation dose. Adjustment for lifestyle factors had almost no impact on the radiation effect estimates. Further follow-up of the LSS cohort is important to clarify the nature of radiation effects for upper digestive tract cancers, especially for oral cavity/pharyngeal and esophageal cancers, for which detailed investigation for dose-response shape could not be conducted due to the small number of cases.

An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems

Based on a modified secant equation, we propose a scalar approximation of the Hessian to be used in the trust region subproblem. Then, we suggest an adaptive nonmonotone trust region algorithm with a simple quadratic model. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan-Moré performance profile. They demonstrate efficiency of the proposed algorithm.

Sound Deposit Insurance Pricing Using a Machine Learning Approach

While the main conceptual issue related to deposit insurances is the moral hazard risk, the main technical issue is inaccurate calibration of the implied volatility. This issue can raise the risk of generating an arbitrage. In this paper, first, we discuss that by imposing the no-moral-hazard risk, the removal of arbitrage is equivalent to removing the static arbitrage. Then, we propose a simple quadratic model to parameterize implied volatility and remove the static arbitrage. The process of removing the static risk is as follows: Using a machine learning approach with a regularized cost function, we update the parameters in such a way that butterfly arbitrage is ruled out and also implementing a calibration method, we make some conditions on the parameters of each time slice to rule out calendar spread arbitrage. Therefore, eliminating the effects of both butterfly and calendar spread arbitrage make the implied volatility surface free of static arbitrage.

Quantifying Allowable Motion to Achieve Safe Dose Escalation in Pancreatic SBRT

PurposeTumor motion plays a key role in the safe delivery of stereotactic body radiation therapy (SBRT) for pancreatic cancer. The purpose of this study was to use tumor motion measured in patients to establish limits on motion magnitude for safe delivery of pancreatic SBRT and to help guide motion-management decisions in potential dose-escalation scenarios. Methods and MaterialsUsing 91 sets of pancreatic tumor motion data, we calculated the motion-convolved dose of the gross tumor volume, duodenum, and stomach for 25 patients with pancreatic cancer. We derived simple linear or quadratic models relating motion to changes in dose and used these models to establish the maximum amount of motion allowable while satisfying error thresholds on key dose metrics. In the same way, we studied the effects of dose escalation and tumor volume on allowable motion. ResultsIn our patient cohort, the mean (range) allowable motion for 33, 40, and 50 Gy to the planning target volume was 11.9 (6.3-22.4), 10.4 (5.2-19.1), and 9.0 (4.2-16.0) mm, respectively. The maximum allowable motion decreased as the dose was escalated and was smaller in patients with larger tumors. We found significant differences in allowable motion between the different plans, suggesting a patient-specific approach to motion management is possible. ConclusionsThe effects of motion on pancreatic SBRT are highly variable among patients, and there is potential to allow more motion in certain patients, even in dose-escalated scenarios. In our dataset, a conservative limit of 6.3 mm would ensure safe treatment of all patients treated to 33 Gy in 5 fractions.

Perfect thermal rectification in a many-body quantum Ising model.

This paper addresses a keystone problem for the progress of phononics: the proposal of efficient thermal diodes. Aiming the disclosure of an easy itinerary for the building of a heat rectifier, I investigate unsophisticated systems linked to simple thermal baths, precisely, asymmetric quantum Ising models, i.e., simple quadratic models, involving only one spin component. I analytically show the occurrence of thermal rectification for the case of a chain with interactions long enough to connect the first to the last site. Moreover, I describe cases of a perfect rectification, i.e., finite heat flow in one direction and zero current in the opposite direction. I argue to indicate that the ingredients for the rectification are just given by the quantum nature of the baths and dynamics, and by the structural asymmetry of the system, here in the intersite interactions. I believe that the description of a perfect thermal rectification in a simple many-body quantum model, that is, the presentation of a simple itinerary for the building of a diode shall stimulate theoretical and experimental research on the theme.