quadratic curve
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2021 ◽  
Author(s):  
Xinli Xiong ◽  
Kuan Wang ◽  
Jianbin Chen ◽  
Tao Li ◽  
Haoyun Deng ◽  
...  

2021 ◽  
Author(s):  
Qianfang Yang ◽  
Shengli Wang ◽  
Cuicui Zhao ◽  
Zhongren Nan

Abstract Ecological environment of remote grassland has become increasingly serious in many countries due to mining, tourism, grazing and other human activities. In this study, a total of 15 pairs of soil-herbage samples were collected in the northeast of the Tibet Plateau to study the relationship between physicochemical properties and content of trace elements in soils and elevation, and to examine the accumulation and fractionation of heavy metals in soil-herbage systems. In addition, the ecological risk of the subalpine grassland was also assessed. The average concentrations of Hg, As, Cu, Zn, Pb, Cd, Cr and Mn in soil were higher than their background values of Gansu soil, but the average concentrations of these heavy metals in herbage satisfied Hygienical Standard for Feeds. The speciation analysis of heavy metals in soil indicated that the exchangeable content of heavy metal was very low, except Pb, Cd, Mn. There was a linear relationship between pH, CaCO3, total phosphorus (TP), organic matter (OM), concentrations of Hg, As, Zn, Pb, Cr and Mn in soils, dry weight of herbage and elevation, while there was a quadratic curve trend between Cu, Cd in soils and elevation. The results of risk assessment showed that there was no obvious ecological risk in the study area.


2020 ◽  
Author(s):  
Bert van der Veen ◽  
Francis K.C. Hui ◽  
Knut A. Hovstad ◽  
Erik B. Solbu ◽  
Robert B. O’Hara

SummaryIt is common practice for ecologists to examine species niches in the study of community composition. The response curve of a species in the fundamental niche is usually assumed to be quadratic. The center of a quadratic curve represents a species’ optimal environmental conditions, and the width its ability to tolerate deviations from the optimum.Most multivariate methods assume species respond linearly to the environment of the niche, or with a quadratic curve that is of equal width and height for all species. However, it is widely understood that some species are generalists who tolerate deviations from their optimal environment better than others. Rare species often tolerate a smaller range of environments than more common species, corresponding to a narrow niche.We propose a new method, for ordination and fitting Joint Species Distribution Models, based on Generalized Linear Mixed-Effects Models, which relaxes the assumptions of equal tolerances and equal maxima.By explicitly estimating species optima, tolerances, and maxima, per ecological gradient, we can better predict change in species communities, and understand how species relate to each other.


Hypertension ◽  
2020 ◽  
Vol 76 (Suppl_1) ◽  
Author(s):  
Aayush Visaria ◽  
David Lo ◽  
Pranay Maniar

The purpose of this cross-sectional, exploratory analysis was to describe age-related patterns of blood pressure (BP) among participants in India (using the 2014 Annual Health Survey) and the United States (using National Health & Nutrition Examination Surveys 2011-2016). We included 10,759 U.S. and 790,641 Indian participants aged ≥20 years with ≥2 BP readings. We plotted mean systolic (SBP) and diastolic BP (DBP) across 5-year age groups and estimated best fit models. SBP increased linearly with age in both sexes and study populations (R 2 : 0.88-0.99; Fig. 1-2). Those with overweight/obese BMI had higher SBP and modestly higher rates of increase in SBP. DBP followed a quadratic curve (R 2 : 0.68-0.99), peaking in the 5-6th decade (45-49 years in U.S. and 50-59 in India) with higher and earlier peaks in those with elevated BMI. The models’ strong fit and similarity between study populations supports the notion that physical processes underly BP’s age-related changes.


Author(s):  
Nghia Truong ◽  
Cem Yuksel ◽  
Larry Seiler

We present a simple degree reduction technique for piecewise cubic polynomial splines, converting them into piecewise quadratic splines that maintain the parameterization and C1 continuity. Our method forms identical tangent directions at the interpolated data points of the piecewise cubic spline by replacing each cubic piece with a pair of quadratic pieces. The resulting representation can lead to substantial performance improvements for rendering geometrically complex spline models like hair and fiber-level cloth. Such models are typically represented using cubic splines that are C1-continuous, a property that is preserved with our degree reduction. Therefore, our method can also be considered a new quadratic curve construction approach for high-performance rendering. We prove that it is possible to construct a pair of quadratic curves with C1 continuity that passes through any desired point on the input cubic curve. Moreover, we prove that when the pair of quadratic pieces corresponding to a cubic piece have equal parametric lengths, they join exactly at the parametric center of the cubic piece, and the deviation in positions due to degree reduction is minimized.


Author(s):  
Sheehan Olver ◽  
Yuan Xu

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.


2019 ◽  
Vol 36 (12) ◽  
pp. 2525-2531
Author(s):  
Qian Geng ◽  
Xiaoli Cui ◽  
Yaqi Zhang ◽  
Lijuan Zhang ◽  
Cai Zhang ◽  
...  

Abstract Purpose To establish a single-nucleotide polymorphism-based analysis (SBA) method to identify triploidy in the miscarriage tissue by using low-coverage whole-genome sequencing (LC-WGS). Methods The method was established by fitting a quadratic curve model by counting the distribution of three heterozygous mutation content intervals. The triploid test result was mainly determined by the opening direction and the axis of symmetry of the quadratic curve, and Z test between the same batch samples was also used for auxiliary judgment. Results Two hundred thirteen diploid samples and 8 triploid samples were used for establishment of the analytical method and 203 unknown samples were used for blind testing. In the blind testing, we found 2 cases positive for triploidy. After chromosome microarray analysis (CMA) and mass spectrometry verification, we found that both samples were true positives. We randomly selected 5 samples from the negative samples for mass spectrometry verification, and the results showed that these samples were all true negatives. Conclusions Our method achieved accurate detection of triploidy in the miscarriage tissue and has the potential to detect more chromosomal abnormality types such as uniparental disomy (UPD) using a single LC-WGS approach.


2019 ◽  
Vol 14 (10) ◽  
pp. 1357-1363 ◽  
Author(s):  
Paul A. Solberg ◽  
Will G. Hopkins ◽  
Gøran Paulsen ◽  
Thomas A. Haugen

Purpose:To quantify age of peak performance and performance improvements in the years preceding peak age in elite weightlifting and powerlifting athletes using results from powerlifting World Championships in 2003–2017 and weightlifting World Championships and Olympic Games in 1998–2017.Methods:Individual performance trends were derived by fitting a quadratic curve separately to each athlete’s performance and age data. Effects were evaluated using magnitude-based inferences.Results:Peak age (mean [SD]) was 35 (7) y for powerlifters and 26 (3) y for weightlifters, a large most likely substantial difference of 9, ±1 y (mean, 90% confidence limit). Men showed possibly higher peak age than women in weightlifting (0.8, ±0.7 y; small) and a possibly lower peak age in powerlifting (1.3, ±1.8 y; trivial). Peak age of athletes who ever won a medal was very likely less than that of nonmedalists in weightlifting (1.3, ±0.6 y; small), while the difference in powerlifters was trivial but unclear. Five-year improvements prior to peak age were 12% (10%) for powerlifters and 9% (7%) for weightlifters, a small possibly substantial difference (2.9, ±2.1%). Women exhibited possibly greater improvements than men in powerlifting (2.7, ±3.8%; small) and very likely greater in weightlifting (3.5, ±1.6%; small). Medalists possibly improved less than nonmedalists among powerlifters (−1.7, ±2.3%; small), while the difference was likely trivial for weightlifters (2.3, ±1.8%).Conclusion:These novel insights on performance development will be useful for practitioners evaluating strategies for achieving success.


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