scholarly journals An Approximate Analytic Solution to a Non-Linear ODE for Air Jet Velocity Decay through Tree Crops Using Piecewise Linear Emulations and Rectangle Functions

2019 ◽  
Vol 9 (24) ◽  
pp. 5440 ◽  
Author(s):  
Dario Friso
Keyword(s):  
Relative Error ◽  
Piecewise Linear ◽  
Single Equation ◽  
Air Velocity ◽  
Tree Crops ◽  
Mean Relative Error ◽  
Air Jet ◽  
Significant Difference ◽  
Non Linear ◽  
Velocity Decay

The velocity of air that crosses the canopy of tree crops when using orchard sprayers is a variable that affects pesticide dispersion in the environment. Therefore, having an equation to describe air velocity decay through the canopy is of interest. It was necessary to start from a more general non-linear ordinary differential equation (ODE) obtained from the momentum theorem. After approximating the non-linearity with some piecewise linear terms, analytic solutions were found. Subsequently, to obtain a single equation for velocity decay, a combination of these solutions was proposed by using rectangle functions formed through the hyperbolic tangent function. This single equation was assessed in comparison to the experimental value obtained on a vineyard row by measuring the air velocity at exit of canopy. The results have shown good correspondence, with a mean relative error of 6.6%; moreover, there was no significant difference. To simplify, a combination of only two linearized solutions was also proposed. Again, there was no significant difference between the experimental value and the predicted one, but the mean relative error between the two equations was 3.6%.

scholarly journals The Triglyceride-Glucose Index, an Insulin Resistance Marker, Was Non-linear Associated With All-Cause and Cardiovascular Mortality in the General Population

2021 ◽  
Vol 7 ◽  
Author(s):  
Xiao-cong Liu ◽  
Guo-dong He ◽  
Kenneth Lo ◽  
Yu-qing Huang ◽  
Ying-qing Feng
Keyword(s):  
Insulin Resistance ◽  
Cardiovascular Disease ◽  
Cox Regression ◽  
Piecewise Linear ◽  
Threshold Value ◽  
Cardiovascular Death ◽  
Tyg Index ◽  
Significant Difference ◽  
Non Linear ◽  
The Relationship

Background: The triglyceride-glucose (TyG) index could serve as a convenient substitute of insulin resistance (IR), but epidemiological evidence on its relationship with the long-term risk of mortality is limited.Methods: Participants from the National Health and Nutrition Examination Survey during 1999–2014 were grouped according to TyG index (<8, 8–9, 9–10, >10). Cox regression was conducted to compute the hazard ratios (HRs) and 95% confidence interval (CI). Restricted cubic spline and piecewise linear regression were performed to detect the shape of the relationship between TyG index and mortality.Results: A total of 19,420 participants (48.9% men) were included. On average, participants were followed-up for 98.2 months, and 2,238 (11.5%) and 445 (2.3%) cases of mortality due to all-cause or cardiovascular disease were observed. After adjusting for confounders, TyG index was independently associated with an elevated risk of all-cause (HR, 1.10; 95% CI, 1.00–1.20) and cardiovascular death (HR, 1.29; 95% CI, 1.05–1.57). Spline analyses showed that the relationship of TyG index with mortality was non-linear (All non-linear P < 0.001), and the threshold value were 9.36 for all-cause and 9.52 for cardiovascular death, respectively. The HRs above the threshold point were 1.50 (95% CI, 1.29–1.75) and 2.35 (95% CI, 1.73–3.19) for all-cause and cardiovascular death. No significant difference was found below the threshold points (All P > 0.05).Conclusion: Elevated TyG index reflected a more severe IR and was associated with mortality due to all-cause and cardiovascular disease in a non-linear manner.

Error-aware Design Procedure to Implement Energy-efficient Approximate Squaring Hardware

2020 ◽  
Vol 10 (4) ◽  
pp. 471-477
Author(s):  
Merin Loukrakpam ◽  
Ch. Lison Singh ◽  
Madhuchhanda Choudhury
Keyword(s):  
Energy Saving ◽  
Relative Error ◽  
Energy Efficient ◽  
Piecewise Linear ◽  
Arithmetic Operation ◽  
Design Procedure ◽  
Digital Signal ◽  
Maximum Relative Error ◽  
Square Function ◽  
Efficient Design

Background:: In recent years, there has been a high demand for executing digital signal processing and machine learning applications on energy-constrained devices. Squaring is a vital arithmetic operation used in such applications. Hence, improving the energy efficiency of squaring is crucial. Objective:: In this paper, a novel approximation method based on piecewise linear segmentation of the square function is proposed. Methods: Two-segment, four-segment and eight-segment accurate and energy-efficient 32-bit approximate designs for squaring were implemented using this method. The proposed 2-segment approximate squaring hardware showed 12.5% maximum relative error and delivered up to 55.6% energy saving when compared with state-of-the-art approximate multipliers used for squaring. Results: The proposed 4-segment hardware achieved a maximum relative error of 3.13% with up to 46.5% energy saving. Conclusion:: The proposed 8-segment design emerged as the most accurate squaring hardware with a maximum relative error of 0.78%. The comparison also revealed that the 8-segment design is the most efficient design in terms of error-area-delay-power product.

scholarly journals Modeling Spatiotemporal Population Changes by Integrating DMSP-OLS and NPP-VIIRS Nighttime Light Data in Chongqing, China

2021 ◽  
Vol 13 (2) ◽  
pp. 284
Author(s):  
Dan Lu ◽  
Yahui Wang ◽  
Qingyuan Yang ◽  
Kangchuan Su ◽  
Haozhe Zhang ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Relative Error ◽  
Urban Areas ◽  
Large Scale ◽  
Population Distribution ◽  
Spatial Optimization ◽  
Distribution Data ◽  
Mountainous Areas ◽  
Mean Relative Error ◽  
Nighttime Light

The sustained growth of non-farm wages has led to large-scale migration of rural population to cities in China, especially in mountainous areas. It is of great significance to study the spatial and temporal pattern of population migration mentioned above for guiding population spatial optimization and the effective supply of public services in the mountainous areas. Here, we determined the spatiotemporal evolution of population in the Chongqing municipality of China from 2000–2018 by employing multi-period spatial distribution data, including nighttime light (NTL) data from the Defense Meteorological Satellite Program’s Operational Linescan System (DMSP-OLS) and the Suomi National Polar-orbiting Partnership Visible Infrared Imaging Radiometer Suite (NPP-VIIRS). There was a power function relationship between the two datasets at the pixel scale, with a mean relative error of NTL integration of 8.19%, 4.78% less than achieved by a previous study at the provincial scale. The spatial simulations of population distribution achieved a mean relative error of 26.98%, improved the simulation accuracy for mountainous population by nearly 20% and confirmed the feasibility of this method in Chongqing. During the study period, the spatial distribution of Chongqing’s population has increased in the west and decreased in the east, while also increased in low-altitude areas and decreased in medium-high altitude areas. Population agglomeration was common in all of districts and counties and the population density of central urban areas and its surrounding areas significantly increased, while that of non-urban areas such as northeast Chongqing significantly decreased.

Passage rate of solids and fluids in the digestive tract of buffaloes, cattle and sheep: selection of non-linear model

1997 ◽  
Vol 64 (1) ◽  
pp. 63-69 ◽  
Author(s):  
A. Amici ◽  
S. Bartocci ◽  
S. Terramoccia ◽  
F. Martillotti
Keyword(s):  
Linear Models ◽  
Latin Square ◽  
Sums Of Squares ◽  
Passage Rate ◽  
Significant Difference ◽  
Age Dependent ◽  
Non Linear ◽  
Best Fitting ◽  
Kinetics Of ◽  
Selection Of

AbstractFive mathematical models were compared to select the most satisfactory model to describe digesta kinetics of solids and fluids in the gastrointestinal tract of buffaloes (Mediterranean bulls), cattle (Friesian bulls) and sheep (Delle Langhe rams) given food at maintenance level, according to a Latin-square arrangement for four consecutive periods of 21 days. Chromium mordanted alfalfa hay and cobalt-ethylenediamine tetraacetic acid were used as nonabsorbable markers and were administered through the rumen cannula in a single dose. Four different isonitrogenous diets (N × 6·25 = 140 g/kg dry matter) with different concentrate:forage ratios (12·5:87·5, 25:75, 37·5:62·5, 50:50) were used.Faecal chromium and cobalt concentration curves were fitted with five non-linear models: three gamma (G2, G3, G4) age-dependent one-compartment, one gamma age-dependent/age-independent two-compartment (G2G1) and one multicompartment (MC).Wilcoxon tests on residual sums of squares of the different models for solids showed that MC and G4 gave a better fit than G2G1, G2, G3 for all the data and within the species. The comparison of MC v. G4 did not show any significant difference (P > 0·05) for all the data computed together or within each species. Nevertheless, MC had a higher number of curves with lower residual sums of squares in comparison with G4 and was also able to produce estimates of digesta kinetics in the second compartment.The cobalt excretion curves for fluids, considering all the data, and only within sheep, showed G4 as the best fitting model. When G4 was compared with other models no significant differences were recorded either for cattle: G4 v. G2 (F = 0·6645), G4 v. G2G1 (P = 0·0620) and for buffalo: G4 v. G2 (P = 0·1575), G4 v.G3(P = 0·0796) and G4 v. G2G1 (P = 0·1641).It is concluded that the multicompartment model (MC) and G4 model were the best fits for solids and for fluids respectively.

scholarly journals Using large-scale structure data and a halo model to constrain generalized dark matter

2019 ◽  
Vol 490 (1) ◽  
pp. 813-831 ◽  
Author(s):  
Daniel B Thomas ◽  
Michael Kopp ◽  
Katarina Markovič
Keyword(s):  
Dark Matter ◽  
Gravitational Lensing ◽  
Large Scale ◽  
Linear Structure ◽  
Microwave Background ◽  
Wavenumber Range ◽  
Significant Difference ◽  
Linear Modelling ◽  
Non Linear ◽  
Order Of Magnitude

ABSTRACT Constraints on the properties of the cosmological dark matter have previously been obtained in a model-independent fashion using the generalized dark matter (GDM) framework. Here we extend that work in several directions: We consider the inclusion of WiggleZ matter power spectrum data (MPS), and show that this improves the constraints on the two perturbative GDM parameters, $c^2_\mathrm{ s}$ and $c^2_\text{vis}$, by a factor of 3, for a conservative choice of wavenumber range. A less conservative choice can yield an improvement of up to an order of magnitude compared to previous constraints. In order to examine the robustness of this result we develop a GDM halo model (HM) to explore how non-linear structure formation could proceed in this framework, since currently GDM has only been defined perturbatively and only linear theory has been used when generating constraints. We then examine how the HM affects the constraints obtained from the MPS data. The less-conservative wavenumber range shows a significant difference between linear and non-linear modelling, with the latter favouring GDM parameters inconsistent with ΛCDM, underlining the importance of careful non-linear modelling when using this data. We also use this HM to establish the robustness of previously obtained constraints, particularly those that involve weak gravitational lensing of the cosmic microwave background. Additionally, we show how the inclusion of neutrino mass as a free parameter affects previous constraints on the GDM parameters.

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