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Concept: Quadratic function


Although the time adolescents spend with digital technologies has sparked widespread concerns that their use might be negatively associated with mental well-being, these potential deleterious influences have not been rigorously studied. Using a preregistered plan for analyzing data collected from a representative sample of English adolescents ( n = 120,115), we obtained evidence that the links between digital-screen time and mental well-being are described by quadratic functions. Further, our results showed that these links vary as a function of when digital technologies are used (i.e., weekday vs. weekend), suggesting that a full understanding of the impact of these recreational activities will require examining their functionality among other daily pursuits. Overall, the evidence indicated that moderate use of digital technology is not intrinsically harmful and may be advantageous in a connected world. The findings inform recommendations for limiting adolescents' technology use and provide a template for conducting rigorous investigations into the relations between digital technology and children’s and adolescents' health.

Concepts: Critical thinking, Function, Technology, Function model, Digital, Recreation, Quadratic function


In order to test the feasibility of computer simulation in field maize planting, the selection of the method of single seed precise sowing in maize is studied based on the quadratic function model Y = A×(D-Dm)2+Ym, which depicts the relationship between maize yield and planting density. And the advantages and disadvantages of the two planting methods under the condition of single seed sowing are also compared: Method 1 is optimum density planting, while Method 2 is the ideal seedling emergence number planting. It is found that the yield reduction rate and yield fluctuation of Method 2 are all lower than those of Method 1. The yield of Method 2 increased by at least 0.043 t/hm2, and showed more advantages over Method 1 with higher yield level. Further study made on the influence of seedling emergence rate on the yield of maize finds that the yields of the two methods are both highly positively correlated with the seedling emergence rate and the standard deviations of their yields are both highly negatively correlated with the seedling emergence rate. For the study of the break-up problem of sparse caused by the method of single seed precise sowing, the definition of seedling missing spots is put forward. The study found that the relationship between number of hundred-dot spot and field seedling emergence rate is as the parabola function y = -189.32x2 + 309.55x - 118.95 and the relationship between number of spot missing seedling and field seedling emergence rate is as the negative exponent function y = 395.69e-6.144x. The results may help to guide the maize seeds production and single seed precise sowing to some extent.

Concepts: Computer graphics, Seed, Plant reproduction, Archimedes, Quadratic equation, Seeds, Quadratic function, Sowing


The study of differential growth in various animals suggests that a similar growth pattern occurs throughout the bilateral animals. This growth pattern is based on the assumption that a quadratic equation describes the relationship between two body measurements, yielding a quadratic parabola in a graphic presentation.

Concepts: Parabola, Polynomial, Equation, Equations, Quadratic equation, Indian mathematics, Elementary algebra, Quadratic function


Vegetation coverage is an important parameter for affecting soil erosion and the physical and chemical properties of soil. To analyze the mutual influence between vegetation coverage and soil quality at different slope aspects in a reclaimed dump, fitting analyses were built between the normalized difference vegetation index and soil physical properties at each slope aspect. Twenty six quadrats were sampled in slope-platform alternate mode. Each quadrat was 10 m × 10 m. Vegetation index and soil physical properties were measured and calculated. Through curve fitting analysis, the results showed that soil bulk density has a negative correlation with the vegetation index on shady and half shady slopes, sunny slopes, and half sunny slopes. Soil porosity has a positive correlation with the vegetation index on shady and half shady slopes, sunny slope, and half sunny slope. The soil mass water content has a concave function relationship with the vegetation index on shady and half shady slopes and has a quadratic function relationship with the vegetation index on sunny and half sunny slopes, with the parabola moving upwards. The soil gravel content has a linear relationship with the vegetation index on shady and half shady slopes, and the image has a negative slope with a quadratic function relationship to the vegetation index on sunny slope and half sunny slope, with the parabola moving downwards. Due to differences among hydrothermal conditions, the relationship between vegetation coverage and soil quality indicators at different slope aspects is different; therefore, reasonable improvement of soil quality indicators on sunny and half sunny slopes could help plants to grow. These findings feed into a reference document that sets out how vegetation and soil quality may be improved in mining areas.

Concepts: Soil, Erosion, Derivative, Porosity, Bulk density, Physical property, Quadratic equation, Quadratic function


This study investigated the characteristics of the small-world brain network architecture of patients with mild traumatic brain injury (MTBI), and a correlation between brain functional connectivity network properties in the resting-state fMRI and Standardized Assessment of Concussion (SAC) parameters. The neurological conditions of 22 MTBI patients and 17 normal control individuals were evaluated according to the SAC. Resting-state fMRI was performed in all subjects 3 and 7days after injury respectively. After preprocessing the fMRI data, cortex functional regions were marked using AAL90 and Dosenbach160 templates. The small-world network parameters and areas under the integral curves were computed in the range of sparsity from 0.01 to 0.5. Independent-sample t-tests were used to compare these parameters between the MTBI and control group. Significantly different parameters were investigated for correlations with SAC scores; those that correlated were chosen for further curve fitting. The clustering coefficient, the communication efficiency across in local networks, and the strength of connectivity were all higher in MTBI patients relative to control individuals. Parameters in 160 brain regions of the MTBI group significantly correlated with total SAC score and score for attention; the network parameters may be a quadratic function of attention scores of SAC and a cubic function of SAC scores. MTBI patients were characterized by elevated communication efficiency across global brain regions, and in local networks, and strength of mean connectivity. These features may be associated with brain function compensation. The network parameters significantly correlated with SAC total and attention scores.

Concepts: Traumatic brain injury, Correlation and dependence, Pearson product-moment correlation coefficient, Concussion, Quadratic equation, Clustering coefficient, Small-world network, Quadratic function


To explore the effectof tumor volume on pulmonary dose-volume parameters by intensity-modulated radiation therapy (IMRT) in non-small cell lung cancer (NSCLC), and to provide a basis for pulmonary dose parameters in IMRT treatment.
 Methods: A total of 204 patients with NSCLC received IMRT were retrospectively analyzed from June, 2009 to October, 2013. The prescribed dose of planning target volume (PTV) for primary tumor was 60-66Gy (2.00-2.25 Gy, 27-33 times in all). The fractional volume percent of the lung received a dose >5 or 20 Gy (V5, V20), and absolute volume of lung received a dose <5 Gy (AVS5).The mean lung dose (MLD) in normal tissues were analyzed. Regression model curve was used to analyze them along with the change of primary tumor volume.
 Results: With the increase in lung tumor volume, the V5, V20 and MLD presented quadratic equation curve, and AVS5 presented logarithmic equation. When the tumor volume, less than a certain value (294.6, 283.2, 304.9 cm3, respectively), the V5, V20 and MLD increased with tumor size and presented an increased quadratic curve; when the tumor volume was higher than a certain value (294.6, 283.2, 304.9 cm3 respectively), the V5, V20 and MLD was declined. The AVS5 was declined in a logarithmic curve along with the increase of tumor volume.
 Conclusion: With the increase in lung tumor volume, the change in rule of V5, V20, MLD and AVS5 is not completely equivalent. When the tumor volume exceeds a certain boundary value (about 300 cubic centimeter), the corresponding tumor diameter is about 7-8 cm. In addition to the focus on pulmonary V5, V20 and MLD, we should also pay more attention to AVS5 restrictions in establishment of IMRT in NSCLC.

Concepts: Cancer, Ionizing radiation, Lung cancer, Non-small cell lung carcinoma, Radiation therapy, Quadratic equation, Quadratic function, Completing the square


Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness.

Concepts: Oxygen, Pharmacology, Medical terms, Medical statistics, Mechanical ventilation, Partial pressure, Quadratic form, Quadratic function


Cement leakage is a serious adverse event potentially occurring during vertebroplasty. Pre-operative in-silico planning of the cement filling process can help reducing complication rates related to leakage. This requires a better understanding of the cement flow along the whole injection path. Therefore, the aim of the present study was to analyze bone cement flow behavior by stepwise injections through medical cannulas. Sixteen cannulas were assigned to four groups for stepwise injection of differently colored cement portions of 1ml volume. Each group differed in the amount of injected cement portions with a range of 1-4ml. After cement curing longitudinal cross-sections of the cannulas were performed and high-resolution pictures taken. Based on these pictures, quadratic polynomial interpolation was applied to the marked intersections between the last two injected cement portions to calculate the leading coefficients. Leading coefficients in the groups with three cement portions (0.287 ± 0.078), four portions (0.243 ± 0.041) and two portions (0.232 ± 0.050) were comparable and significantly higher than the group with one cement portion (0.0032 ± 0.0004), p ≤ 0.016. Based on these findings, cement flow through medical cannulas can be considered as predictable and can therefore be excluded as a source of risk for possible cement leakage complications during vertebroplasty procedures.

Concepts: Adverse event, Numerical analysis, Polynomial, Iatrogenesis, Safe injection site, Polynomials, Quadratic function, Quadratic polynomial


This study was conducted to evaluate the effect of dietary methionine (Met) supplementation in growth performance and reproductive performance of Jing Brown layer hens. A total of 375 9-week-old Jing Brown layer hens were allocated equally to five treatments consisting of 5 replicates with 15 hens. Hens were fed with a diet of corn and soya bean meal supplemented with 0.23%, 0.27%, 0.31%, 0.35% and 0.39% Met respectively. Different Met levels did not significantly affect average daily feed intake (ADFI), average daily gain (ADG) and feed/gain ratio (F/G) (p > 0.05), whereas flock uniformity (FU) and jejunum index were significantly different (p < 0.05), and the largest FU was observed in 0.31% Met. Dietary supplementation of Met significantly affected reproductive system development (p < 0.05), and 0.27-0.31% Met obtained optimal reproductive system development. Different Met levels significantly affected serum uric acid and alkaline phosphatase. Moreover, the relatively higher reproductive hormones in serum were observed in 0.27% Met. Analysis of quadratic curve estimation of flock uniformity, the total number of follicles, the primary follicles and the secondary follicles showed that the optimal Met levels were 0.293%, 0.286%, 0.286% and 0.288%, which could be averaged to 0.288%. These results suggested that the optimal Met requirement for Jing Brown layer hens from 9 to 17 weeks old is 0.29%.

Concepts: Protein, Human, Effect, Affect, Uric acid, Methionine, Quadratic function


Current regimens used to treat pulmonaryMycobacterium abscessusdisease have limited efficacy. There is an urgent need for new drugs and optimized combinations and doses. We performed hollow fiber system studies in whichM. abscessuswas exposed to moxifloxacin lung concentration-time profiles similar to human doses between 0 and 800 mg/day. The minimum bactericidal concentration and MIC were 8 and 2 mg/liter in ourM. abscessusstrain, suggesting bactericidal activity. Measurement of moxifloxacin concentrations in each hollow fiber system revealed an elimination rate (kel) of 0.11±0.05 hr(-1)(half-life of 9.8 h). Inhibitory sigmoid maximal effect (Emax) modeling revealed that the highest Emaxwas 3.15±1.84 log10CFU/ml on day 3, and the exposure mediating 50% of Emax(EC50) was a 0-24 hour area under the concentration time curve (AUC0-24) to MIC ratio of 41.99±31.78 (r(2)=0.99). The EC80was an AUC0-24/MIC of 102.11. However no moxifloxacin concentration killed the bacteria to burdens below the starting inoculum. There was re-growth beyond day 3 in all doses, with replacement by resistant subpopulation that had an MIC >32 mg/liter by the end of experiment. A quadratic function best described the relationship between AUC0-24/MIC and moxifloxacin-resistant subpopulation. Monte Carlo simulations of 10,000 patients revealed that the 400-800 mg/day doses would achieve or exceed the EC80in ≤12.5% of patients. The moxifloxacin susceptibility breakpoint was 0.25 mg/liter, which means almost allM. abscessusclinical strains were moxifloxacin-resistant by these criteria. While moxifloxacin’s efficacy againstM. abscessuswas poor, formal combination therapy studies with moxifloxacin are still recommended.

Concepts: Concentration, Simulation, Monte Carlo, Monte Carlo method, Monte Carlo methods in finance, Computer simulation, Monaco, Quadratic function