Calculated water uptake distribution in the soil profile at different levels of unsaturated diffusivity.

<p>Use inverse method to calculate distribution of water uptake in the soil profile at different unsaturated diffusivity (100<i>D</i>, 10<i>D</i>, 5<i>D</i>, 0.5<i>D</i>, 0.1<i>D)</i>, 100<i>D</i> means the value of unsaturated diffusivity is increased by 100 times than the normal <i>D</i>, and 0.01<i>D</i> means the value of unsaturated diffusivity is reduced by 100 times than the normal <i>D</i>, Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer

<div><p>The widespread use of superabsorbent polymers (SAPs) in arid regions improves the efficiency of local land and water use. However, SAPs’ repeated absorption and release of water has periodic and unstable effects on both soil’s physical and chemical properties and on the growth of plant roots, which complicates modeling of water movement in SAP-treated soils. In this paper, we proposea model of soil water movement for SAP-treated soils. The residence time of SAP in the soil and the duration of the experiment were considered as the same parameter <i>t</i>. This simplifies previously proposed models in which the residence time of SAP in the soil and the experiment’s duration were considered as two independent parameters. Numerical testing was carried out on the inverse method of estimating the source/sink term of root water uptake in the model of soil water movement under the effect of SAP. The test results show that time interval, hydraulic parameters, test error, and instrument precision had a significant influence on the stability of the inverse method, while time step, layering of soil, and boundary conditions had relatively smaller effects. A comprehensive analysis of the method’s stability, calculation, and accuracy suggests that the proposed inverse method applies if the following conditions are satisfied: the time interval is between 5 d and 17 d; the time step is between 1000 and 10000; the test error is ≥ 0.9; the instrument precision is ≤ 0.03; and the rate of soil surface evaporation is ≤ 0.6 mm/d.</p></div

Selection of parameters for numerical testing.

<p>Selection of parameters for numerical testing.</p

Calculated water uptake distribution in the soil profile at different test errors.

<p>Use inverse method to calculate distribution of water uptake in the soil profile at different test errors (<i>per</i> = 0.95, <i>per</i> = 0.90, <i>per</i> = 0.85, <i>per</i> = 0.80, <i>per</i> = 0.70), The bigger the value of <i>per</i>, the smaller the test error. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

Calculated water uptake distribution in the soil profile at different instrument precisions.

<p>Use inverse method to calculate distribution of water uptake in the soil profile at different instrument precisions (<i>w</i> = 0.01, <i>w</i> = 0.03, <i>w</i> = 0.05, <i>w</i> = 0.1), The bigger the value of <i>w</i>, the smaller the instrument precisions. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer - Fig 8

<p>Theoretical moisture and calculated water uptake distribution in the soil profile at different rates of soil surface evaporation (a) Theoretical moisture distribution (b) Calculated water uptake distribution. Use inverse method to calculate distribution of water uptake in the soil profile at different rates of soil surface evaporation (<i>E</i> = 0.03, <i>E</i> = 0.1, <i>E</i> = 0.3, <i>E</i> = 0.6), The “<i>E</i>” stands for evaporation. All the distribution of water uptake in the soil profile are calculated from applying SAP 3d to 15d. Theoretical distribution of moisture and water uptake are calculated from the root water uptake model developed by Shao AJ et al[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

Theoretical moisture and calculated water uptake distribution in the profile of layered soil.

<p>(a) Theoretical moisture distribution; (b) Calculated water uptake distribution. Use inverse method to calculate distribution of water uptake in the profile of layered soil (sandy loam+silty soil), Theoretical distribution of moisture and water uptake are calculated from the root water uptake model developed by Shao AJ et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

Theoretical moisture and calculated water uptake distribution in the soil profile at different times.

<p>(a) Theoretical moisture distribution; (b) Calculated water uptake distribution. Use inverse method to calculate distribution of moisture (apply SAP after 0, 1, 3, 5, 8, 10, 13, 15, 17, 20d) and water uptake (from apply SAP 3d to 5d, 3d to 8d, 3d to 10d, 3d to 13d, 3d to 15d, 3d to 17d, 3d to 20d) in the soil profile at different times. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

Calculated water uptake distribution in the soil profile at different levels of unsaturated hydraulic conductivity.

<p>Use inverse method to calculate distribution of water uptake in the soil profile at different unsaturated hydraulic conductivity (100<i>K</i>, 10<i>K</i>, 5<i>K</i>, 0.5<i>K</i>, 0.1<i>K</i>, 0.01<i>K</i>, 0.001<i>K</i>). 100<i>K</i> means the value of unsaturated hydraulic conductivity is increased by 100 times than the normal <i>K</i>, and 0.01<i>K</i> means the value of unsaturated hydraulic conductivity is reduced by 100 times than the normal <i>K</i>, Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref033" target="_blank">33</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159936#pone.0159936.ref034" target="_blank">34</a>] (<i>S</i> = <i>ET</i>×<i>A</i>×[<i>e^-B</i>(<i>lnZ-C</i>)²]/Z).</p

Table_2_Prognosis signature for predicting the survival and immunotherapy response in esophageal carcinoma based on cellular senescence-related genes.xls

BackgroundCellular senescence occurs throughout life and can play beneficial roles in a variety of physiological processes, including embryonic development, tissue repair, and tumor suppression. However, the relationship between cellular senescence-related genes (CSRGs) and immunotherapy in esophageal carcinoma (ECa) remains poorly defined.MethodsThe data set used in the analysis was retrieved from TCGA (Research Resource Identifier (RRID): SCR_003193), GEO (RRID: SCR_005012), and CellAge databases. Data processing, statistical analysis, and diagram formation were conducted in R software (RRID: SCR_001905) and GraphPad Prism (RRID: SCR_002798). Based on CSRGs, we used the TCGA database to construct a prognostic signature for ECa and then validated it in the GEO database. The predictive efficiency of the signature was evaluated using receiver operating characteristic (ROC) curves, Cox regression analysis, nomogram, and calibration curves. According to the median risk score derived from CSRGs, patients with ECa were divided into high- and low-risk groups. Immune infiltration and immunotherapy were also analyzed between the two risk groups. Finally, the hub genes of the differences between the two risk groups were identified by the STRING (RRID: SCR_005223) database and Cytoscape (RRID: SCR_003032) software.ResultsA six-gene risk signature (DEK, RUNX1, SMARCA4, SREBF1, TERT, and TOP1) was constructed in the TCGA database. Patients in the high-risk group had a worse overall survival (OS) was disclosed by survival analysis. As expected, the signature presented equally prognostic significance in the GSE53624 cohort. Next, the Area Under ROC Curve (AUC=0.854) and multivariate Cox regression analysis (HR=3.381, 2.073-5.514, PConclusionsOur study reveals comprehensive clues that a novel signature based on CSRGs may provide reliable prognosis prediction and insight into new therapy for patients with ECa.</p