Restricted inverse optimal value problem on linear programming under weighted l1l_1 norm

We study the restricted inverse optimal value problem on linear programming under weighted $l_1$ norm (RIOVLP $_1$). Given a linear programming problem $LP_c: \min \{cx|Ax=b,x\geq 0\}$ with a feasible solution $x^0$ and a value $K$, we aim to adjust the vector $c$ to $\bar{c}$ such that $x^0$ becomes an optimal solution of the problem LP$_{\bar c}$ whose objective value $\bar{c}x^0$ equals $K$. The objective is to minimize the distance $\|\bar c - c\|_1=\sum_{j=1}^nd_j|\bar c_j-c_j|$ under weighted $l_1$ norm.Firstly, we formulate the problem (RIOVLP$_1$) as a linear programming problem by dual theories. Secondly, we construct a sub-problem $(D^z)$, which has the same form as $LP_c$, of the dual (RIOVLP$_1$) problem corresponding to a given value $z$. Thirdly, when the coefficient matrix $A$ is unimodular, we design a binary search algorithm to calculate the critical value $z^*$ corresponding to an optimal solution of the problem (RIOVLP$_1$). Finally, we solve the (RIOV) problems on Hitchcock and shortest path problem, respectively, in $O(T_{MCF}\log\max\{d_{max},x^0_{max},n\})$ time, where we solve a sub-problem $(D^z)$ by minimum cost flow in $T_{MCF}$ time in each iteration. The values $d_{max},x^0_{max}$ are the maximum values of $d$ and $x^0$, respectively

Inversion of Different Cultivated Soil Types’ Salinity Using Hyperspectral Data and Machine Learning

Soil salinization is one of the main causes of global desertification and soil degradation. Although previous studies have investigated the hyperspectral inversion of soil salinity using machine learning, only a few have been based on soil types. Moreover, agricultural fields can be improved based on the accurate estimation of the soil salinity, according to the soil type. We collected field data relating to six salinized soils, Haplic Solonchaks (HSK), Stagnic Solonchaks (SSK), Calcic Sonlonchaks (CSK), Fluvic Solonchaks (FSK), Haplic Sonlontzs (HSN), and Takyr Solonetzs (TSN), in the Hetao Plain of the upper reaches of the Yellow River, and measured the in situ hyperspectral, pH, and electrical conductivity (EC) values of a total of 231 soil samples. The two-dimensional spectral index, topographic factors, climate factors, and soil texture were considered. Several models were used for the inversion of the saline soil types: partial least squares regression (PLSR), random forest (RF), extremely randomized trees (ERT), and ridge regression (RR). The spectral curves of the six salinized soil types were similar, but their reflectance sizes were different. The degree of salinization did not change according to the spectral reflectance of the soil types, and the related properties were inconsistent. The Pearson’s correlation coefficient (PCC) between the two-dimensional spectral index and the EC was much greater than that between the reflectance and EC in the original band. In the two-dimensional index, the PCC of the HSK-NDI was the largest (0.97), whereas in the original band, the PCC of the SSK400 nm was the largest (0.70). The two-dimensional spectral index (NDI, RI, and DI) and the characteristic bands were the most selected variables in the six salinized soil types, based on the variable projection importance analysis (VIP). The best inversion model for the HSK and FSK was the RF, whereas the best inversion model for the CSK, SSK, HSN, and TSN was the ERT, and the CSK-ERT had the best performance (R2 = 0.99, RMSE = 0.18, and RPIQ = 6.38). This study provides a reference for distinguishing various salinization types using hyperspectral reflectance and provides a foundation for the accurate monitoring of salinized soil via multispectral remote sensing

Bilevel Traffic Evacuation Model and Algorithm Design for Large-Scale Activities

This paper establishes a bilevel planning model with one master and multiple slaves to solve traffic evacuation problems. The minimum evacuation network saturation and shortest evacuation time are used as the objective functions for the upper- and lower-level models, respectively. The optimizing conditions of this model are also analyzed. An improved particle swarm optimization (PSO) method is proposed by introducing an electromagnetism-like mechanism to solve the bilevel model and enhance its convergence efficiency. A case study is carried out using the Nanjing Olympic Sports Center. The results indicate that, for large-scale activities, the average evacuation time of the classic model is shorter but the road saturation distribution is more uneven. Thus, the overall evacuation efficiency of the network is not high. For induced emergencies, the evacuation time of the bilevel planning model is shortened. When the audience arrival rate is increased from 50% to 100%, the evacuation time is shortened from 22% to 35%, indicating that the optimization effect of the bilevel planning model is more effective compared to the classic model. Therefore, the model and algorithm presented in this paper can provide a theoretical basis for the traffic-induced evacuation decision making of large-scale activities

Efficacy and safety of the compound Chinese medicine SaiLuoTong in vascular dementia: A randomized clinical trial

Introduction: No licensed medications are available to treat vascular dementia (VaD). Methods: Patients were randomly assigned to experimental groups (SaiLuoTong [SLT] 360 or 240 mg for groups A and B for 52 weeks, respectively) or placebo group (SLT 360 mg and 240 mg for group C only from weeks 27 to 52, respectively). Results: Three hundred twenty-five patients were included in final analysis. At week 26, the difference in VaD Assessment Scale-cognitive subscale scores was 2.67 (95% confidence interval, 1.54 to 3.81) for groups A versus C, and 2.48 (1.34 to 3.62) for groups B versus C (both Discussion: This study suggests that SLT is effective for treatment of VaD, and this compound Chinese medicine may represent a better choice to treat VaD