A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

Multiple Empirical Kernel Learning with Majority Projection for imbalanced problems

Traditional Multiple Empirical Kernel Learning (MEKL) expands the expressions of the sample and brings better classification ability by using different empirical kernels to map the original data space into multiple kernel spaces. To make MEKL suit for the imbalanced problems, this paper introduces a weight matrix and a regularization term into MEKL. The weight matrix assigns high misclassification cost to the minority samples to balanced misclassification cost between minority and majority class. The regularization term named Majority Projection (MP) is used to make the classification hyperplane fit the distribution shape of majority samples and enlarge the between-class distance of minority and majority class. The contributions of this work are: (i) assigning high cost to minority samples to deal with imbalanced problems, (ii) introducing a new regularization term to concern the property of data distribution, (iii) and modifying the original PAC-Bayes bound to test the error upper bound of MEKL-MP. Through analyzing the experimental results, the proposed MEKL-MP is well suited to the imbalanced problems and has lower generalization risk in accordance with the value of PAC-Bayes bound.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Study of haze emission efficiency based on new co-opetition data envelopment analysis

As haze intensifies in China, controlling haze emission has become the country's top priority for environmental protection. Because haze moves across different regions, it is necessary to develop a data envelopment analysis (DEA) model underpinned by both competition and cooperation to evaluate the haze emission efficiency in different provinces. This study innovatively adopts the spatial econometrics to construct the co-opetition matrices of Chinese provinces, then builds the co-opetition DEA model to evaluate the haze emission efficiency of them, and finally uses the haze data of 2015 as an example to assess the applicability of the model. The results of the study include the following: First, compared with the traditional CCR (A. Charnes & W. W. Cooper & E. Rhodes) model, this study constructs the co-opetition DEA cross-efficiency model that integrates haze's feature of cross-border moving; thus, it is more in line with the reality of haze emission and movement. Second, compared with the efficiency value gained from the CCR model, the haze emission efficiency values for Tianjin and Guangdong, two decision-making units, register greater variance when using the DEA model. The reason might lie in that they have a different spatial transportation relationship with their surrounding provinces. Third, the haze emission efficiency of provinces, according to the evaluation based on the co-opetition DEA method, varies greatly: Those with high efficiency are mostly inland provinces with slow economic growth and adverse climatic conditions, whereas many of the provinces with low efficiency are located in the relatively prosperous East China. The specific co-opetition DEA model constructed in this study enriches the research on the DEA model, which can be applied to the emission efficiency evaluation of similar pollutants around the world and can contribute empirical support to the haze reducing efforts of the government with its empirical results.     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

The robust knapsack problem with queries

We consider robust knapsack problems where item weights are uncertain. We are allowed to query an item to find its exact weight,where the number of such queries is bounded by a given parameter Q. After these queries are made, we need to pack the items robustly, i.e., so that the choice of items is feasible for every remaining possible scenario of item weights.The central question that we consider is: Which items should be queried in order to gain maximum profit? We introduce the notion of query competitiveness for strict robustness to evaluate the quality of an algorithm for this problem, and obtain lower and upper bounds on this competitiveness for interval-based uncertainty. Similar to the study of online algorithms, we study the competitiveness under different frameworks, namely we analyze the worst-case query competitiveness for deterministic algorithms, the expected query competitiveness for randomized algorithms and the average case competitiveness for known distributions of the uncertain input data. We derive theoretical bounds for these different frameworks and evaluate them experimentally. We also extend this approach to Γ-restricted uncertainties introduced by Bertsimas and Sim.Furthermore, we present heuristic algorithms for the problem. In computational experiments considering both the interval-based and the Γ-restricted uncertainty, we evaluate their empirical performance. While the usage of a Γ-restricted uncertainty improves the nominal performance of a solution (as expected), we find that the query competitiveness gets worse.     

人纤维蛋白原对急诊外伤致创伤性凝血病疗效及相关因素分析

目的:探讨人纤维蛋白原(fibrinogen，FIB)对急诊创伤性凝血病患者的临床疗效及相关因素。方法:将2015年6月至2018年6月本院收治的100例严重创伤患者纳入本研究，根据是否创伤性凝血病分为凝血病组(80例)和非凝血病组(20例)。比较凝血病组和非凝血病组患者收住后第1个24 h的急性生理和慢性健康评分(acute physiology and chronic health evaluation II，APACHE II)、创伤严重程度评分(injury severity score，ISS)、低体温及低灌注发生率等指标。采用Logistic多因素回归方法分析严重创伤患者发生创伤性凝血病的相关因素。将80例创伤性凝血病患者随机分为观察组(40例)和对照组(40例)。对照组按照常规诊疗措施治疗，观察组在对照组处理基础上给予人FIB，比较治疗前后观察组和对照组的凝血功能指标，及治疗后的临床用血量、住院时间及病死率。结果:与治疗前相比，治疗后观察组和对照组的凝血酶原时间(prothrombin time，PT)、活化部分凝血活酶时间(activated partial thromboplastin time，APTT)及D-二聚体水平降低(P<0.05)，FIB水平明显升高(P<0.05)。观察组的红细胞(red blood cell，RBC) 输注量、新鲜冰冻血浆(fresh frozen plasma，FFP)输注量、重症加强护理病房(intensive care unit，ICU)时间及病死率均明显低于对照组，差异具有统计学意义(P<0.05)。创伤性凝血病患者PT>18 s(r=0.623，P=0.024)、APTT>60 s(r=0.722，P=0.018)、凝血酶时间(thrombin time，TT)>15 s(r=0.719，P=0.033)与ISS评分呈正相关。碱缺失(base deficit，BD)≥6(OR=3.678，95%CI=1.065～9.417)、格拉斯哥评分(Glasgow coma scale，GCS)≤8(OR=5.299，95%CI=1.122～8.711)和血小板(platelet，PLT)计数(OR=0.982，95%CI=0.971～0.996)是严重创伤患者发生创伤性凝血病的独立预测因素。结论:人FIB可有效改善创伤性凝血病患者的凝血功能，降低病死率、缩短ICU时间，创伤性凝血病与创伤严重程度、合并休克、低体温和重型颅脑损伤存在一定的相关性。     

A model for semiconductor quantum dot molecule based on the current spin density functional theory

Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrödinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Förster-Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems.     

嵌入式RTOS中任务优先级反转问题研究

针对嵌入式实时系统任务调度策略的特点，任务在运行的时候可能被更高优先级的任务中断。分析了嵌入式RTOS中的最高就绪任务的查找算法，指出该调度算法存在的不同优先级的反转问题，并且针对这一问题进行研究，给出了相应的优先级继承方案。较好地解决了RTOS中任务调度中的优先级的反转问题。