This work investigates numerical approximations of index 1 stochastic differential algebraic equations (SDAEs) with non-constant singular matrices under non-global Lipschitz conditions. Analyzing the strong convergence rates of numerical solutions in this setting is highly nontrivial, due to both the singularity of the constraint matrix and the superlinear growth of the coefficients. To address these challenges, we develop an approach for establishing mean square convergence rates of numerical methods for SDAEs under global monotonicity conditions. Specifically, we prove that each stochastic theta method with θ∈ [1/2,1] achieves a mean square convergence rate of order 1/2. Theoretical findings are further validated through a series of numerical experiments.

In this paper, we consider a distributed stochastic composite optimization problem with infinite variance, taking the form ‘smooth/nonsmooth + nonsmooth’, where (sub-)gradient information may be unavailable. We present a mini-batch zeroth-order proximal clipped gradient algorithm with shifts, which utilizes the well-known Gaussian smoothing technique to yield unbiased zeroth-order gradient estimators of the surrogate problem. The proposed algorithm employs the clipping gradient to tackle the infinite variance noise, which is one of the keys to deriving good high-probability guarantees. Under the convexity assumption on both terms and other moderate conditions, we derive high probability bounds for the gap between the iterative loss function values and optimal objective values for the proposed algorithm. Furthermore, under only the (μ , x^*) -quasi-strong convexity (may be nonconvex) assumption on the first term, we established high probability bounds for the distance between iteration points and the stationary point. Finally, the proposed scheme is numerically compared with some existing zeroth-order methods as well as a stochastic subgradient algorithm on a phase retrieval problem and an online absolute linear regression task.

The abuse of community detection algorithms may bring the risk of privacy leakage. To protect personal privacy in complex networks, community detection attack algorithms are proposed, which can hide the true community structure of the whole network from the community detection algorithms by adding and deleting subtle edges. However, most of the existing algorithms perform attack based on a community structure so that a specific community detection method is usually adopted for obtaining the communities, which causes the algorithms to not perform well when the attacked community detection algorithm is unknown. To this end, a local structure-based community detection attack heuristic approach (LSHA) is proposed in this article, where the local structures, including several nodes with dense connections instead of the whole community structures, are considered. Unlike the whole community structures obtained by different community detection algorithms, which are usually different, the nodes in such a local structure are often assigned into the same community so that the attack is more general for different community detection algorithms. Specifically, in LSHA, a local structure selection strategy is proposed to maximize the attack effect, which selects two local structures for rewiring attack. Furthermore, two metrics, i.e., edge vulnerability and node entropy, are also suggested to select the nodes and edges for attack. In the experiments, the proposed LSHA is compared with five state-of-the-art attack algorithms. The experimental results against five representative community detection algorithms on nine real-world networks show that the proposed algorithm LSHA achieves good performance on both the attack effectiveness and the efficiency.

This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the considered equations and its numerical approximations generated by the stochastic theta (ST) methods with theta within (1/2,1]. It is shown that the random periodic solution of each ST method converges strongly in the mean square sense to that of SDEs for all step size. More precisely, the mean square convergence order is 1/2 for SDEs with multiplicative noise and 1 for SDEs with additive noise. Numerical results are finally reported to confirm these theoretical findings.

A novel explicit time-stepping scheme, called Lamperti smooth sloping truncation (LSST) scheme, is devised in this paper to strongly approximate the Wright–Fisher model, whose coefficients violate the Lipschitz condition and whose solution process takes values in a bounded domain. The LSST scheme is constructed by combining the Lamperti-type transformation and the smooth sloping truncation. Under appropriate condition, it is proved that the convergence order of the LSST scheme can be up to one. Moreover, it is shown that the proposed scheme has a unique stationary distribution, which converges to that of the original model. Numerical examples are reported to confirm our theoretical findings.

针对船舶与海洋工程领域螺旋桨敞水动力性能实验教学中学生参与性不强的现状,设计并开发了一套螺旋桨敞水动力性能实验教学装置.选取合适大小水箱在其侧壁开口依次连接竖直观测筒、 流量计、 伺服水泵;观测筒上方依次安装电机、 自航仪和螺旋桨,学生自行操作测量推力和扭矩完成螺旋桨敞水实验教学.改变水温,将频闪灯调至与螺旋桨转速相同频率,观测空泡现象完成螺旋桨空泡实验教学.本装置可完成螺旋桨敞水和空泡教学实验,学生在动手完成实验数据测量和实验现象观测的过程中,增强对知识的理解,提高自主创新和动手实践能力.

Extant literature suggested that executive cognitive ability is a critical perspective to answering why and how enterprises perform business model innovation. However, the effect of executive cognitive ability on business model innovation is still insufficiently explored. Drawing on entrepreneurial bricolage theory, we developed a moderated mediation model which takes entrepreneurial bricolage as the mediating mechanism and environmental dynamics as the moderating mechanism to explain how executive cognitive ability influences business model innovation. We collected the data of 316 executives of Chinese start-ups through questionnaires for the model test. Results showed that new venture executives' cognitive ability significantly positively affects business model innovation by mediating with entrepreneurial bricolage. Environmental dynamism positively moderates the effect of executives' cognitive ability on business model innovation. Moreover, environmental dynamism positively moderates the mediating role of entrepreneurial bricolage in executive cognitive ability and business model innovation. This study broadens the research scope of entrepreneurial bricolage theory from the perspective of cognitive ability and provides ideas for new ventures' business model innovation.

The two-stage stochastic linear complementarity problem (TSLCP), which can be regarded as a special and important reformulation of two-stage stochastic linear programming, has arisen in various fields, such as stochastic programming, game theory, traffic equilibrium, and theoretical economics. Considerable effort has been devoted to designing numerical methods for solving TSLCPs. A popular approach is to integrate the progressive hedging algorithm (PHA) as a subalgorithm into a discretization framework. In this paper, aiming to solve large-scale TSLCPs, we propose two kinds of stochastic methods: the stochastic approximation method based on projection (SAP) and the dynamic sampling SAP (DS-SAP), both of which offering more direct and improved control of the computational costs of the involved subproblems, especially compared with the PHA. In particular, the linear complementarity subproblems are solved inexactly during each iteration, and the convergence analysis of both SAP and DS-SAP with an inexactness criterion is presented. Moreover, numerical implementations and practical applications demonstrate the efficiency of our proposed methods.

In order to solve the problem of untimely customer response and increased delivery costs caused by the dynamic changes in customer demand for express companies, a rolling cycle scheduling method for express vehicles that combines batch processing and emergency scheduling is proposed. And the determination method of dispatching time, dispatching scope and inserting position of dynamic demand for express delivery vehicles is expounded. Then, a novel m-TSP scheduling algorithm using hybrid ant colony algorithm is designed to tackle this model. We perform a series of experiments to validate the proposed model and algorithm. Experimental results clearly show the strength of handling dynamic customer needs and the superiority of the presented scheduling method over the original method.

This paper conducted a discrete choice experiment to design information to motivate users to comply with barrage etiquette on video website. In the experiment, the impact of six attributes derived from information framework was examined. By collecting data from 633 online users, we found that the users were more willing to comply with barrage etiquette when they were reminded by Cyberspace Administration of China, message was delivered in a gain frame, the unqualified barrage could affect user’ right on the website, and the barrage could affect other audience’ experience about the online video.

In this paper, we consider the sample average approximation method for stochastic multiobjective optimization problems without the scalarization parameters. By virtue of the gap function, we transform stochastic multiobjective optimization problems into stochastic optimization reformulation problems. Some properties of the reformulation problems are discussed. Then, we propose a sample average approximation method for solving the reformulation problems, and the convergence and the rates of convergence of optimal values and optimal solutions of the approximation problems are investigated. Furthermore, the rates of convergence of the weakly Pareto optimal for sample average approximation multiobjective problem are discussed under the error bound condition.

A novel explicit time-stepping scheme, called Lamperti smoothing truncation scheme, is devised in this paper to strongly approximate a stochastic SIS epidemic model, whose solution process takes values in a bounded domain and whose coefficients violate the global monotonicity condition. The proposed scheme is based on combining a Lamperti-type transformation with an explicit truncation method. The new scheme results in numerical approximations preserving the domain of the original SDEs and is proved to retain a mean-square convergence rate of order one. Numerical examples are finally reported to confirm our theoretical findings.

设计一种船用推力扭矩测量传感器,分析其推扭特性,并制作传感器实物进行标定完成验证.分析传感器设计原理,重点阐述如何避免推扭干扰问题,在Workbench中用数值仿真方法计算推力-应变、扭矩-应变曲线,判断其线性度.同时加载推力和扭矩,分别与单独加载力或扭矩对比,分析其推力扭矩干扰特性.制造传感器,粘贴应变片,以实物标定方式验证传感器设计可行性.

The employees’ violation of information security policy (ISP) poses a major threat to the information resources of the employer. This paper constructs an integrated framework based on the theories on rational choice and general deterrence, and applies it to explain effects on sanction on ISP violation by employees. The model was tested by a scenario-based experiment on 320 employees from two universities and three companies in China. The results show that the certainty, severity and celerity of sanction have positive impacts on ISP compliance; the relationship between sanction severity and ISP compliance is mediated by the cost of noncompliance, and sanction celerity. The research findings have important theoretical and practical implications on the ISP compliance.

This thesis contains three works in both continuous-time and distributionally robust mean-variance Markowitz models. In the first work, we study naive strategies in the continuous-time mean-variance model. We propose a new type of agent to approximate the dynamic of the naive agent by partitioning the time line into numerous small equal length time intervals. Then, we prove that, the wealth process of the proposed agent converges to that of the naive agent and derive the explicit formula for the limiting wealth process and its corresponding portfolio process. In the end, we compare the naive strategies with two equilibrium strategies in the Black-Scholes market. The second work contributes to the mean-variance model by considering its distributionally robust counterpart, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem to an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive backtesting results on the S&P 500 that compares the performance of our model with those of several well-known models, including the Fama – French model and the Black – Litterman model. In the last part, we develop a distributionally robust model based on the Sharpe ratio optimization problem. We transform the problem into an equivalent convex optimization problem that can be solved numerically. In this model, we do not need to choose the target return parameter, which has to be decided by subjective judgement in previous distributionally robust mean-variance models. As a result, the distributionally robust Sharpe ratio model is completely data-driven. We also provide guidance on the choice of ambiguity set size by using a much simpler scheme than that employed in the second work. In the end, we compare the performance of this model to that of the second work and some other well-known models on S&P500.

基于音响放大器系统实验具有综合性、设计性、创新性和可拓展性强的特点,结合该课程完善的MOOC资源,将其应用于多层次实验教学当中.学生根据各自能力兴趣特点,选择不同层次的实验设计方案完成实验.该实验丰富了实验教学内容,使实验在广度和深度具有多个层次,改善了实验教学效果,激发学生实践学习的兴趣,培养学生自适应学习能力和创新能力,为培养创新型实践人才奠定了良好的基础.

This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost sure decay stability of the above system and its stochastic theta-method approximation are investigated in this paper. The author establishes numerical stability under a monotone-type condition in unbounded delay setting. An example is presented to illustrate the result.

This paper considers the sample average approximation method for the Expected-value formulation of stochastic mixed variational inequality problems (SMVIP). The existence and uniqueness of solution of the Expected-value formulation of SMVIP are investigated under some suitable coercivity condition and uniformly monotonicity. Besides, a constrained optimization reformulation is proposed by using a regularized gap function. Under some mild conditions, an implementable sample average approximation method for this reformulation is established and the limiting behaviors of the optimal values and the optimal solutions of the approximation problems as the sample size increases are investigated as well. Some numerical results are also obtained to show the effectiveness of the proposed method.

Numerical stability plays an important role in numerical analysis. The author analysis the numerical stability of the stochastic delay differential equations (SDDEs). Traditional stability theory for numerical methods applied to SDDEs requires a global Lipschitz assumption or one-side linear growth condition on the coefficients. In this paper we want to further relax the condition. Under polynomial growth condition, this paper shows that the semi implicit method can reproduce almost sure exponential stability of the exact solutions to the SDDEs. This improves the existing results considerably.

In this paper, we study a class of stochastic mixed variational inequality problems (SMVIPs) in finite dimensional spaces. It can be observed that the SMVIP may have no common solution for almost every realization in general. In order to get a reasonable resolution, we first present a deterministic formulation, the expected residual minimization (ERM) formulation, for the SMVIP by means of some merit function. Then we establish some basic properties of the ERM problem and propose a quasi-Monte Carlo approximation approach to solve it. We also obtain some convergence results of optimal solutions and stationary solutions of the approximation problem to their true counterparts.