Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

This paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-Jacobi-Bellman Variational Inequality, which is solved for both pricing models using a implicit finite difference approach. The regime switching model is found to more closely match the behavior of futures prices than the single regime model. In addition, analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models.     

变分法原理计算加筋土地基沉降

加筋土的沉降量是反映加筋土地基工作状态的一个重要的参数,但目前并没有成熟的方法,本文建立了简化的加筋土计算模型,根据变分法原理推导出文克尔弹性地基上加筋土的沉降计算公式。并与相关试验的数据作了比较,验证了推导的公式正确性,并和已有的计算方法相比较,得出推导的公式在外荷载较小时具有一定的合理性,同时也指出了它的不足之处,为加筋土地基的优化设计提供参考。     

A new method for automatic synthesis of tolerances for complex assemblies based on polychromatic sets

In computer-aided tolerance design (CAT), integrated design of dimensional and geometric tolerances is still one of the research hotspots. Polychromatic sets theory (PST) is a new mathematic tool, which is especially suitable for formal hierarchical structure models. Based on PST, in this article, a new hierarchical representation model for tolerance synthesis is presented to realise integrated design of dimensional and geometric tolerances. According to the inference relations between unified and individual colours of PST, the synthesis matrices of variational geometric constraints (VGC) are established in the VGC tier of the model, and the synthesis matrices of tolerance types are established in the tolerance type tier of the model. On this basis, the synthesis processes from the feature tier to the VGC tier and from the VGC tier to the tolerance type tier can be realised. VGCs, which are achieved by the synthesis matrices of VGCs, can be combined together to establish a well-constrained VGC network (VGCN). Tolerance types, which are achieved by the synthesis matrices of tolerance types, can be added to the well-constrained VGCN to construct a well-constrained tolerance network. An application example is given in the article to illustrate the synthesis steps.     

MATLAB概述及在解单调变分不等式中的应用

本文综述了Matlab的基本命令及Matlab的特性,并结合数学实验,说明了Matlab在数学实验中的应用。最后,采用超梯度Mann迭代算法,用Matlab编程计算单调变分不等式问题的解。     

Estimation of Biological and Economic Parameters of a Bioeconomic Fisheries Model Using Dynamical Data Assimilation

A new approach of model parameter estimation is used with simulated measurements to recover both biological and economic input parameters of a natural resource model. The data assimilation technique is the variational adjoint method (VAM) for parameter estimation. It efficiently combines time series of artificial data with a simple bioeconomic fisheries model to optimally estimate the model parameters. Using identical twin experiments, it is shown that the parameters of the model can be retrieved. The procedure provides an efficient way of calculating poorly known model parameters by fitting model results to simulated data. In separate experiments with exact and noisy data, we have demonstrated that the VAM can be an efficient method of analyzing bioeconomic data.     

基于路径可靠性的区域运输网络模型及算法

通过对经典运输问题在实际规模网络中进行扩展,建立了基于路径可靠性的区域运输网络运量分布模型。通过引入路径运输费用协方差矩阵,并进行类似金融网络中交易风险最小化的处理,建立明确的数值型最优化模型。在将最优化模型转化为等价的变分不等式后,充分利用运输网络的自身特征,提出了两阶段化的投影算法。新算法的投影算子具有明确的表达式,因此简单易行。通过一个算例,最终解的运量分布模式唯一性和算法的有效性得到了验证。     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题。借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型。结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响。结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大。     

Securing the Sustainability of Global Medical Nuclear Supply Chains Through Economic Cost Recovery,Risk Management,and Optimization

In this paper, we develop a new generalized network model for the optimization of the complex operations of medical nuclear supply chains in the case of the radioisotope molybdenum, with a focus on minimizing the total operational cost, the total waste cost, and the risk associated with this highly time-sensitive and perishable, but critical, product used in health-care diagnostics. Our model allows for the evaluation of transitioning the production and processing of the radioisotope from highly enriched uranium targets to low enriched uranium targets. A case study for North America demonstrates how our model and computational framework can be applied in practice.     

稀土出口管制程度最优调整路径研究

稀土是一种重要的不可再生资源,积极探索其出口管制程度的最优调整路径,有利于中国在一系列限制条件下获取最大经济利益。通过用变分法对最优调整路径进行模拟结果表明,当政府要加强出口管制,采取先慢后快的管制调整策略有助于稀土行业企业获取最大经济利益,当政府需要放松稀土出口管制时,采取逐步加大放松管制幅度的方式有助于稀土行业企业获取最大经济利益。     

Multi-subject stochastic blockmodels with mixed effects for adaptive analysis of individual differences in human brain network cluster structure

Recently, there has been a renewed interest in the class of stochastic blockmodels (SBM) and their applications to multi-subject brain networks. In our most recent work, we have considered an extension of the classical SBM, termed heterogeneous SBM (Het-SBM), that models subject variability in the cluster-connectivity profiles through the addition of a logistic regression model with subject-specific covariates on the level of each block. Although this model has proved to be useful in both the clustering and inference aspects of multi-subject brain network data, including fleshing out differences in connectivity between patients and controls, it does not account for dependencies that may exist within subjects. To overcome this limitation, we propose an extension of Het-SBM, termed Het-Mixed-SBM, in which we model the within-subject dependencies by adding subject- and block-level random intercepts in the embedded logistic regression model. Using synthetic data, we investigate the accuracy of the partitions estimated by our proposed model as well as the validity of inference procedures based on the Wald and permutation tests. Finally, we illustrate the model by analyzing the resting-state fMRI networks of 99 healthy volunteers from the Human Connectome Project (HCP) using covariates like age, gender, and IQ to explain the clustering patterns observed in the data.