一种基于自适应相似矩阵的谱聚类算法

为了消除在构建谱聚类算法的相似矩阵时,高斯核函数中尺度参数的波动影响,构建了一种自适应相似矩阵,并应用到谱聚类算法中。自适应相似矩阵中数据点间的距离度量采用测地距离算法,相距较近的两点间的距离近似于欧氏距离,相距较远的两点则先根据欧氏距离得到每个数据点的k个近邻点,然后累加近邻点的测地距离,由此得到每对数据点间的最短距离。两点间的局部密度用共享近邻的定义来表示,更好地刻画了数据集的本征结构。在5个人工数据集和国际通用UCI数据库中的5个真实数据集上进行实验。实验结果表明,所提算法的聚类准确率高于对比算法的准确率,对复杂分布数据有很强的自适应能力。研究成果为数据挖掘及机器学习提供了思路和方法。     

青藏线运输能力适应性综合评价分析

在分析影响青藏线运输能力因素的基础上,建立了青藏线运输能力适应性模糊综合评价指标体系和模型,分3个层次对该线运输能力适应性进行综合评价,认为青藏线运输能力适应性水平是高的,整个运输组织方案是可行的,但还需对特大灾害和事故下的应对方案和措施进行研究。     

Numerical computation of Theta in a jump-diffusion model by integration by parts

Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black–Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods.     

数学金融中的经验与洞察

本文阐述了作者数学金融中的经验与洞察,系统介绍了数学金融的发展及研究模型,并对数学金融应用于实践边界等问题提出了自己的观点,分析了尤其是在面临风险的情况下,非数学要素往往起到的决定作用,如人性因素、制度因素等等。     

常用预测方法的模糊综合评判模型

本文对预测中的评价问题进行了系统的研究。在此基础上,建立了一个常用预测方法的模糊综合评判模型,为预测者评价和选择预测方法提供依据。     

“剪刀差”问题的对策研究

本文首先指出了传统的房地产销售预测方法的不足。为了改进原有的预测方法 ,作者结合影响单个房地产销售量各项因素的特殊性和模糊性 ,运用模糊数学的理论与方法 ,建立了新的数学模型并将其成功地运用于实践 ,取得了较好的效果 ,其理论与方法具有较高的参考和应用价值。     

输送机托辊阻力及跑合试验综合性能测试仪的设计(下)——测试仪硬、软件控制系统

阐述了系统硬件的电气原理及电路的设计思路和参数选择,讨论了硬件系统的工作过程,建立了测试阻力参数和跑合试验参数的数学模型,给出了测试仪软件系统及数据处理的总体结构,并对主要应用程序进行了设计。     

Unbounded liabilities,capital reserve requirements and the taxpayer put option

When firms access unbounded liability exposures and are granted limited liability, then an all equity firm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the firm. We contribute by (i) valuing this taxpayer put, and (ii) determining the level for reserve capital without a reference to ratings. Reserve capital levels are designed to mitigate the adverse incentives for unnecessary risk introduced by the taxpayer put at the firm level. In our approach, the level of reserve capital is set to make the aggregate risk of the firm externally acceptable, where the specific form of acceptability employed is positive expectation under a concave distortion of the cash flow distribution. It is observed that, in the presence of the taxpayer put, debt holders may not be relied upon to monitor risk as their interests are partially aligned with equity holders by participating in the taxpayer put. Furthermore, the taxpayer put leads to an equity pricing model associated with a market discipline that punishes perceived cash shortfalls.     

论高等数学教学改革的实践

高等数学是大学一门极其重要的基础课程。传统的教学模已经越来越不能适应高等教育事业的迅猛发展了,这样需要在现实教学中实施教学改革。     

基于互联网的高等数学自助学习资源建设探讨

充分利用互联网普及、传递信息快、使用方便等特点,建立了自助学习形式的高等数学学习资源库。该资源库对学生学好高等数学、用好数学原理解决实际问题具有重要意义。