Correlations of continuous random data with major world events

The interaction of consciousness and physical systems is most often discussed in theoretical terms, usually with reference to the epistemo-logical and ontological challenges of quantum theory. Less well known is a growing literature reporting experiments that examine the mind-matter relationship empirically. Here we describe data from a global network of physical random number generators that shows unexpected structure apparently associated with major world events. Arbitrary samples from the continuous, four-year data archive meet rigorous criteria for randomness, but pre-specified samples corresponding to events of broad regional or global importance show significant departures of distribution parameters from expectation. These deviations also correlate with a quantitative index of daily news intensity. Focused analyses of data recorded on September 11, 2001, show departures from random expectation in several statistics. Contextual analyses indicate that these cannot be attributed to identifiable physical interactions and may be attributable to some unidentified interaction associated with human consciousness.     

Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise

The principal component analysis is to recursively estimate the eigenvectors and the corresponding eigenvalues of a symmetric matrix A based on its noisy observations Ak=A+Nk, where A is allowed to have arbitrary eigenvalues with multiplicity possibly bigger than one. In the paper the recursive algorithms are proposed and their ordered convergence is established: It is shown that the first algorithm a.s. converges to a unit eigenvector corresponding to the largest eigenvalue, the second algorithm a.s. converges to a unit eigenvector corresponding to either the second largest eigenvalue in the case the largest eigenvalue is of single multiplicity or the largest eigenvalue if the multiplicity of the largest eigenvalue is bigger than one, and so on. The convergence rate is also derived.     

公债市场波动、消费动态与经济增长——基于递归效用与习惯形成的分析

本文在考虑公债市场波动的经济增长模型中引入递归效用和习惯形成,建立基于递归效用和习惯形成的随机经济增长模型,求得均衡时的最优消费和政府债券需求,讨论递归效用和习惯形成对最优消费和政府债券需求的影响,推导出消费的动态路径和经济增长路径,研究递归效用和习惯形成对消费动态路径和经济增长路径的影响.     

Anharmonic resonances with recursive delay feedback

We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators.     

基于机器学习方法的丙型肝炎病毒非结构蛋白5B聚合酶抑制剂活性预测

在丙型肝炎病毒(HCV)的基因复制和蛋白质成熟的过程中, 非结构蛋白5B(NS5B)作为RNA依赖的RNA聚合酶起到了重要的作用. 抑制NS5B聚合酶可以阻止丙型肝炎病毒的RNA复制, 因此成为一种治疗丙型肝炎的有效方法. 通过计算机方法进行虚拟筛选和预测NS5B聚合酶抑制剂已经变得越来越重要. 本文主要采用机器学习方法(支持向量机(SVM)、k-最近相邻法(k-NN)和C4.5决策树(C4.5 DT))对已知的丙型肝炎病毒NS5B蛋白酶抑制剂与非抑制剂建立分类预测模型. 1248个结构多样性化合物(552个NS5B抑制剂与696个非NS5B抑制剂)被用于测试分类预测系统, 并用递归变量消除法选择与NS5B抑制剂相关的性质描述符以提高预测精度. 独立验证集的总预测精度为84.1%-85.0%, NS5B抑制剂的预测精度为81.4%-91.7%, 非NS5B抑制剂的预测精度为78.2%-87.2%. 其中支持向量机给出最好的NS5B抑制剂预测精度(91.7%); C4.5决策树给出最好的非NS5B抑制剂预测精度(87.2%); k-最近相邻法给出最好的总预测精度(85.0%). 研究表明机器学习方法可以有效预测未知数据集中潜在的NS5B抑制剂, 并有助于发现与其相关的分子描述符.     

Efficient Algorithm for Computing Maximum Likelihood Estimates in Linear Transformation Models

Linear transformation models, which have been extensively studied in survival analysis, include the two special cases: the proportional hazards model and the proportional odds model. Nonparametric maximum likelihood estimation is usually used to derive the efficient estimators. However, due to the large number of nuisance parameters, calculation of the nonparametric maximum likelihood estimator is difficult in practice, except for the proportional hazards model. We propose an efficient algorithm for computing the maximum likelihood estimates, where the dimensionality of the parameter space is dramatically reduced so that only a finite number of equations need to be solved. Moreover, the asymptotic variance is automatically estimated in the computing procedure. Extensive simulation studies indicate that the proposed algorithm works very well for linear transformation models. A real example is presented for an illustration of the new methodology.     

Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process

Abstract

We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler process and the proposed quantizations. We show in particular that at every discretization step t_k of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times t₀ = 0 to time t_k. For numerics, we restrict our analysis to the one-dimensional setting and show how to compute the optimal grids using a Newton–Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method.     

基于高光谱成像技术的不同产地小米判别分析

高光谱成像技术被广泛应用于农产品的检测。基于高光谱成像技术结合机器学习算法无损鉴别不同地区的小米样本。将来源7个省份共计23份样品的小米样本根据地理区域划分为东北地区、河北、陕西、山东和山西共5大类，其中东北地区共6份样品，山西地区5份样品，河北、陕西和山东各4份样品。将每份样品均分为10等份并利用高光谱成像仪采集900～1 700 nm波段内小米的高光谱数据。为了减少光照不均匀和暗电流对实验的影响，对采集到的高光谱数据进行黑白校正。利用ENVI软件选取小米高光谱图像的感兴趣区域(ROI)，每份小米样品选取9个ROI。计算ROI内的平均光谱值，以此平均值作为该样本的一条光谱记录，最后共收集到2 070条光谱曲线，其中东北类540条，山西类450条，其他河北类、山东类、陕西类各360条。为了减少样品表面的不平整性引起的散射现象，进而影响小米的真实光谱信息，对收集到的原始光谱进行多元散射校正预处理(MSC)。采用随机划分法对校正过后的光谱数据划分训练集和测试集，测试集占的比例为0.3。利用线性判别分析(LDA)对不同产地小米的光谱数据进行可视化分析，将测试集代入训练好的LDA模型，做出预测结果的混淆矩阵(Confusion Matrix)，结果表明LDA对于陕西和山西类的预测准确率为0.84和0.99，对于东北、河北和山东的预测准确率仅为0.68，0.68和0.40。进而采用递归特征消除(RFE)对小米的光谱信息进行特征选择，去除冗余的信息，提高模型的预测准确率。将RFE分别与支持向量机(SVM)和逻辑回归(LR)结合，对不同产地小米的判别进行对比分析。将小米光谱数据的训练集分别代入SVM-RFE和LR-RFE模型并结合3折交叉验证技术，以模型F值的微平均(Micro-averaging)最优选择出相应的特征子集。结果表明，LR-RFE选择的波长数为74个，其模型的Micro_F为0.59；SVM-RFE选择的波长数为220，其模型的Micro_F为0.66。将选择后的特征子集应用到测试集并将测试集分别代入SVM和LR模型，采用模型预测结果的混淆矩阵和模型的受试者工作特征曲线(ROC)作为评价方法。结果表明SVM-RFE对东北地区、河北、陕西、山东和山西的预测准确率分别为1，0.37，0.72，0和1，其ROC曲线下面积(AUC)分别为0.82，0.92，0.93，0.70和0.99。LR-RFE的预测准确率分别为0.92，0，0.97，0和0.80，其AUC分别为0.72，0.74，0.94，0.66和0.88。从预测结果可以看出SVM-RFE模型的综合分类性能优于LR-RFE，而对陕西类的判别LR-RFE要优于SVM-RFE，对于河北类和山东类两个模型都不能有效判别。这两个模型的预测准确率相比LDA有了一定的提升。     

Numerical solutions of random mean square Fisher-KPP models with advection

This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.