On the concept of exact solution for nonlinear differential equations of fractional‐order

In this article, the new exact travelling wave solutions of the nonlinear space‐time fractional Burger's, the nonlinear space‐time fractional Telegraph and the nonlinear space‐time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. The ‐expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd.     

高光谱数据的刚竹毒蛾虫害程度检测

刚竹毒蛾虫害检测对毛竹的生长和竹业的发展起着至关重要的作用.根据高光谱冠层光谱信息与刚竹毒蛾虫害程度之间的关系,提取冠层光谱中与虫害紧密相关的特征波长、指数以及光谱参数等,利用Fisher判别分析法建立刚竹毒蛾虫害程度检测模型.分别以原始光谱的400～508,586～693和724～900 nm处的波长、包络线去除光谱...     

Hellmann–Feynman connection for the relative Fisher information

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS link and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided.     

Rigorous properties and uncertainty-like relationships on product-complexity measures: Application to atomic systems

Most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values, and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework, valid for any arbitrary n-dimensional distribution. In the present work, different product-complexities, constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated. Different results on product-complexities, such as rigorous bounds, uncertainty-like inequalities, relationships among themselves and also statistical interpretations are given. For the sake of completeness, some of these analytical results on product-complexities are numerically checked for the one-particle densities of atomic systems in both conjugated spaces.     

Restoration of a Poisson distributed image using a principle of extreme physical information

Suppose that an object which reflects or emits light is captured by a sensor. The image data are distorted in various ways. The aim is to restore the object. For this purpose, a new restoration method is devised. It uses the Fisher-information based principle of extreme physical information (EPI). This solves a variational problem I − J = extremum, expressing a flow of information J → I from source to output in the restoration problem. Here, the source of information is the Poissonian image data, and J is modeled as its Hartley information level. Also, I is the Fisher information in the output restored object. The approach dates from the 1980s. It has been already shown that many fundamental physical laws may be derived using EPI. In this paper, the EPI approach is applied to the restoration problem, wherein it regards the unknown restoration as another fundamental law. It models the source information J as obeying Poisson statistics, and assumes additional image distortions that are due to additive Gaussian noise and quantization of the image data. It is found that the quantization level determines the degree of smoothness (or sharpness) of the restored signal. An optimal level of image quantization can be accomplished by adjusting its cross entropy. Finally, the restoration method by EPI is validated by numerical simulations of the image forming and restoring system.     

Parameter estimation by decoherence in the double-slit experiment

We discuss a parameter estimation problem using quantum decoherence in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer.     

基于Fisher判别分析与随机森林的马尾松毛虫害检测

虫害检测算法的构建是耦合“地-天”特征的过程,是实现其遥感监测的重要保障。以福建省三明市、将乐县、沙县、南平市延平区等4个县(区、市)为试验区,收集182组马尾松毛虫害样本数据,随机划分为训练集与验证集,设置5次重复试验及1次指标筛除试验。结合马尾松毛虫危害下的寄主表征,获取松林叶面积指数LAI、叶面积指数标准误SEL、归一化差值植被指数NDVI、缨帽变换湿度轴WET及影像绿光波段B₂、红光波段B₃、近红外波段B₄等7个地面与遥感特征指标,建立其危害等级的Fisher判别分析与随机森林模型,从检测精度、Kappa系数、ROC曲线等角度综合比较两种算法的检测效果,并给予配对t检验。结果表明：7个指标均具备虫害响应能力,SEL和NDVI相对较弱;Fisher判别分析6次试验的虫害平均检测精度为73.26%,Kappa系数为0.631 9,而RF法则分别为79.30%,0.715 1,显著优于前者(p＜0.05);RF法对无危害、轻度危害、中度危害3个虫害等级的检测精度、Kappa系数、AUC均显著高于Fisher判别分析(p＜0.05),对于重度危害等级,Fisher判别分析则占优。总体而言,RF法对马尾松毛虫害的检测效果优于Fisher判别分析,但Fisher判别分析对重度危害等级有更高准确性且模型明确、易于推广,可综合应用两种算法开展虫害监测工作。该成果为马尾松毛虫害及其他森林病虫害的有效检测提供技术参考,奠定其遥感监测的基础。     

密度泛函活性理论中的信息论方法

密度泛函活性理论(DFRT)运用简单的密度泛函探讨和定量化分子的反应活性,是近来发展起来的一个关于分子活性理论的新方法。在新近的文献中,这样的简单密度泛函的例子包括香农熵,费舍尔信息以及其它来自信息论中的密度泛函。本文综述了DFRT信息论方法的原理,包括物理信息极小原理、最小信息增益原理和信息守恒原理。总结了DFRT信息论方法在电子密度、形态密度和分子中的原子三种表述下的理论框架。此外,还介绍了运用信息论方法在定量描述空间位阻效应、亲电性、亲核性和区域选择性中的突出应用,以及对亲电芳香取代反应的邻对间位取代效应的起源和本质提供的一个全新诠释。最后简要地展望了该领域的几个可能的未来发展方向。     

基于无机元素分析对地理标志五常大米鉴别技术的研究

五常大米是我国著名地理标志产品之一,品质高、产量低,导致制假售假的现象严重。为维护五常大米的品牌形象和消费者利益,急需一种有效鉴别五常大米的方法。应用电感耦合等离子体光谱及电感耦合等离子体质谱测定大米中无机元素含量,结合主成分分析(PCA)、Fisher判别、人工神经网络(ANN)对五常大米鉴别模型进行研究。结果表明：PCA法对样品的分类效果较差,采用Fisher判别和ANN则可准确识别五常地区的大米样品和其他地区的大米样品。Fisher判别法对校正集和验证集样品平均准确识别率分别为93.5%,而ANN法对同样的校正集和验证集样品的平均准确识别率为96.4%,优于Fisher判别法。可准确对五常大米进行鉴别,为该产品的地理标志保护提供了一种技术手段。     

Entropy,Fisher Information and Variance with Frost-Musulin Potenial

This study presents the Shannon and Renyi information entropy for both position and momentum space and the Fisher information for the position-dependent mass Schrödinger equation with the Frost-Musulin potential. The analysis of the quantum mechanical probability has been obtained via the Fisher information. The variance information of this potential is equally computed. This controls both the chemical properties and physical properties of some of the molecular systems. We have observed the behaviour of the Shannon entropy. Renyi entropy, Fisher information and variance with the quantum number n respectively.