A class of mixture of experts models for general insurance: Theoretical developments

In the Property and Casualty (P&C) ratemaking process, it is critical to understand the effect of policyholders’ risk profile to the number and amount of claims, the dependence among various business lines and the claim distributions. To include all the above features, it is essential to develop a regression model which is flexible and theoretically justified. Motivated by the issues above, we propose a class of logit-weighted reduced mixture of experts (LRMoE) models for multivariate claim frequencies or severities distributions. LRMoE is interpretable, as it has two components: Gating functions, which classify policyholders into various latent sub-classes; and Expert functions, which govern the distributional properties of the claims. Also, upon the development of denseness theory in regression setting, we can heuristically interpret the LRMoE as a “fully flexible” model to capture any distributional, dependence and regression structures subject to a denseness condition. Further, the mathematical tractability of the LRMoE is guaranteed since it satisfies various marginalization and moment properties. Finally, we discuss some special choices of expert functions that make the corresponding LRMoE “fully flexible”. In the subsequent paper (Fung et al., 2019b), we will focus on the estimation and application aspects of the LRMoE.     

A dynamic analysis of corporate investments and emission tax policy in an oligopoly market with network externality

We investigate the product innovation, green R&D investments and the emission tax policy in an oligopoly market with network externality. It is shown that an appropriate tax policy should be deployed to effectively control pollution and motivate innovation. At the early stage of the market, the emission tax should gradually reduce to motivate firms to achieve optimal investments. Later at the mature stage, the emission tax policy should carefully consider both the market competition and green technology levels.     

润滑油冷却液污染的拉曼光谱检测方法研究

对船舶柴油机而言,润滑油常受到冷却液的污染,引起润滑油劣化变质,从而导致其功能失效。冷却液的主要成分是水、乙二醇及少量的防腐蚀、抗穴蚀、消泡沫等添加剂。将拉曼光谱用于检测润滑油被冷却液污染的浓度,是一种针对复杂混合物的拉曼光谱检测问题,单个拉曼峰强度的定量分析方法无法满足浓度的定量检测。为此,将拉曼光谱分析和LSTM神经网络数据挖掘方法应用于检测润滑油冷却液污染的浓度。在实验室条件下,配制了冷却液污染浓度为2%,1.5%,1%,0.5%,0.25%和0%的柴油机润滑油油样,对每个油样取样50次,并进行拉曼光谱分析,共获得300个拉曼光谱数据,随机抽取其中80%的数据作为神经网络训练样本,剩余20%的数据作为测试样本,拉曼光谱样本数据的光谱范围为300～2 000 cm-1;对数据进行预处理,包括采样、拟合、离散点平均梯度估计等;构建训练样本集,将LSTM神经网络和多层全连接层（FC）结合,建立4种不同的神经网络模型结构;得到其在训练集和测试集上的平均误差曲线、测试集上的检测准确率曲线。分析结果表明,FCs,LSTM-FCs-1,LSTM-FCs-2和LSTM-FCs-3等4种神经网络模型,检测准确率分别为96.7%,93.3%,98.3%和83.3%。选取任意1%的波数点,加入幅值随机正负变化1%的噪声之后,4种神经网络模型的检测准确率分别为88.3%,90.0%,96.7%和78.3%。可见,相比于其他3种神经网络结构模型,LSTM-FCs-2模型更适用于进行润滑油冷却液污染的定量估计,加噪后最高准确率仍可以达到96.7%,鲁棒性优于其他三种模型。拉曼光谱结合LSTM网络中的LSTM-FCs-2模型,应用于冷却液污染浓度分别为0.2%和0.4%的实际油样检测,相对误差分别为5.0%和7.5%,结果表明该方法可用于在用润滑油冷却液污染浓度的检测。     

基于变换域PCNN的近红外与彩色可见光融合

针对近红外与彩色可见光图像融合后对比度低、细节丢失和颜色失真等问题,提出一种基于多尺度变换和自适应脉冲耦合神经网络(PCNN-pulse coupled neural network,PCNN)的红外与彩色可见光图像融合的新算法。首先将彩色可见光图像转换到HSI（hue saturation intensity)空间,HSI色彩空间包含亮度、色度和饱和度三个分量,并且这三个分量互不相关,因此利用这个特点可对三个分量分别进行处理。将其亮度分量与近红外图像分别进行多尺度变换,变换方法选择Tetrolet变换。变换后分别得到低频和高频分量,针对图像低频分量,提出一种期望最大的低频分量融合规则;针对图像高频分量,采用高斯差分算子调节PCNN模型的阈值,提出一种自适应的PCNN模型作为融合规则。处理后的高低频分量经过Tetrolet逆变换得到的融合图像作为新的亮度图像。然后将新的亮度图像和原始的色度和饱和度分量反向映射到RGB空间,得到融合后的彩色图像。为了解决融合带来的图像平滑化和原始图像光照不均的问题,引入颜色与锐度校正机制(colour and sharpness correction, CSC)来提高融合图像的质量。为了验证方法的有效性,选取了5组分辨率为1 024×680近红外与彩色可见光图像进行试验,并与当前高效的四种融合方法以及未进行颜色校正的本方法进行了对比。实验结果表明,同其他图像融合算法进行对比分析,该方法在有无CSC颜色的情况下均能保留最多的细节和纹理,可见度均大大提高,同时本方法的结果在光照条件较弱的情况下具有更多的细节和纹理,均具有更好的对比度和良好的色彩再现性。在信息保留度、颜色恢复、图像对比度和结构相似性等客观指标上均具有较大优势。     

Evolving Stochastic Learning Algorithm based on Tsallis entropic index

In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method.     

A hybrid genetic algorithm–neural network strategy for simulation optimization

Simulation optimization aims at determining the best values of input parameters, while the analytical objective function and constraints are not explicitly known in terms of design variables and their values only can be estimated by complicated analysis or time-consuming simulation. In this paper, a hybrid genetic algorithm–neural network strategy (GA–NN) is proposed for such kind of optimization problems. The good approximation performance of neural network (NN) and the effective and robust evolutionary searching ability of genetic algorithm (GA) are applied in hybrid sense, where NNs are employed in predicting the objective value, and GA is adopted in searching optimal designs based on the predicted fitness values. Numerical simulation results and comparisons based on a well-known pressure vessel design problem demonstrate the feasibility and effectiveness of the framework, and much better results are achieved than some existed literature results.     

双阈值二元神经网络极限环的存在惟一性

研究具负反馈的双阈值二元神经网络模型的动力学性质。在一定的初始函数空间内，对设定的阈值范围证明了模型存在惟一稳定极限环。     

网络流在清理三角债问题中的应用

本文把清理三角债中两种优化数学模型问题，化成求解相应网络上最小费用流的问题，从而得到（强）多项式算法，并把另外的一种优化数学模型问题。化成线性规划问题.于是解答了文[3]中提出的清理三角债的三个基本问题．     

Spin-orbit scattering in the quantum Hall effect

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing, while the intrachannel potential is periodic (non-random); the channels represent two spin states. We consider channel mixing as function of the energy separation of the two extended states, and show that the phase diagram is different from the standard quantum Hall diagram for random intrachannel potential.     

Inverse estimation of temperature dependent emissivity of solid metals

An algorithm in the form of inverse problem to estimate the surface emissivity versus temperature of solids of variable thermal properties separated by a non-participating medium is proposed. The estimations are reproduced by the connection of variable slope stretches (piece-wise function) with no information of the temperature dependence of the emissivity. The input data (measurements) come from the solution of the direct problem by adding a random error to the temperature field. Both the direct and inverse problem are numerically solved by means of the network simulation method. The influence of different parameters in the estimation is studied and the resulting estimations are compared with exact solutions in order to verify the effectiveness of the proposed method.