Estimating the covariance matrix and the generalized variance under a symmetric loss

For estimating the power of a generalized variance under a multivariate normal distribution with unknown means, the inadmissibility of the best affine equivariant estimator relative to the symmetric loss is shown, and a class of improved estimators is given. The problem of estimating the covariance matrix is also discussed.     

非自持和非麦氏分布情况下托卡马克堆芯等离子体功率平衡

本文给出一组托卡马克堆芯等离子体功率平衡方程,它描述了在非自持和非麦氏分布情况下等离子体功率平衡的问题,计算结果表明。在现实可行的聚变堆工程和相应的等离子体参数情况下,堆芯中每秒可产生聚变中子PN大于10~19。     

On differential stability in stochastic programming

In this paper optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution. Their directional derivatives, in the sense of Gâteaux, are calculated by applying some recent results from the sensitivity analysis of nonlinear programs. These derivatives are employed as a heuristic device in order to derive the asymptotic distribution of statistical estimators of the optimal solutions.     

高频金融数据的标度分析

高频金融数据通常具有尖峰厚尾的非正态特征，常用稳定分布来拟合。本文采用稳定分布的性质对高频上证指数收益率的分布作了标度分析，求得特征指数为1．48，说明我们在分析证券指数分布时可以用稳定分布，而非正态分布。     

Improved charge transport and trap-state distribution in donor–acceptor-type semiconducting copolymer with a fluoropolymer dielectric film

This study presents a p-type doping method for donor–acceptor-type conjugated semiconducting copolymer-based field-effect transistors (FETs) with a fluoropolymer dielectric film. The polymeric FET, which initially comprises a non-polar polymer dielectric layer (poly (methyl methacrylate), PMMA), shows ambipolar behavior owing to the well-balanced electron-accepting and -donating properties of the cyclopentadithiophene (CDT) and pyridyl-2,1,3-thiadiazole (PTz)-based conjugated polymer backbone system. However, when combined with an amorphous fluoropolymer (CYTOP) dielectric layer, the FET device exhibits that their ambipolar behavior remarkably changes to a high-performance p-type FET; the hole mobility enhanced by a factor of ~3 and the threshold voltage significantly shifted from −29 V to −12 V. The density of trap states in the CDT-PTz-based polymeric FETs with a CYTOP dielectric layer, which was estimated from the temperature-dependent transfer characteristics, was narrower and shallower than that of polymeric FETs with a PMMA dielectric layer. As such, it can be inferred that the deep-trap states are filled with additional doped charges from the surface polarization induced by the fluorinated dielectrics at the semiconductor-dielectric interface.     

A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.     

Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field

The response of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics subjected to alternating current(AC) or direct current(DC) bias magnetic field is evaluated by the reaction–diffusion equation for the probability distribution function of the molecular concentration in the spherical coordinate system. The magnetization function and the probability distribution function of the magnetic particles in the reaction system are derived by using the Legendre polynomials and Laplace transform. We discuss the characteristics of magnetization and probability distribution of the magnetic particles with different anisotropic parameters driven by a DC and AC magnetic fields, respectively. It is shown that both the magnetization and the probability distribution decrease with time increasing due to the reaction process. The uniformity of the probability distribution and the amplitude of the magnetization are both affected by the anisotropic parameters.Meanwhile, the difference between the case with linear reaction dynamics and the non-reaction case is discussed.     

Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.