响应分布的线性化预测及矩信息的作用研究

以Duffing系统为例,探讨了非线性恢复力系统稳态随机响应线性化概率分布预测及矩信息的作用问题。分析了几种等效线性化方法及其解析解的精度。结果表明:采用线性化模型,仅利用已知方差信息的预测精度最高,线性化模型在一定程度上限制了信息的作用;存在一个体现系统线性因素影响力的综合指标,该指标越大,线性化模型预测精度越高。

基于矩信息的不确定投资组合优化问题

在已知随机变量的部分矩信息的条件下,对带有机会约束的投资组合优化问题进行研究.首先,对初始机会约束进行鲁棒性处理,得到分布鲁棒机会约束优化问题;然后,通过引入条件风险价值(CVaR)来近似地表示分布鲁棒机会约束,给出最坏情况下的CVaR近似且表明其精确性.

金融市场风险度量方法的发展

本文综述有关市场风险度量方法的发展过程和前沿问题.在分类概述基于收益分布矩信息的风险度量、随机优势准则、VaR、Coherent风险度量、凸风险度量和多期动态风险度量等定量模型的基础上,指出各类模型的优点、所存在的问题及可能的解决办法,并对未来风险度量方法的研究进行展望.

基于最大熵的新型冠状病毒代际间隔分布估计

传染病代际间隔τ对于探究病毒传播规律具有重要的理论与实用价值,而通常其概率分布函数是未知的。因此,尝试利用最大熵方法推断代际间隔分布函数的最概然形式,详细分析了全球20个国家4986个新型冠状病毒病例信息,在充分考虑样本多样性的基础上估计了该病毒代际间隔的总体均值和方差,然后基于此方法推定了全球新型冠状病毒代际间隔分布函数并以此计算了中国的基本再生数。研究结论有助于进一步客观地分析病毒传播特征,为制定常态化疫情防控对策和相关领域研究提供重要的参考价值。

A Low Resolution Image Restoration Method based on BP Neural Network

In order to investigate the restoration of low resolution images, the linear and nonlinear interpolation methods were applied for the interpolation of the com- mon information matrix obtained from a series of pictures, getting the restructuring matrix. The characteristic block with the best restoration effect was determined by analyzing the pixel difference of the common information of each image at the same position. Then the characteristic blocks and their original blocks were used to build and train neural network. Finally, images were restored by the neural network and the differences between pictures were reduced. Experimental results showed that this method could significantly improve the efficiency and precision of algorithm.

Decryption of pure-position permutation algorithms

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm,we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption al-gorithm. Finally, some simulation results are shown.

Multi-Domain Collaborative Recommendation with Feature Selection

Collaborative f iltering, as one of the most popular techniques, plays an important role in recommendation systems. However,when the user-item rating matrix is sparse,its performance will be degenerate. Recently,domain-specific recommendation approaches have been developed to address this problem.The basic idea is to partition the users and items into overlapping domains, and then perform recommendation in each domain independently. Here, a domain means a group of users having similar preference to a group of products. However, these domain-specific methods consisting of two sequential steps ignore the mutual benefi t of domain segmentation and recommendation. Hence, a unified framework is presented to simultaneously realize recommendation and make use of the domain information underlying the rating matrix in this paper. Based on matrix factorization,the proposed model learns both user preferences of multiple domains and preference selection vectors to select relevant features for each group of products. Besides, local context information is utilized from the user-item rating matrix to enhance the new framework.Experimental results on two widely used datasets, e.g., Ciao and Epinions, demonstrate the effectiveness of our proposed model.

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related.We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.

Geometric Properties of AR(q) Nonlinear Regression Models

This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].

The Velocity Measurement of Two-phase Flow Based on Particle Swarm Optimization Algorithm and Nonlinear Blind Source Separation

In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.

Basic Entropies for Positive-Definite Matrices

We extend basic entropies in the classical information theory to matrix ones in the quantum information theory. Then we show that relations between matrix entropies similar to the classical ones hold.

Statistical Properties of The Exponentiated Nakagami Distribution

This paper is an improvement over beta-Nakagami distribution developed by Shittu and Adepoju （2013）. Here we propose the addition of one parameter to the two parameter continuous Nakagami-m distribution （Nakagami, 1960） that was designed for modeling the fading of radio signals. The resulting distribution referred to as Exponentiated Nakagami （ENAK） distribution is a generalization of the classical Nakagami distribution. The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with the class of Nakagami distributions. Our findings showed that the Exponentiated Nakagami distribution is more flexible than beta-Nakagami distribution with better representation and less computational effort.

A Study on Mixture of Exponentiated Rayleigh and Exponentiated Exponential Distributions Based on Order Statistics

Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.

The matrix representation for the mathematic structure of Shannon’s information measures

Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.

Second-Order Consensus of Multiple Agents with Coupling Delay

In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities （LMIs） is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.

Measurement of Incompatible Probability in Information Retrieval:A Case Study with User Clicks

The incompatible probability represents an important non-classical phenomenon, and it describes conflicting observed marginal probabilities, which cannot be satisfied with a joint probability. First, the incompatibility of random variables was defined and discussed via the non-positive semi-definiteness of their covariance matrixes. Then, a method was proposed to verify the existence of incompatible probability for variables. A hypothesis testing was also applied to reexamine the likelihood of the observed marginal probabilities being integrated into a joint probability space, thus showing the statistical significance of incompatible probability cases. A case study with user click-through data provided the initial evidence of the incompatible probability in information retrieval (IR), particularly in user interaction. The experiments indicate that both incompatible and compatible cases can be found in IR data, and informational queries are more likely to be compatible than navigational queries. The results inspire new theoretical perspectives of modeling the complex interactions and phenomena in IR.

Two-way Markov random walk transductive learning algorithm

Researchers face many class prediction challenges stemming from a small size of training data vis-a-vis a large number of unlabeled samples to be predicted. Transductive learning is proposed to utilize information about unlabeled data to estimate labels of the unlabeled data for this condition. This work presents a new transductive learning method called two-way Markov random walk(TMRW) algorithm. The algorithm uses information about labeled and unlabeled data to predict the labels of the unlabeled data by taking random walks between the labeled and unlabeled data where data points are viewed as nodes of a graph. The labeled points correlate to unlabeled points and vice versa according to a transition probability matrix. We can get the predicted labels of unlabeled samples by combining the results of the two-way walks. Finally, ensemble learning is combined with transductive learning, and Adboost.MH is taken as the study framework to improve the performance of TMRW, which is the basic learner. Experiments show that this algorithm can predict labels of unlabeled data well.

Finite rate of innovation sparse sampling for a binary frequency-coded ultrasonic signal

To achieve sparse sampling on a coded ultrasonic signal,the finite rate of innovation(FRI)sparse sampling technique is proposed on a binary frequency-coded(BFC)ultrasonic signal.A framework of FRI-based sparse sampling for an ultrasonic signal pulse is presented.Differences between the pulse and the coded ultrasonic signal are analyzed,and a response mathematical model of the coded ultrasonic signal is established.A time-domain transform algorithm,called the high-order moment method,is applied to obtain a pulse stream signal to assist BFC ultrasonic signal sparse sampling.A sampling of the output signal with a uniform interval is then performed after modulating the pulse stream signal by a sampling kernel.FRI-based sparse sampling is performed using a self-made circuit on an aluminum alloy sample.Experimental results show that the sampling rate reduces to 0.5 MHz,which is at least 12.8 MHz in the Nyquist sampling mode.The echo peak amplitude and the time of flight are estimated from the sparse sampling data with maximum errors of 9.324%and 0.031%,respectively.This research can provide a theoretical basis and practical application reference for reducing the sampling rate and data volume in coded ultrasonic testing.

Graph publishing method based on differential privacy protection

There are growing concerns surrounding the data security of social networks because large amount of user information and sensitive data are collected. Differential privacy is an effective method for privacy protection that can provide rigorous and quantitative protection. Concerning the application of differential privacy in social networks,this paper analyzes current trends of research and provides some background information including privacy protection standards and noise mechanisms.Focusing on the privacy protection of social network data publishing,a graph-publishing model is designed to provide differential privacy in social networks via three steps: Firstly,according to the features of social network where two nodes that possess certain common properties are associated with a higher probability,a raw graph is divided into several disconnected sub-graphs,and correspondingly dense adjacent matrixes and the number of bridges are obtained. Secondly,taking the advantage of quad-trees,dense region exploration of the adjacent matrixes is conducted. Finally,using an exponential mechanism and leaf nodes of quad-trees,an adjacent matrix of the sanitized graph is reconstructed. In addition,a set of experiments is conducted to evaluate its feasibility,availability and strengths using three analysis techniques: degree distribution,shortest path,and clustering coefficients.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.