微波腔内波混沌散射的初步研究

通过建立的微波腔模拟产生大量腔体散射矩阵和辐射散射矩阵,并转化得到归一化散射矩阵和阻抗矩阵。利用戴桑环系综对归一化散射矩阵的本征值和本征相位进行了统计分析,其本征值的模和本征相位具有统计独立性,且本征相位近似均一分布,验证了腔体中波混沌散射的存在。对数值模拟和随机矩阵理论预测得到的归一化阻抗的统计特性进行了比较,其结果基本一致,说明随机矩阵理论对归一化阻抗具有一定的预测功能。     

Scalable Network Coding for Heterogeneous Devices over Embedded Fields

In complex network environments, there always exist heterogeneous devices with different computational powers. In this work, we propose a novel scalable random linear network coding (RLNC) framework based on embedded fields, so as to endow heterogeneous receivers with different decoding capabilities. In this framework, the source linearly combines the original packets over embedded fields based on a precoding matrix and then encodes the precoded packets over GF(2) before transmission to the network. After justifying the arithmetic compatibility over different finite fields in the encoding process, we derive a sufficient and necessary condition for decodability over different fields. Moreover, we theoretically study the construction of an optimal precoding matrix in terms of decodability. The numerical analysis in classical wireless broadcast networks illustrates that the proposed scalable RLNC not only guarantees a better decoding compatibility over different fields compared with classical RLNC over a single field, but also outperforms Fulcrum RLNC in terms of a better decoding performance over GF(2). Moreover, we take the sparsity of the received binary coding vector into consideration, and demonstrate that for a large enough batch size, this sparsity does not affect the completion delay performance much in a wireless broadcast network.     

Logical Entropy of Information Sources

In this paper, we present the concept of the logical entropy of order m, logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions X1 and X2 is always less than the sum of the logical entropy of the variables X1 and X2. We define the logical Shannon entropy and logical metric permutation entropy to an information system and examine the properties of this kind of entropy. Finally, we examine the amount of the logical metric entropy and permutation logical entropy for maps.     

岩石冲击凿入过程的随机分析

利用一个典型凿岩机的测试结果,对其入射应力波形的随机特性进行了分析,给出了各类凿岩机入射波的最大应力和冲击能量的随机分布,从而揭示了各类凿岩机品质特性的物理实质。还对岩石凿入过程的随机特性进行了分析,导出了凿深的随机分布特征,揭示了输出方差和的相关性,可以作为凿入系统合理匹配的依据。     

测定概率疲劳长裂纹扩展门槛值的新方法

提出了合理测定随机疲劳长裂纹扩展门槛值的“局部概率Paris关系法”．揭示了常规法不能保证各试样门槛值数据处于相同扩展率水平,测定结果不尽合理的缺陷．以Paris-Erdogan方程描述门槛值附近局部试验数据,考虑数据分散性规律和试样数量两方面的影响,在应力强度因子服从对数正态分布下建立了包含存活概率和置信度的局部概率关系模型,以可接受临界扩展率对应概率因子为依据测定概率门槛值．LZ50钢车轴试验数据分析验证了方法的合理性和有效性．     

随机变量数学期望的一个注记

介绍一种计算随机变量数学期望的方法,利用这种方法容易得到数学期望的相关性质,很多概率与矩的不等式证明也因之变得更为简洁.     

Covariance operator estimation of a functional autoregressive process with random coefficients

We deal with the covariance and cross covariance operators estimation of a Hilbert space valued autoregressive process with random coefficients. We establish bounds for empirical estimators in mean square error and almost sure convergence in Hilbert–Schmidt norm. Consistent estimators of the eigenvalues are also derived.     

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

Rating the raters in a mixed model: An approach to deciphering the rater reliability

Rating the raters has attracted extensive attention in recent years. Ratings are quite complex in that the subjective assessment and a number of criteria are involved in a rating system. Whenever the human judgment is a part of ratings, the inconsistency of ratings is the source of variance in scores, and it is therefore quite natural for people to verify the trustworthiness of ratings. Accordingly, estimation of the rater reliability will be of great interest and an appealing issue. To facilitate the evaluation of the rater reliability in a rating system, we propose a mixed model where the scores of the ratees offered by a rater are described with the fixed effects determined by the ability of the ratees and the random effects produced by the disagreement of the raters. In such a mixed model, for the rater random effects, we derive its posterior distribution for the prediction of random effects. To quantitatively make a decision in revealing the unreliable raters, the predictive influence function (PIF) serves as a criterion which compares the posterior distributions of random effects between the full data and rater-deleted data sets. The benchmark for this criterion is also discussed. This proposed methodology of deciphering the rater reliability is investigated in the multiple simulated and two real data sets.