Sufficiency and fuzziness in random experiments

In previous papers, the consequences of the “presence of fuzziness” in the experimental information on which statistical inferences are based were discussed. Thus, the intuitive assertion «fuzziness entails a loss of information» was formalized, by comparing the information in the “exact case” with that in the “fuzzy case”. This comparison was carried out through different criteria to compare experiments (in particular, that based on the “pattern” one, Blackwell's sufficiency criterion). Our purpose now is slightly different, in the sense that we try to compare two “fuzzy cases”. More precisely, the question we are interested in is the following: how will different “degrees of fuzziness” in the experimental information affect the sufficiency? In this paper, a study of this question is carried out by constructing an alternative criterion (equivalent to sufficiency under comparability conditions), but whose interpretation is more intuitive in the fuzzy case. The study is first developed for Bernoulli experiments, and the coherence with the axiomatic requirements for measures of fuzziness is also analyzed in such a situation. Then it is generalized to other random experiments and a simple example is examined.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .     

Optimal estimation in random coefficient regression models

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations are discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.     

Shift-tolerance Property of Optical Security System using Phase-based Virtual Image

The shift-tolerance property of the encrypted image or the Fourier decrypting key in the Fourier space is proposed based on a phase-encoded virtual image. The encrypted data is obtained by the Fourier transform of the product of a phase-encoded virtual image to camouflage the original one and a random phase image. Therefore, even if unauthorized users analyze the encrypted image, they cannot reconstruct the required image. This virtual image protects the original one from being counterfeited and from unauthorized access. We demonstrate the robustness to data loss and shift of the encrypted data or the Fourier decrypting key in the proposed decryption technique using an interferometer.     

Fractal porous media III: Transversal Stokes flow through random and Sierpinski carpets

The transversal Stokes flow of a Newtonian fluid through random and Sierpinski carpets is numerically calculated and the transversal permeability derived. In random carpets derived from site percolation, the average macroscopic permeability varies as (- _c)^3/2, close to the critical porosity _c. This exponent is found to be slightly different from the conductivity exponent. Results for Sierpinski carpets are presented up to the fourth generation. The Carman equation is not verified in these two model porous media.     

Analysis of resistive switching behaviors of vanadium oxide thin film

We demonstrated the polarization of resistive switching for Cu/VO_x/Cu memory cell. Switching behaviors of Cu/VO_x/Cu cell were tested by semiconductor device analyzer (Agilent B1500A), and the relative micro-analysis of I-V characteristics of VO_x/Cu was characterized by conductive atomic force microscope (CAFM). The I-V test results indicated that both forming and the reversible resistive switching between low resistance state (LRS) and high resistance state (HRS) can be observed under either positive or negative sweep. The CAFM images for LRS and HRS directly exhibited evidences of the formation and rupture of filaments based on positive or negative voltage. Cu/VO_x/Cu sandwiched structure exhibits a reversible resistive switching behavior and shows potential applications in the next generation nonvolatile memory field.     

Erdös Rényi随机网络上爆炸渗流模型相变性质的数值模拟研究

基于改进的Newman和Ziff算法以及有限尺寸标度理论, 通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟, 分析研究了Erdös Rényi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明: 尽管序参量表现出了不连续相变的特征, 但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erdös Rényi随机网络中的爆炸渗流相变是一种奇异相变, 它既不是标准的不连续相变, 又与常规随机渗流表现出的连续相变处于不同的普适类. 关键词： Erdös Rényi随机网络 爆炸渗流模型 相变 幂律标度行为