2×2列联表中二属性相关的Bayes检验

2×2列联表中二属性相关的假设检验是定性数据分析中的热点问题,针对此问题的研究频率学派已做过大量的工作,其理论方法已趋于成熟.利用Bayes检验研究2×2列联表中二属性的相关性迄今为止国内外的相关文献还为数不多.将依据Bayes理论对此问题提出新的检验方法,推出其Bayes因子计算公式,利用正态近似研究三项假设计算出有关的后验概率,不仅解决了频率学派难以处理的问题,并且为吸烟有害健康提供了理论支撑.     

稀磁半导体Cd_（1－x）Fe_xTe的磁光光谱

在７０－３００Ｋ温度范围内测量了组分ｘ为０．０１和０．０４的Ｃｄ１－ｘＦｅｘＴｅ及ＣｄＴｅ的法拉第效应随入射光子能量的变化，首次获得了Ｃｄ１－ｘＦｅｘＴｅ在布里渊区Γ点和Ｌ点的有效ｇ因子及其与温度的关系。给出了Ｆｅ２＋离子与载流子间的ｓｐ－ｄ交换作用常数Ｎ０（β－α）＝（－１．５７±０．０３）ｅＶ。     

A Factor Analysis Perspective on Linear Regression in the ‘More Predictors than Samples’ Case

Linear regression (LR) is a core model in supervised machine learning performing a regression task. One can fit this model using either an analytic/closed-form formula or an iterative algorithm. Fitting it via the analytic formula becomes a problem when the number of predictors is greater than the number of samples because the closed-form solution contains a matrix inverse that is not defined when having more predictors than samples. The standard approach to solve this issue is using the Moore–Penrose inverse or the L2 regularization. We propose another solution starting from a machine learning model that, this time, is used in unsupervised learning performing a dimensionality reduction task or just a density estimation one—factor analysis (FA)—with one-dimensional latent space. The density estimation task represents our focus since, in this case, it can fit a Gaussian distribution even if the dimensionality of the data is greater than the number of samples; hence, we obtain this advantage when creating the supervised counterpart of factor analysis, which is linked to linear regression. We also create its semisupervised counterpart and then extend it to be usable with missing data. We prove an equivalence to linear regression and create experiments for each extension of the factor analysis model. The resulting algorithms are either a closed-form solution or an expectation–maximization (EM) algorithm. The latter is linked to information theory by optimizing a function containing a Kullback–Leibler (KL) divergence or the entropy of a random variable.     

A Note on a Paper by P. Amodio and F. Mazzia

In 1999 Amodio and Mazzia presented a new backward error analysis for LU factorization and introduced a new growth factor _n . Their very interesting approach allowed them to obtain sharp error bounds. In particular, they derive nice results assuming that partial pivoting is used. However, the forward error bound for the solution of a linear system whose coefficient matrix A is an M-atrix given in Theorem 4.1 of that paper is not correct. They first obtain a bound for the condition number (U) assuming that one has the LU factorization of an M-matrix and then they apply the bounds obtained when partial pivoting is used. But if P is the permutation associated with partial pivoting then PA = LU can fail to be an M-atrix and the bound for (U) can be false, as shown in our Example 1.1. We also prove that, for a pivoting strategy presented in the paper, the growth factor of an M-matrix A is _n(A) = 1 and (U) (A), where U is the upper triangular matrix obtained after applying such a pivoting strategy.This revised version was published online in October 2005 with corrections to the Cover Date.     

我国工业污染分布状况研究

环境污染越来越受到我国的重视,而工业污染是造成环境污染的重要原因.为了对我国的环境污染分布状况进行深入了解,从总量出发,利用聚类分析和因子分析法分析了我国工业污染的分布情况,并探讨了各类地区工业污染差异的原因,为我国进行侧重点治理环境污染提出可行性建议.     

Enhanced locking region in injection-locked two-section lasers

In this Letter, we investigate the criteria for achieving an enhanced stable locking region in the parameter space of injected field E_inj and frequency detuning ω in two-section semiconductor lasers subject to optical injection. Using the rate equations, a stability analysis is performed and the conditions for an enhanced locking region are deduced from the requirement for the average linewidth enhancement factor appearing in the locking-bandwidth equation to be close to zero. We calculate a stability map for an injection-locked two-section laser with an almost-symmetrical locking region that is greatly enhanced compared to a single-section injection-locked laser with identical material and control parameters.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

Space- and time-like electromagnetic pion form factors in light-cone pQCD

We present a combined analysis of the space- and time-like electromagnetic pion form factors in light-cone perturbative QCD with transverse momentum dependence and Sudakov suppression. Including the genuine non-perturbative “soft” QCD and the power suppressed twist-3 corrections to the standard twist-2 perturbative QCD result, the experimental form factor data available at moderate energies/momentum transfers can be explained reasonably well. To this end, the bulk of the existing discrepancy between the space- and time-like experimental data is ostensibly reconciled.     

Bayesian Binary Segmentation Procedure for a Poisson Process With Multiple Changepoints

We observe n events occurring in (0, T] taken from a Poisson process. The intensity function of the process is assumed to be a step function with multiple changepoints. This article proposes a Bayesian binary segmentation procedure for locating the changepoints and the associated heights of the intensity function. We conduct a sequence of nested hypothesis tests using the Bayes factor or the BIC approximation to the Bayes factor. At each comparison in the binary segmentation steps, we need only to compare a singlechangepoint model to a no-changepoint model. Therefore, this method circumvents the computational complexity we would normally face in problems with an unknown (large) number of dimensions. A simulation study and an analysis on a real dataset are given to illustrate our methods.     

An Injectable Integration of Autologous Bioactive Concentrated Growth Factor and Gelatin Methacrylate Hydrogel with Efficient Growth Factor Release and 3D Spatial Structure for Accelerated Wound Healing

Growth factors are essential for wound healing owing to their multiple reparative effects. Concentrated growth factor (CGF) is a third-generation platelet extract containing various endogenous growth factors. Herein, a CGF extract solution is combined with gelatin methacrylate (GM) by physical blending to produce GM@CGF hydrogels for wound repair. The GM@CGF hydrogels show no immune rejection during autologous transplantation. Compared to CGF, GM@CGF hydrogels not only exhibit excellent plasticity and adhesivity but also prevent rapid release and degradation of growth factors. The GM@CGF hydrogels display good injectability, self-healing, swelling, and degradability along with outstanding cytocompatibility, angiogenic functions, chemotactic functions, and cell migration-promoting capabilities in vitro. The GM@CGF hydrogel can release various effective molecules to rapidly initiate wound repair, stimulate the expressions of type I collagen, transform growth factor β1, epidermal growth factor, and vascular endothelial growth factor, promote the production of granulation tissues, vascular regeneration and reconstruction, collagen deposition, and epidermal cell migration, as well as prevent excessive scar formation. In conclusion, the injectable GM@CGF hydrogel can release various growth factors and provide a 3D spatial structure to accelerate wound repair, thereby providing a foundation for the clinical application and translation of CGF.