C-半群的Lumer-Phillips定理与C-Hermitian算子

本文给出了稠定闭算子A(或A的扩张)生成压缩C-半群的充分条件,且在C是等距算子时,证明了该条件是必要的,推广了Lumer-Phillips定理.并用结果刻划了等距C-群的生成元.     

能量选择中子成像技术及其应用

能量选择中子成像技术是利用特定范围波长(能量)的中子进行成像。在热/冷中子范围内(<25meV),能量选择中子成像技术主要基于布拉格边效应和衍射机制,相比常规中子成像技术不但可以显著提高图像对比度,而且能分析应变、应力、织构。在超热中子范围内(>1eV),能量选择中子成像技术主要基于中子共振吸收,中子截面随能量变化是同位素特有的,存在明显的共振吸收峰,因此可以进行同位素的“指纹”识别。能量选择中子成像技术在工程、材料、化学、物理、生物、考古等众多科研领域中有着非常广阔的应用前景。     

Integral Operators Between Fock Spaces∗

In this paper, the authors study the integral operator Sφf(z) = Z C φ(z, w)f(w)dλα(w) induced by a kernel function φ(z, ·) ∈ F ∞α between Fock spaces. For 1 ≤ p ≤ ∞, they prove that Sφ : F 1 α → F p α is bounded if and only if sup a∈C kSφkakp,α < ∞, (?) where ka is the normalized reproducing kernel of F 2 α; and, Sφ : F 1 α → F p α is compact if and only if lim |a|→∞ kSφkakp,α = 0. When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness of Sφ : F q α → F p α . In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F 2 α, for 1 ≤ q < p < ∞, they show that Sφ : F p α → F q α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give sufficient conditions for the boundedness or compactness of the operator Sφ : F p α → F q α.     

EGFAFS: A Novel Feature Selection Algorithm Based on Explosion Gravitation Field Algorithm

Feature selection (FS) is a vital step in data mining and machine learning, especially for analyzing the data in high-dimensional feature space. Gene expression data usually consist of a few samples characterized by high-dimensional feature space. As a result, they are not suitable to be processed by simple methods, such as the filter-based method. In this study, we propose a novel feature selection algorithm based on the Explosion Gravitation Field Algorithm, called EGFAFS. To reduce the dimensions of the feature space to acceptable dimensions, we constructed a recommended feature pool by a series of Random Forests based on the Gini index. Furthermore, by paying more attention to the features in the recommended feature pool, we can find the best subset more efficiently. To verify the performance of EGFAFS for FS, we tested EGFAFS on eight gene expression datasets compared with four heuristic-based FS methods (GA, PSO, SA, and DE) and four other FS methods (Boruta, HSICLasso, DNN-FS, and EGSG). The results show that EGFAFS has better performance for FS on gene expression data in terms of evaluation metrics, having more than the other eight FS algorithms. The genes selected by EGFAGS play an essential role in the differential co-expression network and some biological functions further demonstrate the success of EGFAFS for solving FS problems on gene expression data.     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

利用可见近红外光谱多指标综合预测生鲜牛肉储存期

建立了牛肉基于TVB-N、菌落总数、pH值和肉色参数L*多个指标的储存期预测模型,利用可见近红外光谱(Vis/NIR)技术结合区间偏最小二乘(iPLS)和遗传算法(GA)建立了各个指标的PLS预测模型,实现了多指标综合无损快速预测4 ℃下牛肉的储存期。用iPLS和iPLS-GA提取有效波长变量建立PLS预测模型,以预测相关系数和预测标准差作为模型评价标准,结果表明用iPLS-GA选择变量建立的各个指标的PLS预测模型均优于全波段和iPLS组合的PLS模型。由多个指标的预测值和储存期的预测模型,对校正集和预测集样品储存期进行预测,其预测相关系数和标准差分别是0.903, 0.897和1.88, 2.24。说明利用光谱技术结合得出的储存期预测模型可以实现多指标综合预测牛肉储存期,为无损快速检测牛肉储存期或货架期提供了一种新方法。      

基于无信息变量消除法与岭极限学习机的新型变量选择方法：以CO气体浓度反演为例

变量选择是光谱分析领域一个重要的组成部分。为了克服传统区间选择法的缺点与不足,基于无信息变量消除法和岭极限学习机提出一种新型的变量选择与评价方法。首先,利用无信息变量消除法剔除整个光谱区间中无信息的波长点;其次,为了解决传统建模方法(偏最小二乘法、BP神经网络等)存在的共线性问题,采用岭极限学习机方法建立回归模型;最后,最佳的特征光谱波长点组合利用特征选择路径图和稀疏度-误差折中曲线进行确定。CO气体的浓度反演实验结果表明：(1)利用无信息变量消除法可以有效筛选出最能表征CO气体透过光谱的特征波长点;(2)岭极限学习机方法具有快速建模、避免共线性和高精度等优点(CO气体浓度反演模型的决定系数可达0.995);(3)特征选择路径图和稀疏度-误差折中曲线可以直观地帮助用户寻找出最佳的特征波长点组合。     

Random frog: An efficient reversible jump Markov Chain Monte Carlo-like approach for variable selection with applications to gene selection and disease classification

The identification of disease-relevant genes represents a challenge in microarray-based disease diagnosis where the sample size is often limited. Among established methods, reversible jump Markov Chain Monte Carlo (RJMCMC) methods have proven to be quite promising for variable selection. However, the design and application of an RJMCMC algorithm requires, for example, special criteria for prior distributions. Also, the simulation from joint posterior distributions of models is computationally extensive, and may even be mathematically intractable. These disadvantages may limit the applications of RJMCMC algorithms. Therefore, the development of algorithms that possess the advantages of RJMCMC methods and are also efficient and easy to follow for selecting disease-associated genes is required. Here we report a RJMCMC-like method, called random frog that possesses the advantages of RJMCMC methods and is much easier to implement. Using the colon and the estrogen gene expression datasets, we show that random frog is effective in identifying discriminating genes. The top 2 ranked genes for colon and estrogen are Z50753, U00968, and Y10871_at, Z22536_at, respectively. (The source codes with GNU General Public License Version 2.0 are freely available to non-commercial users at: http://code.google.com/p/randomfrog/.)     

A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

一种分解指数算符的简洁方法

提出一种新的分解指数算符的方法,这种方法不仅简单易懂,而且有助于找到更多的算符恒等式.