依据列相关性优化高斯测量矩阵

为了提高信号重建的精度以及稀疏度适用范围,提出了一种新的测量矩阵优化方法,减小测量矩阵和稀疏变换矩阵的相关性。首先,由测量矩阵和稀疏变换矩阵的乘积构造Gram矩阵;根据Gram矩阵的维数,计算互相关函数的下确界即Welch界;其次,由Welch界确定阈值,收缩Gram矩阵中大于阈值的非对角元;然后,由新得的Gram矩阵和稀疏变换矩阵反解出测量矩阵,迭代更新,从而达到减小相关性,优化测量矩阵的目的。实验结果表明：依据Welch界优化测量矩阵,能快速降低压缩感知矩阵相关性的最大值,提高OMP算法的性能,例如在误差率为10_-0.9时,原高斯随机矩阵需要23个观测值,算法优化后只需16个观测值,相对于Elad、Zhao等观测矩阵优化方法,文中提出的算法具有更小的重构误差,性能和稳定性也略有提升。     

Neural Estimator of Information for Time-Series Data with Dependency

Novel approaches to estimate information measures using neural networks are well-celebrated in recent years both in the information theory and machine learning communities. These neural-based estimators are shown to converge to the true values when estimating mutual information and conditional mutual information using independent samples. However, if the samples in the dataset are not independent, the consistency of these estimators requires further investigation. This is of particular interest for a more complex measure such as the directed information, which is pivotal in characterizing causality and is meaningful over time-dependent variables. The extension of the convergence proof for such cases is not trivial and demands further assumptions on the data. In this paper, we show that our neural estimator for conditional mutual information is consistent when the dataset is generated with samples of a stationary and ergodic source. In other words, we show that our information estimator using neural networks converges asymptotically to the true value with probability one. Besides universal functional approximation of neural networks, a core lemma to show the convergence is Birkhoff’s ergodic theorem. Additionally, we use the technique to estimate directed information and demonstrate the effectiveness of our approach in simulations.     

Local structural order in carbonic acid polymorphs: Raman and FT‐IR spectroscopy

Two different polymorphs of carbonic acid, α‐ and β‐H₂CO₃, were identified and characterized using infrared spectroscopy (FT‐IR) previously. Our attempts to determine the crystal structures of these two polymorphs using powder and thin‐film X‐ray diffraction techniques have failed so far. Here, we report the Raman spectrum of the α‐polymorph, compare it with its FT‐IR spectrum and present band assignments in line with our work on the β‐polymorph [Angew. Chem. Int. Ed. 48 (2009) 2690–2694]. The Raman spectra also contain information in the wavenumber range ∼90–400 cm⁻¹, which was not accessible by FT‐IR spectroscopy in the previous work. While the α‐polymorph shows Raman and IR bands at similar positions over the whole accessible range, the rule of mutual exclusion is obeyed for the β‐polymorph. This suggests that there is a center of inversion in the basic building block of β‐H₂CO₃ whereas there is none in α‐H₂CO₃. Thus, as the basic motif in the crystal structure we suggest the cyclic carbonic acid dimer containing a center of inversion in case of β‐H₂CO₃ and a catemer chain or a sheet‐like structure based on carbonic acid dimers not containing a center of inversion in case of α‐H₂CO₃. This hypothesis is strengthened when comparing Raman active lattice modes at < 400 cm⁻¹ with the calculated Raman spectra for different dimers. In particular, the intense band at 192 cm⁻¹ in β‐H₂CO₃ can be explained by the inter‐dimer stretching mode of the centrosymmetric RC(OHO)₂ CR entity with ROH. The same entity can be found in gas‐phase formic acid (RH) and in β‐oxalic acid (RCOOH) and produces an intense Raman active band at a very similar wavenumber. The absence of this band in α‐H₂CO₃ confirms that the difference to β‐H₂CO₃ is found in the local coordination environment and/or monomer conformation rather than on the long range. Copyright © 2011 John Wiley & Sons, Ltd.     

带偏好DEA在“科学研究基金”管理中的应用研究

将带偏好锥DEA理论引入科学研究基金管理中,在包含"拥挤"迹象的生产可能集基础上建立了三个带偏好锥的平行网络结构DEA模型,对科研基金投入后产生的"成效"进行评价.这些模型分别从三个层面探讨了科研基金使用效率、分配合理性,以及最佳基金预算的确定方法.     

房地产行业的数学建模分析

分别建立了需求模型,供给模型,房地产与其他产业的关系模型,房价模型及房地产发展趋势的预测模型,并对影响模型的相应因素做了简要的分析.     

Mass dependence of mutual diffusion coefficient: computer simulation study

Molecular dynamic computer simulations are performed to study the mass dependence of mutual diffusion coefficient in an isotopic, equimolar binary system. The particles of the system are assumed to be interacting via Lennard-Jones potential. The self- and mutual diffusion coefficients are calculated from the time dependence of the mean square displacement and from the velocity correlation function using the Green–Kubo formula. The study has been carried out at different densities and temperatures. Like the self-diffusion coefficient, the mutual diffusion coefficient is also found to be weakly dependent on the mass ratio. Our study also shows that the temperature of the system has a negligible effect on the mass dependence of the diffusion coefficients.     

Fidelity and Mutual Entropy in Mixed States for Fermi-resonance Coupling Vibrations of CS2

states of Fermi-resonance coupling vibrations in molecule CS₂. It is demonstrated that those fidelities are dominant-positively correlated with each other, one of which by Wang et al. (Phys. Lett. A 373, 58 (2008)) is the most striking in dominant anti-correlation with quantum mutual entropy. That is useful for molecular quantum computing and quantum information.     

基于等概率符号分析方法计算互信息确定延迟时间

用互信息函数确定混沌时间序列相空间重构最佳延迟时间.针对常规符号分析方法计算互信息准确度不高的缺陷,提出等概率符号分析方法计算互信息,即对时间序列按值域大小重排列,再对重排后的序列进行等概率分割,分割的组数由分组经验公式确定,然后取每组的边界值组成符号分析方法的临界点集合进行计算.通过对Lorenz方程和强迫Brusselator振子进行仿真实验,得到的最佳延时与Fraser等概率分格子法得到的结果一致,而算法上更容易实现,证明方法有效.     

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.     

利用变压器研究两个互感线圈的串并联

利用变压器研究了两个互感线圈串并联的等效电感。