Stability and stabilization of Boolean networks

The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

高阶张量信号的稀疏表示

为了有效地压缩多线性信号,提出了高阶张量信号的稀疏表示框架。基于提出的张量信号的稀疏性度量准则,建立了张量信号稀疏表示的模型。并对于所建立的模型,设计了交替式求解方法。在交替式方法中,先将每个优化问题分解为若干个有次序的非凸子优化问题,再利用组织进化算法来求解这些子优化问题。实验结果表明,当交替式方法运行信号的阶数次时,模型的解已非常接近平稳点,同时有效地获得了信号的稀疏表示。     

Interactive Fibre Structure Visualization of the Heart

The heart consists of densely packed muscle fibres. The orientation of these fibres can be acquired by using Diffusion Tensor Imaging (DTI) ex vivo. A good way to visualize the fibre structure in a cross section of the heart is by showing short line segments originating from the cross section and aligned with the local direction of the fibres. If the line segments are placed dense enough, one can see how the fibre orientations change. However, generation of the line segments takes time and thus the user has to wait for new geometry to be generated when the plane defining the cross section is changed. We present a new direct rendering method for the visualization of the 3D vector field in a 2D user‐definable cross section of a heart. On the intersection of the plane with the vector field, the full 3D vectors are rendered as 3D line segments with a local ray casting approach. No preprocessing of the data is needed and no geometry is generated. This technique allows a fast inspection of the data to identify interesting areas where further analysis is necessary (e.g. quantification or generation of streamlines). We also show how the technique is generalized to other glyph shapes than line segments by implementing ellipsoids.     

High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution

In this article we develop a new method to segment high angular resolution diffusion imaging (HARDI) data. We first estimate the orientation distribution function (ODF) using a fast and robust spherical harmonic (SH) method. Then, we use a region-based statistical surface evolution on this image of ODFs to efficiently find coherent white matter fiber bundles. We show that our method is appropriate to propagate through regions of fiber crossings and we show that our results outperform state-of-the-art diffusion tensor (DT) imaging segmentation methods, inherently limited by the DT model. Results obtained on synthetic data, on a biological phantom, on real datasets and on all 13 subjects of a public NMR database show that our method is reproducible, automatic and brings a strong added value to diffusion MRI segmentation.

基于结构张量的自适应CTV彩色图像恢复模型

讨论一种基于非线性扩散方程的彩色图像去噪方法。在图像去噪的3个基本要求的基础上,总结出调和项模型和彩色总变差去噪模型中的不足,利用图像的局部信息构造函数使得模型在接近图像边缘处各向异性平滑并保持边界。在平坦区域各向同性平滑,防止阶梯效应的产生,并利用角点信息保持了角点形状。实验结果表明,所建模型能够较好地保持图像中目标的几何结构,同时具有良好的去噪能力。     

基于张量的XML相似度计算方法

扩展标记语言(XML) 带有一定的结构和语义信息, 与普通文本相比, XML具有描述精确、表现形式丰富等特点, 但同时也使得传统的自然语言处理和数据挖掘等技术不能直接应用. 根据XML内容和结构并非独立, 内容影响结构, 结构作用于内容, 提出一种基于张量的XML特征降维及综合相似度计算方法. 针对XML文档, 使用张量表示并采用基于最大互信息的方法对其进行降维, 采用将XML结构和内容相融合的综合相似度度量方法确定结构和内容的内在联系及共同作用方式, 提高XML综合相似度计算性能. 实验及结果分析验证了所提出方法的有效性.

     

一种张量扩展的条件随机场模型及其在自然语言处理任务中的应用

传统的自然语言处理方法是将大量手工制定的特征输入到统计学习模型中,以完成文本的加工处理。目前,条件随机场模型在多种自然语言处理任务中都取得了较好的效果,但手工特征制定的方式以及庞大的特征数量增加了模型建立的难度,降低了模型运算的速度,同时易使模型“过拟合”。为了解决上述问题,提出一种张量扩展的条件随机场模型,利用张量变换自动构建出复杂的特征,减少了手工特征制定的工作量,并使用Tucker分解算法加速模型,得到的模型可用于多种自然语言处理任务。实验表明,在提取相同基本特征的前提下,与传统的条件随机场模型相比,文中的模型在多种自然语言处理任务中的性能都有所提高,具有一定的使用价值。     

基于模体演化的时序链路预测方法

时序链路预测是动态网络分析的重要组成部分,具有极大的理论和应用价值. 传统的时序链路预测方法往往直接对边的演化规律进行分析,忽略了网络中其他微观结构的演化对链路形成的影响. 基于此分析,本文引入非负张量分解和时间序列分析对网络模体的演化规律进行研究,进而提出一种基于模体演化的链路预测方法. 在三个真实数据集上的实验结果表明,该方法能有效提高链路预测精度.     

Texture segmentation using independent-scale component-wise Riemannian-covariance Gaussian mixture model in KL measure based multi-scale nonlinear structure tensor space

This paper proposes a novel texture segmentation approach using independent-scale component-wise Riemannian-covariance Gaussian mixture model (ICRGMM) in Kullback-Leibler (KL) measure based multi-scale nonlinear structure tensor (MSNST) space. We use the independent-scale distribution and full-covariance structure to replace the covariant-scale distribution and 1D-variance structure used in our previous research. To construct the optimal full-covariance structure, we define the full-covariance on KL, Euclidean, log-Euclidean, and Riemannian gradient mappings, and compare their performances. The comparison experiments demonstrate that the Riemannian gradient mapping leads to its optimum properties over other choices when constructing the full-covariance. To estimate and update the statistical parameters more accurately, the component-wise expectation-maximization for mixtures (CEM²) algorithm is proposed instead of the originally used K-means algorithm. The superiority of the proposed ICRGMM has been demonstrated based on texture clustering and Graph Cuts based texture segmentation using a large number of synthesis texture images and real natural scene textured images, and further analyzed in terms of error ratio and modified F-measure, respectively.