The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Sparse-grid finite-volume multigrid for 3D-problems

We introduce a multigrid algorithm for the solution of a second order elliptic equation in three dimensions. For the approximation of the solution we use a partially ordered hierarchy of finite-volume discretisations. We show that there is a relation with semicoarsening and approximation by more-dimensional Haar wavelets. By taking a proper subset of all possible meshes in the hierarchy, a sparse grid finite-volume discretisation can be constructed.The multigrid algorithm consists of a simple damped point-Jacobi relaxation as the smoothing procedure, while the coarse grid correction is made by interpolation from several coarser grid levels.The combination of sparse grids and multigrid with semi-coarsening leads to a relatively small number of degrees of freedom,N, to obtain an accurate approximation, together with anO(N) method for the solution. The algorithm is symmetric with respect to the three coordinate directions and it is fit for combination with adaptive techniques.To analyse the convergence of the multigrid algorithm we develop the necessary Fourier analysis tools. All techniques, designed for 3D-problems, can also be applied for the 2D case, and — for simplicity — we apply the tools to study the convergence behaviour for the anisotropic Poisson equation for this 2D case.     

Characterization of CNS disorders and evaluation of therapy using structural and functional MRI

Modern drug development requires technologies that allow rapid translation from the preclinical to the clinical stage. It is obvious that non-invasive imaging modalities such as magnetic resonance imaging (MRI) will play a central role in this regard. This article reviews the use of structural and functional MRI readouts for characterization of central nervous system (CNS) disorders and evaluation of the efficacy of potential CNS drugs. Examples comprise dementia of Alzheimer's type, cerebral ischemia, and neuroinflammation covering both clinical and preclinical aspects. In these examples MRI has been used to obtain relevant structural information on brain atrophy, on the location and extent of ischemic brain areas, and on the number and distribution of demyelinated plaques. These structural data are complemented by readouts assessing the functional consequences associated with the pathomorphological changes. In the last decade, MRI has evolved into a standard tool for the development of CNS drugs. With regard to target-specific/molecular imaging applications MRI is limited by its inherently low sensitivity; complementary imaging modalities utilizing optical and radionuclear reporter systems will thus be required.     

顺磁性聚酯金属配合物的合成及其驰豫性能的研究

本文通过二乙三胺五乙酸（ＤＴＰＡ）或乙二胺四乙酸（ＥＤＴＡ）的双酸酐与二元醇或二元酚进行聚合反应，制备了两个系列共１５种新的聚酯型大分子配体及其顺磁性金属配合物，用核磁、红外光谱以及元素分析表征了配体和配合物的结构。初步试验结果表明，与相应的小分子金属配合物相比，聚酯金属配合物具有较高的弛豫性能。     

Synthesis, binding affinity, and relaxivity of target-specific MRI contrast agents

Although magnetic resonance imaging (MRI) is one of the most important imaging modalities of the central nervous system (CNS), one of the main drawbacks of MRI is its limited specificity. This can potentially be partially alleviated by target-specific contrast agents. In the present paper we describe a simple high yield synthesis of two such gadolinium-based spiperone targeted MRI contrast agents, 1a and 1b. The R₁ relaxivities of 1a and 1b were evaluated and found to be 5.94 and 8.31 mM⁻¹ s⁻¹, respectively at 9.4T, while their R₂ relaxivities at the same magnetic field were found to be 18.05 and 22.60 mM⁻¹ s⁻¹, respectively. In addition and very importantly compound 1a, which is a gadolinium-based, spiperone-targeted MRI contrast agent, was found to preserve some of the spiperone affinity toward the dopamine D2 receptor. Compounds 1a and 1b thus represent potential agents for in vitro dopamine receptor imaging using MRI in experimental models. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On solving sparse band systems with three algorithms of the ABS family

In this paper, we examine three algorithms in the ABS family and consider their storage requirements on sparse band systems. It is shown that, when using the implicit Cholesky algorithm on a band matrix with band width 2q+1, onlyq additional vectors are required. Indeed, for any matrix with upper band widthq, onlyq additional vectors are needed. More generally, ifa _kj 0,j>k, then thejth row ofH _i is effectively nonzero ifj>i>k. The arithmetic operations involved in solving a band matrix by this method are dominated by (1/2)n ² q. Special results are obtained forq-band tridiagonal matrices and cyclic band matrices.The implicit Cholesky algorithm may require pivoting if the matrixA does not possess positive-definite principal minors, so two further algorithms were considered that do not require this property. When using the implicit QR algorithm, a matrix with band widthq needs at most 2q additional vectors. Similar results forq-band tridiagonal matrices and cyclic band matrices are obtained.For the symmetric Huang algorithm, a matrix with band widthq requiresq–1 additional vectors. The storage required forq-band tridiagonal matrices and cyclic band matrices are again analyzed.This work was undertaken during the visit of Dr. J. Abaffy to Hatfield Polytechnic, sponsored by SERC Grant No. GR/E-07760.     

MRI相关定量参数在肩峰下撞击综合征诊断中的价值及与肩关节功能、治疗效果的关系

为分析MRI相关定量参数对肩峰下撞击综合征(SIS)的诊断价值,本研究将56例SIS患者设为SIS组,同期56例健康体检者设为对照组,对比了两组对象的一般资料、肩关节功能评分(Constant评分)及MRI相关定量参数水平,探讨了 MRI定量参数与Constant评分、SIS发病相关影响因素、治疗效果的关系及对SIS的...     

磁共振成像谱仪梯度波形分析

梯度是磁共振成像（MRI）的关键环节.通过采集谱仪梯度波形信号并进行分析,提取出各通道波形的特征点,从而有助于快速准确地判断谱仪梯度硬件电路或脉冲序列编写是否存在问题.采用虚拟仪器LabVIEW软件控制高速采集卡DAQ-2005设计实现多路采集系统,对谱仪的梯度输出进行采集.通过对波形数据进行直方图统计、滤波、差分计算等分析,提取出波形的特征点,这些特征点包含时间与幅度信息.使用实验室自主研发的谱仪进行了多次实验,对该方法进行验证,证明了该方法的有效性,也为谱仪研制和脉冲序列开发提供了一种辅助测试方法.     

基于可见-近红外光谱与稀疏表示的注水肉识别

为了能快速准确的识别原料肉与注水肉, 提出了一种基于可见-近红外光谱和稀疏表示的无损的识别方法。通过向猪肉样本(包括猪皮、脂肪层和肌肉层)注水的方法建立注水肉模型, 采集未注水的原料肉和6类不同注水量的注水肉的可见和近红外漫反射光谱数据。为了消除光谱数据中的冗余信息并提高分类效果, 对光谱数据进行光调制和归一化等预处理并截取有效波段, 根据是否注水以及注水量的多少对样本进行分类。用所有训练样本构成原子库(字典), 通过ｌ1最小化将测试样本表示为这些原子的最稀疏的线性组合。计算测试样本与各类的投影误差, 将最小投影误差对应的类作为测试样本的所属类别, 并应用留一法进行交叉检验, 比较了稀疏表示法与支持向量机的识别结果。实验结果表明, 利用稀疏表示法对于原料肉与注水肉的识别准确率可达到90%以上, 获得了较好的分类效果, 优于支持向量机的识别结果。而对于不同注水量的注水肉识别准确率与注水量之差正相关。稀疏方法不需要进行传统模式识别模型的前期学习与特征提取, 适用于高维、小样本量数据的处理, 计算成本低, 将其用于注水肉的光谱数据识别具有一定的创新性, 并取得了较满意的结果, 为原料肉和注水肉的无损识别提供了一种有效方法。     

Sparse non-negative matrix factorizations for ultrasound factor analysis

Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of Factor Analysis of Dynamic Structures (FADS) is that the solution is not mathematically unique when only non-negativity constraints are used to determine factors and factor coefficients. In this paper, we introduce a novel method to correct FADS solutions by constructing and minimizing a new objective function. The method is improved from non-negative matrix factorizations (NMFs) algorithm by adding a sparse constraint that penalizes multiple components in the images of the factor coefficients. The technique is tested on computer simulations, and a patient ultrasound liver study. The results show that the method works well in comparison to the truth in computer simulations and to region of interest (ROI) measurements in the experimental studies.