Enhanced spectral resolution by high-dimensional NMR using the filter diagonalization method and "hidden" dimensions

High-dimensional (HD) NMR spectra have poorer digital resolution than low-dimensional (LD) spectra, for a fixed amount of experiment time. This has led to "reduced-dimensionality" strategies, in which several LD projections of the HD NMR spectrum are acquired, each with higher digital resolution; an approximate HD spectrum is then inferred by some means. We propose a strategy that moves in the opposite direction, by adding more time dimensions to increase the information content of the data set, even if only a very sparse time grid is used in each dimension. The full HD time-domain data can be analyzed by the filter diagonalization method (FDM), yielding very narrow resonances along all of the frequency axes, even those with sparse sampling. Integrating over the added dimensions of HD FDM NMR spectra reconstitutes LD spectra with enhanced resolution, often more quickly than direct acquisition of the LD spectrum with a larger number of grid points in each of the fewer dimensions. If the extra-dimensions do not appear in the final spectrum, and are used solely to boost information content, we propose the moniker hidden-dimension NMR. This work shows that HD peaks have unmistakable frequency signatures that can be detected as single HD objects by an appropriate algorithm, even though their patterns would be tricky for a human operator to visualize or recognize, and even if digital resolution in an HD FT spectrum is very coarse compared with natural line widths.     

Application of the Filter Diagonalization Method to One- and Two-Dimensional NMR Spectra

A new non-Fourier data processing algorithm, the filter diagonalization method (FDM), is presented and applied to phase-sensitive 1D and 2D NMR spectra. FDM extracts parameters (peak positions, linewidths, amplitudes, and phases) directly from the time-domain data by fitting the data to a sum of damped complex sinusoids. Grounded in a quantum-mechanical formalism, FDM shares some of the features of linear prediction and other linear algebraic approaches, but is numerically more efficient, scaling like the fast Fourier transform algorithm with respect to data size, and has the ability to correctly handle spectra with thousands or even millions of lines where the competing methods break down. Results obtained on complex spectra are promising.     

Phase-sensitive spectral estimation by the hybrid filter diagonalization method

A more robust way to obtain a high-resolution multidimensional NMR spectrum from limited data sets is described. The Filter Diagonalization Method (FDM) is used to analyze phase-modulated data and cast the spectrum in terms of phase-sensitive Lorentzian "phase-twist" peaks. These spectra are then used to obtain absorption-mode phase-sensitive spectra. In contrast to earlier implementations of multidimensional FDM, the absolute phase of the data need not be known beforehand, and linear phase corrections in each frequency dimension are possible, if they are required. Regularization is employed to improve the conditioning of the linear algebra problems that must be solved to obtain the spectral estimate. While regularization smoothes away noise and small peaks, a hybrid method allows the true noise floor to be correctly represented in the final result. Line shape transformation to a Gaussian-like shape improves the clarity of the spectra, and is achieved by a conventional Lorentzian-to-Gaussian transformation in the time-domain, after inverse Fourier transformation of the FDM spectra. The results obtained highlight the danger of not using proper phase-sensitive line shapes in the spectral estimate. The advantages of the new method for the spectral estimate are the following: (i) the spectrum can be phased by conventional means after it is obtained; (ii) there is a true and accurate noise floor; and (iii) there is some indication of the quality of fit in each local region of the spectrum. The method is illustrated with 2D NMR data for the first time, but is applicable to n-dimensional data without any restriction on the number of time/frequency dimensions.     

Ultra-high resolution 3D NMR spectra from limited-size data sets

The advantage of the filter diagonalization method (FDM) for analysis of triple-resonance NMR experiments is demonstrated by application to a 3D constant time (CT) HNCO experiment. With a 15N-,13C-labeled human ubiquitin sample (1.0 mM), high spectral resolution was obtained at 500 MHz in 25 min with only 6-8 increments in each of the CT dimensions. This data set size is about a factor of 50-100 smaller than typically required, yet FDM analysis results in a fully resolved spectrum with a sharp peak for each HNCO resonance. Unlike Fourier transform (FT) processing, in which spectral resolution in each dimension is inversely proportional to the acquisition time in this dimension, FDM is a true multi-dimensional method; the resolution in all dimensions is determined by the total information content of the entire signal. As the CT dimensions of the 3D HNCO signal have approximate time-reversal symmetry, they can each be doubled by combining the usual four hyper-complex data sets. This apparent quadrupling of the data is important to the success of the method. Thus, whenever raw sensitivity is not limiting, well-resolved n-dimensional spectra can now be obtained in a small fraction of the usual time. Alternatively, to maximize sensitivity, evolution periods of faster relaxing nuclei may be radically shortened, the total required resolution being obtained through chemical shift encoding of other, more slowly relaxing, spins. Improvements similar to those illustrated with a 3D HNCO spectrum are expected for other triple-resonance spectra, where CT evolution in the indirect dimensions is implemented.     

The Multidimensional Filter Diagonalization Method: II. Application to 2D Projections of 2D, 3D, and 4D NMR Experiments

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343–356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin–spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.     

基于谱图还原的中阶梯光栅光谱仪有效波长提取算法

中阶梯光栅光谱仪具有高色散、高分辨率、宽波段、全谱瞬态直读等诸多优点,是先进光谱仪器的代表之一。在中阶梯光栅光谱仪民用化、商品化的发展趋势之下,其二维谱图图像处理的地位越来越重要。目前,国内一般先利用质心提取算法计算光斑质心再结合谱图还原算法计算有效波长,但这种方法难以达到较为理想的要求。为了提升运算速度、波长提取精度以及成像误差补偿能力,提出了基于谱图还原的有效波长提取算法。利用谱图还原算法,将探测器拍摄的二维谱图转换为一维图,通过改进的直方图双峰法选取阈值对一维图降噪,实现了二维谱图中全部有效(x, y)点对应波长的一次性提取。先将二维谱图转换为一维图进行图像处理,使算法在提升运算速度的基础上提取精度也得到了改善,还可以对一定范围内的成像误差进行补偿。采用标准汞灯作为待测光源开展了中阶梯光栅光谱仪成像实验,并使用该算法进行数据处理。实验结果表明,不仅能够自动补偿光谱仪0.05 μm(两个像元)以内的成像偏差,而且能在精确提取有效波长的基础上大幅提升运算速度,波长误差小于0.02 nm,满足中阶梯光栅光谱仪图像处理的要求。     

X荧光能谱分析中探测器响应函数建立方法

在X荧光能谱测量及分析过程中,通过建立探测器响应函数,可以实现对X荧光能谱中的全能峰峰形描述,有助于提高X荧光能谱分析速度、准确度和自动化程度。在X荧光能谱测量中,针对半导体探测器建立响应函数模型的理论与建模技术,文中对三种典型探测器响应函数建模方法,以及全能峰标准差、法诺因子等关键参数的求取进行了论述,并对已有研究进行了总结和比较。最后,对X荧光能谱测量中探测器响应函数建模方法给出了建议。     

The multidimensional filter diagonalization method

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various "ersatz" or "hybrid" spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N(total) = N(1) x N(2) x vertical ellipsis x N(D), where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357-366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

Regularization of the two-dimensional filter diagonalization method: FDM2K

We outline an important advance in the problem of obtaining a two-dimensional (2D) line list of the most prominent features in a 2D high-resolution NMR spectrum in the presence of noise, when using the Filter Diagonalization Method (FDM) to sidestep limitations of conventional FFT processing. Although respectable absorption-mode spectra have been obtained previously by the artifice of “averaging” several FDM calculations, no 2D line list could be directly obtained from the averaged spectrum, and each calculation produced numerical artifacts that were demonstrably inconsistent with the measured data, but which could not be removed a posteriori. By regularizing the intrinsically ill-defined generalized eigenvalue problem that FDM poses, in a particular quite plausible way, features that are weak or stem from numerical problems are attenuated, allowing better characterization of the dominant spectral features. We call the new algorithm FDM2K.     

Small copper clusters: Study of the local atomic and electronic structure by the XANES and DFT methods

The Cu L ₃ edge X-ray absorption spectra of free Cu _n clusters containing 5–15 atoms were obtained for the first time. It is shown that the geometry of small clusters, including the bond length and bond angle, can be studied by analyzing the X-ray absorption spectra. The experimental X-ray absorption spectra of Cu₁₃ clusters were theoretically interpreted using the self-consistent method of full multiple scattering, the finite difference method in the muffin-tin potential approximation, and the full potential method for the icosahedral cluster structure. Good agreement between the theoretical and experimental spectra is achieved for the calculation in the full potential approximation.     

近红外光谱用于植物样品中水溶性氯离子含量的测定

基于离散小波变换(DWT)和最小二乘支持向量回归(LSSVR)方法,建立了近红外光谱测定植物样品中水溶性氯离子的回归校正模型。以烟草样品中水溶性氯离子含量的测定为研究对象,首先采用DWT对近红外光谱进行数据压缩和背景扣除,再用LSSVR建立氯离子的校正模型。结果表明,与偏最小二乘回归(PLSR)和传统的LSSVR方法相比,作者所建模型的预测准确性具有一定优势。     

Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a superoperator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is represented by a matrix continued fraction whose coefficients can be obtained from the nonsymmetric block-Lanczos method. The resulting algorithm, which is particularly convenient when large basis sets are used, allows for the calculation of the full spectrum of a system with a computational workload only a few times larger than needed for static polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.     

基于野外实测光谱统计分析的蚀变矿物填图

提出了一种新的基于野外实测光谱统计分析的蚀变矿物填图方法。该方法首先对野外测量得到的大量样本光谱数据进行聚类处理,从光谱的整体特征上将不同类型的样本区分开。第二步对各聚类结果中不同蚀变矿物分别建立其各自的判别函数。第三步在遥感影像上按照聚类得到的参考光谱分别进行大蚀变类的划分,最后在此基础上采用第二步得到的各蚀变类型的判别函数进行蚀变矿物的细化填图,得到最终的填图结果。该方法充分考虑了不同蚀变类型及蚀变组合的地区差异性,建立的蚀变矿物的判别函数更具有科学性,并且填图结果可在一定程度上进行可靠度评价。将该方法应用到新疆包古图地区的某一研究子区中,获得了较好的成果。     

Sound pulse scattering from an edge of thick elastic plates:experimental and numerical investigations

I.IntroductionItisdifficulttoanaIysesoundscattcringfromanedgeofathickpIatetheoretica11y.Inmostprevious.ork['-'],thecdgcdifTractionsofidca1ha1fp1aneswereconsidered,i.e.theplanesarepcrfcct1yhardorpcrfcctlysoftoroncsurfacehardandonesurfacesoftandtheirthicknessisneg1cctcd,thccorrespondingthporicsarcquitecomp1ctc.Inthisstudy,thecdgcscattcringfromthickelasticplatesinwatcrisinvestigated.Theex'perimentalrcsultsarccxamincdphysica1lybythcp1atethcoryandcomparcdquantitative1ywithca1culationsfromanumeric…     

基于节块展开法的Jacobian-Free Newton Krylov联立求解物理-热工耦合问题

目前反应堆物理热工耦合程序通常采用固定点迭代思路, 这可能导致部分工况收敛速度慢, 甚至出现不收敛的现象, 严重影响了计算效率. 基于此, 本文将高效的粗网节块展开法(NEM)与Jacobian-Free Newton-Krylov (JFNK)方法结合, 成功地开发出了一套新方法NEM_JFNK, 实现了联立求解物理热工耦合问题. 首先将NEM推广到热工问题的求解, 之后使用NEM来离散物理-热工耦合问题的所有控制方程, 使得所有变量都能在粗网格下进行离散, 从而大大减小求解问题的规模; 其次将NEM离散后的方程经过某些特殊的处理, 成功地嵌入JFNK的计算框架, 最终开发出了基于线性预处理的NEM_JFNK, 即LP_NEM_JFNK. 此外, 为了充分利用原有的迭代程序, 避免JFNK残差方程的重新建立, 本文还开发了无需重构残差方程的NEM_JFNK, 即NRC_NEM_JFNK, 并实现“黑箱”耦合. 文中以一维中子-热工模型为例, 给出LP_NEM_JFNK和NRC_NEM_JFNK数学模型, 并对计算结果进行分析. 结果表明:新方法无论是收敛速度还是计算效率都具有明显优势.     

HD2+通过超薄碳膜的"尾流"效应

快分子离子穿过固体时会产生库仑爆炸(Coulomb Explosion),尾流效应是库仑爆炸中的一个显著特性.HD2 的爆炸能谱在实测中发现了一些引人注目的特性:1)H 的尾流效应特别显著;2)H 的能谱结构非常类似HeH 中H 的能谱;3)尾流效应在D 的能谱中体现得很弱.这些特性对分析了解HD2 的结构和物理化学性质有很大的帮助.本文依照“尾流”效应(Wake Effect)的等离子体模型,将爆炸中两个D 产物的尾流场近似认为一个He 的尾流场,模拟计算了1.4977 MeV HD2在100 nm碳膜中分解后0°方向的能谱形式.给出了相同条件下的实验结果,得到了非常接近的结果,并将两者作了比较和分析.文中同时给出了D 的实验能谱,对D 的尾流效应相对较弱作了分析,指出对不同产物分辨的差异、产物的非直线运动等是造成D 尾流效应弱的原因.     

1,8,15,22-四（3-戊氧基）自由酞菁的结构、性质和红外光谱研究

利用密度泛函理论(DFT)中的B3LYP方法,在6-31G(d)基组水平上对1,8,15,22-四(3-戊氧基)自由酞菁的分子结构、分子轨道、原子电荷分布和红外光谱进行了研究。对酞菁骨架结构计算的键长 和晶体结构相差最大仅0.002 nm,最小的不足0.000 3 nm,表明了计算的酞菁骨架结构与晶体数据很吻合;对实验红外光谱图上的峰和模拟的峰的波数进行对应线性拟合,得出拟合直线的斜率为1.039, 截距为58 cm-1,说明计算的红外光谱和实验测得的对应得非常好。上述结果验证了所选取的理论方法和基组的可靠性。通过与未取代自由酞菁结构和性质的比较,发现烷氧基取代后的酞菁 分子中原子电荷仍然主要分布在酞菁环的内部,烷氧基的氧原子也带有较多负电荷。但是α-位烷氧基取代对整个酞菁分子结构和性质都产生很大的影响,烷氧基取代升高了HOMO和LUMO的能量,降低了 HOMO-LUMO能级,从而降低了其稳定性。借助正则坐标分析,对红外光谱中的重要吸收峰进行了详细的指认。     

Simulations of chemical exchange lineshapes in CP/MAS spectra using floquet theory and sparse matrix methods

This paper presents a general method for simulating the effect of chemical exchange on MAS NMR spectra of solid samples. The complication in MAS spectra is that the Hamiltonian itself is time-dependent, due to the spinning of the sample. The approach taken in this work is to use Floquet theory to convert the problem into a time-independent form, and then use established methods (used in liquid NMR simulations) to calculate the lineshape. Floquet theory has been admired for its elegance, but criticized for its computational inefficiencies. This is because it removes the time dependence of the system by expanding the problem in a Fourier-like series. This makes a relatively small, time-dependent calculation into a much larger time-independent one. Typically, we use twice as many Floquet blocks as there are spinning sidebands, so the increase in size is substantial. The problem that this creates stems from the fact that the usual Householder methods for diagonalizing a matrix scale as the cube of the size of the matrix. This would make a Floquet calculation prohibitively long. However, the Floquet matrix is inherently sparse, so sparse matrix methods can produce substantial computational savings. Also, fully diagonalizing a matrix is expensive, but converting the matrix to a tridiagonal form (using iterative Lanczos methods) is much cheaper. The use of the Lanczos methods makes the Floquet calculations feasible as a general method for systems of more than one spin. We show how to set up the full matrix describing chemical exchange in a spinning sample, but the details of how the Lanczos methods work are not included-they are described elsewhere. We then validate the theory by simulating the MAS spectra of dimethyl sulfone both with natural abundance (13)C and with methyl groups labeled with (13)C. The latter system has both dipolar and chemical shielding anisotropy terms contributing to the spectrum. Copyright 2000 Academic Press.     

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.