ELIMINATING COMPLEX EIGENVECTORS AND EIGENVALUES IN MULTIWAY ANALYSES USING THE DIRECT TRILINEAR DECOMPOSITION METHOD

The direct trilinear decomposition method(DTDM)is an algorithm for performing quantitative curveresolution of three-dimensional data that follow the so-called trilinear model,e.g.chromatography-spectroscopy or emission-excitation fluorescence.Under certain conditions complexeigenvalues and eigenvectors emerge when the generalized eigenproblem is solved in DTDM.Previouspublications never treated those cases.In this paper we show how similarity transformations can be usedto eliminate the imaginary part of the complex eigenvalues and eigenvectors,thereby increasing theusefulness of DTDM in practical applications.The similarity transformation technique was first used byour laboratory to solve the similar problem in the generalized rank annihilation method(GRAM).Because unique elution profiles and spectra can be derived by using data matrices from three or moresamples simultaneously,DTDM with similarity transformations is more efficient than GRAM in the casewhere there are many samples to be investigated.     

RECENT DEVELOPMENTS IN MULTIVARIATE CALIBRATION

With the goal of understanding global chemical processes,environmental chemists have some of the mostcomplex sample analysis problems.Multivariate calibration is a tool that can be applied successfully inmany situations where traditional univariate analyses cannot.The purpose of this paper is to reviewmultivariate calibration,with an emphasis being placed on the developments in recent years.The inverseand classical models are discussed briefly,with the main emphasis on the biased calibration methods.Principal component regression(PCR)and partial least squares(PLS)are discussed,along with methodsfor quantitative and qualitative validation of the calibration models.Non-linear PCR,non-linear PLSand locally weighted regression are presented as calibration methods for non-linear data.Finally,calibration techniques using a matrix of data per sample(second-order calibration)are discussed briefly.     

Charophyta: their use in paleolimnology

Charophyta are common algae in limnic waters from many regions and are an interesting group from an evolutionary point-of-view, as they are believed to be related to the Chlorophyceae and land plants. Paleontological-botanical systematics are discussed, taking into consideration some new advances. Charophytes live in all types of inland waters and are sensitive to ecological change, and so they are very useful paleolimnological markers. Gaps concerning gyrogonite morphology in extant taxa and their responses to different environmental conditions must be described. This paper discusses data concerning ecological factors affecting the distribution of Argentinian Charophyta (principally distributed between 30°S and 40°S), gyrogonite morphology related to different ecological conditions, and the way that Charophyta can modify the environment.This is the fifth in a series of papers published in this issue on Paleolimnology in Southern South America. Dr C. A. Fernández served as guest editor for these papers.     

A simple notation for differential vector expressions in orthogonal curvilinear coordinates

We present a simple notation for performing differential vector operations in orthogonal curvilinear coordinates, and for easily obtaining partial differential expressions in terms of the physical components. We express n th-order tensors as the summed products of the physical components and n th-order polyads of unit vectors (an extension of Gibbs dyadic notation convenient for a summation convention). By defining a gradient operator with partial derivatives balanced by the inverse scale factors, differential vector (or tensor) operations in orthogonal coordinates do not require the covariant/contravariant notation. Our primary focus is on spherical-polar coordinates, but we also derive formulae which may be applied to arbitrary orthogonal coordinate systems. The simpler case of cylindrical-polar coordinates is briefly discussed. We also offer a compact form for the gradient and divergence of general second-order tensors in orthogonal curvilinear coordinates, which are generally unavailable in standard handbooks. We show how our notation relates to that of tensor analysis/differential geometry. As the analysis is not restricted to Euclidean geometry, our notation may be extended to Riemannian surfaces, such as spherical surfaces, so long as an orthogonal coordinate system is utilized. We discuss the Navier-Stokes equation for the case of spatially variable viscosity coefficients.     

基于层次分析法和GIS的西昌市空间形态变化特征研究

城市空间形态变化研究涉及到自然条件、资源分布、人类活动、社会经济发展等诸多方面,运用层次分析法对复杂因素构成的整体问题进行层次分解和重新构造,建立多目标的综合评价指标体系和模型。以西昌市为例,将影响城市化发展和空间形态发展变化的特征因子概括分解为自然因子和人类活动因子两大类,并基于DEM数据分别提取出坡度、相对高程、坡向、地面粗糙度数据,利用两个不同时期的遥感数据求取出土地变化率数据,从而作为分析西昌市空间形态变化特征的驱动力因子。结合层次分析法计算出来的5个因子权重值,在ArcGIS 9.3中利用栅格计算器进行叠置分析,求取出西昌市空间形态变化模式趋势图和空间发展模式分类图。     

Separation of local and regional information in distorted GDS response functions by hypothetical event analysis

Electromagnetic investigations are usually intended to examine regional structures where induction takes place at a given period range. However, the regional information is often distorted by galvanic effects at local conductivity boundaries. Bahr (1985) and Groom & Bailey (1989) developed a physical distortion model for decomposing the MT impedance tensor, based upon local galvanic distortion of a regional 2-D electromagnetic field. We have extended their method to predict the magnetic variation fields created at an array of sites. The magnetic response functions at periods around 1000 s may be distorted by large-scale inhomogeneities in the upper or middle crust. In this period range, the data measured by a magnetometer array contain common information that can be extracted if the data set is treated as a unit, for example by using hypothetical event analysis. With this technique it is always possible to recover the regional strike direction from distorted data, even if a strong, spatially varying regional vertical field component is present in the data set. The determination of the regional impedance phases, on the other hand, is far more sensitive to deviations from the physical distortion model.
The approach has been used to investigate the Iapetus data set. For the array, which covers an area of 200  km × 300  km in northern England/southern Scotland, the technique revealed a common regional strike azimuth of ca . N125° E in the period range 500–2000  s. This direction differs from the strike indicated by the induction arrows, which seem influenced mainly by local current concentrations along the east–west-striking Northumberland Trough and a NE–SW-striking mid-crustal conductor. Both impedance phases are positive and differ by ca . 10°, which supports the assumptions of distortion fields in the data set and that the regional structure is 2-D.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

Insights from a Qualitative Study of Rural Communes: Physical and Social Dimensions of Place

Existing research on people–place dynamics often focuses on either physical environment or social dimensions, but many theoretical models posit that both factors are important. I argue that rural communes provide unique settings to explore both social and environmental aspects of place. Based on qualitative interview data with members of two communes, I address emotional connection to the land, changing social relationships over time, and the interplay of physical and social aspects of place. Results demonstrate how the connections to land and social ties are both prevalent. However, social interaction has decreased while commitment to sharing and protecting the physical environment has endured.     

COMPRESSION OF nth-ORDER DATA ARRAYS BY B-SPLINES.PART 1:THEORY

For efficient handling of very large data arrays,pretreatment by compression is mandatory.In the presentpaper B-spline methods are described as good candidates for such data array compression.Themathematical relation between the maximum entropy method for compression of data tables andthe B-spline of zeroth degree is described together with the generalization of B-spline compression tonth-order data array tables in matrix and tensor algebra.     

中国高分辨率温度和降水模拟数据的验证

PRISM模型是一种基于地理特征和回归统计方法生成气候图的模型。基于中国及其周边国家地区2450多个气象台站观测数据,以PRISM模型模拟生成了中国2.5′×2.5′(≈4～5km)逐月温度和降水数据。利用独立于模拟数据的中国生态系统研究网络18个野外观测站的长年气候观测数据,检验了PRISM模型的模拟结果,表明PRISM模型较好地模拟了我国温度和降水的空间分布及季节变化,除了在高山和亚热带地区由于地表覆盖和局部地形的差异影响模拟结果,其模拟值与实测值之间的趋势线同1∶1线基本一致,具有显著相关关系,其中降水效果略差     

Co-Phase Analysis of Atmospheric Wave Data

Summary Co-phase is a statistic designed for the detection and parameter estimation of signals by detector arrays. Ionospheric motions detected by an array of four phase-path sounders following a large earthquake are found by the co-phase technique to have a phase velocity equal to that of seismic Rayleigh waves of the same period, and to arrive from the direction of the epicentre. The calculation of co-phase for an 80-min sample of data from an 8-element array of microbarographs detects the presence of a signal from a high energy event despite a signal-to-noise ratio of less than unity. Co-phase analysis of acoustic signals generated by the Saturn-Apollo rocket launches indicates that these signals originate at ionospheric heights and propagate in a waveguide between a soundspeed maximum and a steep density gradient in the mesosphere.     

基于空间可达性分析的客家民系迁移路径模拟

以人地关系为视角,引入空间可达性的概念,探讨赣闽粤交界地区客家先民迁移路线的选择与所处的自然环境和社会历史背景之间的关系。利用GIS技术建立地形和古交通通道数据库,分别构建栅格与矢量数据结构最优路径模型,分析了客家民系迁移路径选择与空间可达性的关系。结果表明:可达性分析结果与客家民系的空间分布拟合的较好,受迁移时期的生产力水平限制,高大山脉、隘口等地形因素对迁移路线影响巨大,自然、社会、历史因素共同影响客家民系迁移及分布格局,赣州、长汀、梅州等"客家首府"城市位于所模拟的最优迁移路径上。     

Namaqualand—A brief overview of the physical and floristic environment

This paper provides a brief introduction to the physical environment of Namaqualand as well as an overview of patterns of plant diversity. The diverse array of parent material and geological processes that have shaped the region since the break up of Gondwanaland have created a complex, and sometimes dynamic physical environment, that is partly responsible for the patterns and processes observed in the biota today. The contemporary climate is characterised by relatively reliable, albeit low (50–250 mm pa), winter rainfall (>60% winter precipitation) arriving between May and September. East of the central mountains, tropical thunderstorms penetrate the region in late summer (February–April). The presence of the cold Atlantic Ocean in the west not only moderates temperatures throughout Namaqualand (mean max summer temperature <30 °C), but also provides alternative sources of moisture in the form of coastal fog and heavy dew experienced in winter months. Recent analyses show that the flora of the Succulent Karoo is part of the Cape Floral Kingdom, now termed the Greater Cape Floral Kingdom. It is one of only two desert regions recognised as a global biodiversity hot-spot and contains an estimated 6356 plant species in 168 families and 1002 genera. Namaqualand, which comprises about one quarter of the area of the Succulent Karoo, contains about 3500 species in 135 families and 724 genera, with about 25% of this flora endemic to Namaqualand. This remarkable diversity, however, is not distributed evenly throughout the region, but is concentrated in many local centres of endemism usually associated either with quartzite mountain complexes or lag-gravel plains (quartz-patches). A major exception to the general pattern of centres of diversity is the true Fynbos vegetation of the highest Kamiesberg peaks where rainfall exceeds 400 mm pa. Suggested determinants of the region's exceptional floral diversity include the complex physical environment, a unique past and present climate and the region's diverse fauna, most notably insects. The challenge for the current inhabitants and scientists working in the region is to develop a better understanding of this ecosystem so that they will be equipped to deal with the challenges posed by the demands for land and the prospect of global climate change.     

河相关系研究的各种方法及其间关系

河相关系的研究旨在寻求河床地貌形态与流域因子的定量关系。除了传统的水文统计方法外,已有多种理论被用来对这一问题进行探索,这些研究方法相互之间都存在一定的关系,发现和认识这些关系将对河相关系的研究产生深刻的影响。本文在这方面作了探讨。     

新疆全要素生产率估算及其经济增长源泉分析

为深入探究新疆经济增长的驱动因素,基于1990-2015年新疆统计数据,运用索洛残差法对新疆的全要素生产率进行了估算,并对估算结果与影响新疆全要素生产率变动的技术进步因素和制度变迁因素进行了计量分析。研究表明：（1）新疆经济增长主要依赖资本和劳动力等要素投入驱动,是一种典型的要素投入型经济增长方式。（2）新疆全要素生产率变化具有很强的累积性和路径依赖性,其中技术转移和转化是新疆全要素生产率变化的主要原因,而制度进步和自主研发对新疆全要素生产率变化的影响不明显。（3）新疆制度发育尚不完全,阻碍生产要素优化配置的因素很多。（4）新疆的R&D经费投入偏低,尚未形成规模效应,未能显著地促进新疆全要素生产率的提高。基于本文的研究结论给出相应的政策启示。     

The role of urban surface characteristics on the extent of gullying in Auchi, Bendel State, Nigeria

Through the use of rigorous analytical procedures, the spatial characteristics of gullies in Auchi were shown to vary in three principal ways. They vary over space in terms of (a) gully size, (b) degree of dissection and (c) their linear pattern. Significantly, ground cover and terrain characteristics (i.e. urban surface or anthropogenic factors) alone are inadequate in explaining the extent of gullying in Auchi. A combination of both the anthropogenic factors and physical factors (such as soil material resistance factor) greatly improved the prediction of the dimensions and extent of gullying. In environments where material resistance is limiting, the process of accelerated erosion cannot be explained by human-related factors alone, even in areas where the critical population carrying capacity is very low.     

ADVANCES IN SECOND-ORDER CALIBRATION

Several multivariate methods are now available for the calibration of second-order or hyphenatedinstruments(e.g.GC/MS).When applied to bilinear data,it has been shown that calibration can beperformed in the presence of unknown interferences-a significant advantage over first-order calibration.In this paper,non-bilinear rank annihilation(NBRA),a method which has the potential of handling,second-order non-bi-linear data,is studied through theoretical analysis and computer simulation.It isfound that the second-order advantage can be carried over to non-bilinear data if a property defined asnet analyte rank(NAR)holds for the analyte of interest.The net analyte signal(NAS)is definedaccordingly for second-order calibration and the analogy to and difference from lower-order calibrationare discussed.With NAS,some analytical figures of merit such as signal-to noise ratio,selectivity,sensitivity and limit of determination can be calculated for second order calibration.An application toMS/MS data is also given.     

SHORT COMMUNICATION COMMENTS ON THE RESIDUAL BILINEARIZATION METHOD

Through theoretical analysis and computer simulation,this short communication comments on theresidual bilinearization(RBL)method and compares it with non-bilinear rank annihilation(NBRA)forthe treatment of second-order calibration with non-bilinear data.It is found that these two methods aremathematically equivalent but have different noise propagation properties.The second-order advantage,namely quantitation in the presence of unknown interferences,can be carried over to non-bilinear dataonly if there exists a net analyte rank(NAR)for the analyte of interest.     

THREE-WAY METHODS FOR THE CALIBRATION OF CHROMATOGRAPHIC SYSTEMS:COMPARING PARAFAC AND THREE-WAY PLS

For the calibration of chromatographic systems,different methods can be used.One class of methodsutilizes three-way approaches.The calibration problem is stated in such a way that the decompositionof a three-way array can serve for the prediction of retention on new stationary phases.Two three-way approaches are presented:the Unfold-PCA and PARAFAC models.The theory ofboth methods is presented and the differences are highlighted,the main difference being that PARAFACis a trilinear decomposition whereas Unfold-PCA is not.Both three-way methods are evaluated on asmall data set consisting of retention measurements of eight solutes at six mobile phase compositions onsix stationary phases.The differences in performance of the two models are minor,For calibration purposes,two variants of the methods are discussed:three-way PLS and an extensionof PARAFAC.Again the theory and differences between the two methods are explained.The predictiveperformance of the two methods is compared using the same data set as earlier.The differences inpredictive performance,however,are minor.Both methods are capable of predicting 98% of thevariation in the test sets.Yet,there are other considerations when comparing methods than predictiveperformance,e.g.the quality of the predictions.