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.     

AN IMPROVED ALGORITHM FOR THE GENERALIZED RANK ANNIHILATION METHOD

An improved algorithm for the generalized rank annihilation method(GRAM)is presented.GRAM isa method for multicomponent calibration using two-dimensional instruments,such as GC-MS.In thispaper an orthonormal base is first computed and used to project the calibration and unknown sampleresponse matrices into a lower-dimensional subspace.The resulting generalized eigenproblem is thensolved using the QZ algorithm.The result of these improvements is that GRAM is computationally morestable,particularly in the case where the calibration sample contains chemical constituents not present inthe unknown sample and the unknown contains constituents not present in the calibration(the mostgeneral case).     

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.     

广东省耕地粮食综合生产能力研究

农用地分等成果(主要为利用等)与实际粮食产量在空间分布上具有良好的相关性。通过收集广东省耕地利用等指数、粮食综合生产能力等数据并进行大样本统计分析,构建粮食综合生产能力测算模型;对模型进行可信度、方差及回归分析,得出广东省和7个省级二级区的耕地粮食综合生产能力。检验表明,耕地粮食综合生产能力测算结果较为合理,为其他省(市、区)利用农用地分等成果测算耕地粮食综合生产能力,制定区域土地利用总体规划、农业结构调整以及协调区域内城镇化、工业化建设与耕地保护之间的矛盾提供了科学依据。     

水文气象序列趋势分析与变异诊断的方法及其对比

日趋频繁的极端天气和水文事件对经济发展和人类生命安全构成重大危害,水文气象序列的趋势变化分析与预测研究是避免和控制这些破坏性全球环境变化的前提,也是目前亟待解决的科学问题之一。基于现代数学和统计学理论,气象学和水文学研究人员对水文气象要素趋势检验和突变点识别的方法做了大量的研究。针对当今普遍采用的参数统计、非参数秩检验和小波分析方法及其本质原理,在分类阐述的基础上,系统归纳总结了各个方法在应用过程中存在的问题及解决方案,并以黑河流域托勒气象站年平均气温为实例对比分析各方法计算结果的差异性,凝练出水文气象序列趋势分析与变异诊断的理论与方法系统体系,为今后理论方法的进一步改进及应用发展提供参考。     

TENSORIAL RESOLUTION:A DIRECT TRILINEAR DECOMPOSITION

Modern instrumentation in chemistry routinely generates two-dimensional(second-order)arrays of data.Considering that most analyses need to compare several samples,the analyst ends up with a three-dimensional(third-order)array which is difficult to visualize or interpret with the conventional statisticaltools.Some of these data arrays follow the so-called trilinear model,(?)These trilinear arrays of data are known to have unique factor analysis decompositions which correspondto the true physical factors that form the data,i.e.given the array (?),a unique solution can be found inmany cases for each order X,Y and Z.This is in contrast to the well-known second-order bilinear datafactor analysis,where the abstract solutions obtained are not unique and at best cannot be easilycompared with the underlying physical factors owing to a rotational ambiguity.Trilinear decompositions have had the disadvantage,however,that a non-linear optimization withmany parameters is necessary to reach a least-squares solution.This paper will introduce a method forreducing the problem to a rectangular generalized eigenvalue-eigenvector equation where the eigenbectorsare the contravariant form(pseudo-inverse)of the actual factors.It is shown that the method works wellwhen the factors are linearly independent in at least two orders(e.g.X_(jr),and Y_(jr) are full rank matrices).Finally,it is shown how trilinear decompositions relate to multicomponent calibration,curve resolutionand chemical analysis.     

行政区划调整对政区位势的影响与定量化测度

行政区划是国家治理和社会发展的重要支撑,行政区划调整是促进区域协调发展的重要手段。在全球化与区域化背景下,适时推进行政区划调整是重构区域发展格局,改变区域政区位势的基本途径。本文立足于区域协调发展的视角,构建基于区域相互作用理论、空间场能模型和幂指数函数的政区位势模型,以合肥—芜湖地区为例,测算2011年原巢湖地级市拆分后其政区位势的变化情况以及对区域协调发展的影响效能。研究表明:① 政区位势与政区的行政管辖能力、行政资源和区域协调发展潜力密切相关。② 2005—2015年期间研究区整体政区位势和协调发展潜力增幅分别由地级巢湖市撤销前的61.79%和0.21%提高到116.51%和3.05%;且行政区划调整后政区位势增速明显快于经济发展与人口增速。③ 运用政区位势模型能对行政区划调整进行测度和空间化表达,其测度结果既能与社会发展等复杂影响相区别,又能与真实的社会经济发展状况相符合,既重视个体发展又兼顾区域协调发展。行政区划调整能显著提高研究区的政区位势,促进社会经济进步,且有利于破除空间障碍和行政壁垒,推进区域协调可持续发展。     

土地利用分区与主体功能分区协调探讨——以县级为例

阐述主体功能分区与土地利用分区的内涵,深刻分析两者协调的缘起及基础,以县级土地利用分区为例,引用"优势度"概念及模型,对问卷调查方式获取的数据进行定量分析,主要研究结果表明不同土地利用分区的优势度差距很大,调查对象和地域差异对调查结果影响很大。针对分析结果,从法律、理念、技术、公众参与等方面提出协调两者的基本策略,以此为新一轮土地利用总体规划修编划分土地利用区工作及其与主体功能分区协调提供一定参考。     

整合等级与顺序的黄土高原小流域沟道结构理论研究

沟道等级结构与顺序结构都可看作是沟道拓扑结构,在黄土高原小流域坝系规划研究中,往往需要将Horton-Strahler的沟道分级模型与较长沟道优先的顺序编码模型进行整合。该文提出一个沟道结构假说,即在黄土高原小流域尺度上,存在一个最小集水面积与最短沟道长度的适宜取值区间,使得基于DEM提取的沟道网络上任意节点对应的较长沟道作为主沟道,其Horton-Strahler沟道等级不低于汇入支流。搜集的黄土高原丘陵沟壑区多个副区的一些典型小流域数据有效验证了上述假说,从而为实现整合等级结构与顺序结构的沟道编码模型的进一步研究提供理论基础。     

Similarities and differences of city-size distributions in three main urban agglomerations of China from 1992 to 2015: A comparative study based on nighttime light data

Comparing the city-size distribution at the urban agglomeration (UA) scale is important for understanding the processes of urban development. However, comparative studies of city-size distribution among China’s three largest UAs, the Beijing-Tianjin-Hebei agglomeration (BTHA), the Yangtze River Delta agglomeration (YRDA), and the Pearl River Delta agglomeration (PRDA), remain inadequate due to the limitation of data availability. Therefore, using urban data derived from time-series nighttime light data, the common characteristics and distinctive features of city-size distribution among the three UAs from 1992 to 2015 were compared by the Pareto regression and the rank clock method. We identified two common features. First, the city-size distribution became more even. The Pareto exponents increased by 0.17, 0.12, and 0.01 in the YRDA, BTHA, and PRDA, respectively. Second, the average ranks of small cities ascended, being 0.55, 0.08 and 0.04 in the three UAs, respectively. However, the average ranks of large and medium cities in the three UAs experienced different trajectories, which are closely related to the similarities and differences in the driving forces for the development of UAs. Place-based measures are encouraged to promote a coordinated development among cities of differing sizes in the three UAs.     

城市体系规模结构研究的新方法——位序累积规模模型

利用位序累积规模模型与位序-规模法则定量分析2000~2014年中国城市体系规模结构的省际差异及其变化特征。结论如下：使用位序-规模法则进行区域城市体系规模结构对比与演变分析时会存在较大的不确定性,而位序累积规模模型更能准确刻画区域城市体系规模结构的特征;中国各省区\begin{array}{c}\beta \end{array}值排名靠前的多属于自然地理条件优越、社会经济比较发达的地区,其变化大致表现出增幅东大西小、增长率南高北低的特征;位序累积规模模型能较准确地反映出自然与社会经济条件对区域城市体系规模结构的影响,但随着社会经济的发展,自然地理和基础设施条件对城市体系规模分布的影响不再显著。     

RESOLUTION OF MULTICOMPONENT FLUORESCENT MIXTURES BY ANALYSIS OF THE EXCITATION-EMISSION-FREQUENCY ARRAY

Fluorescence lifetime provides a third independent dimension of information for the resolution of totalluminescence spectra of multicomponent mixtures.The incorporation of this parameter into theexcitation-emission matrix(EEM)by the phase modulation technique results in a three-dimensionalexcitation-emission-frequency array (EEFA).Multicomponent analysis based on the three-dimensionalEEFA brings a qualitative change for the resolved spectra,i.e.individual spectra can be uniquely resolved,which is impossible with any two-dimensional analysis.In this paper we present a method for analyzingthe EEFA.We show mathematically that with the three-dimensional analysis of the EEFA individualspectra and lifetimes can be obtained.Our algorithm is developed in mathematical detail and isdemonstrated by its application to a two-component mixture.     

中原城市群城市规模等级的时空演变分析

综合运用分形、马尔科夫转移矩阵、等级钟和空间自相关等方法对中原城市群城市规模等级的时空演变进行了分析,得出结论:①城市规模等级分布趋于"扁平化",首位城市郑州的垄断性较弱;城市在不同规模类型间的转移过程中,小城市向中等城市的转移概率低,中等城市向大城市的转移概率高,中等规模城市数量增长缓慢;城市个体位序的变化相对较小,城市规模发展具有较强的路径依赖和连续性;②城市规模分布依然以省辖市为基础,在省辖市与周围县市的空间互动上,开封和平顶山对周围县市有显著的极化作用,郑州和新乡对周围县市产生了极化作用但不显著,其余省辖市与周围县市未形成紧密的空间互动关系.     

中国城市交通运输发展水平等级差异变动特征

选取中国183 个城市的1991 年、1995 年、1999 年和2003 年4 个时间段的统计数据, 在Arcmap 软件中采用自然断裂法进行等级划分, 将城市交通运输总体发展水平的等级划分为5 级, 利用SPSS 统计分析软件进行分析, 得到1991-2003 年中国城市交通运输发展水平等级差异变动特征: 中国城市交通运输发展水平等级呈现明显的“纺锤形”结构, 交通运输发展水平明显高于平均发展水平的城市个数和明显低于平均发展水平的城市个数所占比例低于32%, 68%以上的城市其交通运输发展水平接近全国平均水平; 发展水平较高的城市在以省区为单位的空间分布上呈现集中-分散-分散-集中的特征, 而等级较低的城市在空间上呈现分散无规则分布格局; 中国城市交通运输发展水平的等级差异呈现“U” 形变化, 1991- 1995 年差距逐渐缩小, 1995-1999 年差距逐渐增大, 1999-2003 年差距逐渐缩小, 但各时间段内的变动幅度不大; 城市交通运输发展水平上升的城市在空间分布上集中于河南、山东、江苏等省, 城市交通运输发展水平下降的城市集中于黑龙江、吉林、陕西、湖北和湖南等省。     

黑河流域莺落峡站河道内生态需水研究

生态需水是当前水问题研究中的一个热点问题, 对于生态环境急剧恶化的内陆干旱区来说, 这一研究尤为紧迫。气候变化及人类活动导致水文变异, 进而改变了当地生态系统的水文及生态平衡状况。文章采用黑河流域莺落峡站1947-2006 年月径流序列资料, 运用差积曲线-秩检验联合法来识别水文过程变异点并分析变异成因, 然后对各月平均流量序列用线性矩法推求GEV分布参数, 求出概率密度最大流量, 将其视为相应月河道内生态流量, 可以得到黑河莺落峡站河道内生态需水情况。结果表明, 基于水文变异情况分析河道内生态需水的计算方法在黑河上游是可行的;水文变异前后, 站点满足生态需水频率会发生显著变化, 因气候原因而导致的径流量变化是很难避免的, 科学合理计算生态需水对干旱区河流生态管理和经济社会可持续发展有重要作用和意义。     

江苏中部海岸潮沟的形态变化特征

作为一种典型的潮滩地貌单元,潮沟(tidal creeks) 在江苏中部海岸潮间带广泛发育,并表现出复杂的摆动性。本文根据1981-2010 年遥感影像和野外观测数据,对该区潮沟的平面形态变化进行了分析。结果显示,江苏中部海岸潮沟(根据其长度差异) 一般分为4 级,1~3 级潮沟的个数分别为21、97 和688 (1:5:33),其平均长度分别为7587±1544 m、1921±916 m和327±200 m;潮沟在中潮带比较发育,其密度和分汊率明显大于高潮带和低潮带;主潮沟曲率从高潮带向低潮带呈减小趋势;外来引种互花米草扩展和大规模滩涂围垦活动对潮沟产生了较大影响,其中后者明显地抑制了潮沟的发育。研究区潮沟的摆动性具有明显的区域和级别差异。与研究区北部的潮滩区域相比,海岸潮差较大的南部潮滩区潮沟的摆动性较大;同一个潮沟系统其1 级潮沟的摆动性>2 级潮沟>3 级潮沟;同一条潮沟其下段的摆动性>中段>上段;同一区段弯曲岸段的摆动性>顺直岸段;1 级潮沟上段、2 级潮沟中上段、3 级潮沟或位于盐沼内的潮沟其摆动性不明显。     

SHIFTS IN THE WHOLESALE TRADE STATUS OF U.S. METROPOLITAN AREAS*

Considerable instability exists among large U.S. metropolitan areas in their status as wholesale trade centers. Differences in wholesale trade growth rates, changes in national shares, and shifts in rank position reflect not only population growth patterns, but also structural changes in the national economy. In the latter instance, the wholesale product mix of SMSAs is an important factor in explaining their differential fortunes within the wholesaling hierarchy.     

Multiple Point Metrics to Assess Categorical Variable Models

Geostatistical models should be checked to ensure consistency with conditioning data and statistical inputs. These are minimum acceptance criteria. Often the first and second-order statistics such as the histogram and variogram of simulated geological realizations are compared to the input parameters to check the reasonableness of the simulation implementation. Assessing the reproduction of statistics beyond second-order is often not considered because the “correct” higher order statistics are rarely known. With multiple point simulation (MPS) geostatistical methods, practitioners are now explicitly modeling higher-order statistics taken from a training image (TI). This article explores methods for extending minimum acceptance criteria to multiple point statistical comparisons between geostatistical realizations made with MPS algorithms and the associated TI. The intent is to assess how well the geostatistical models have reproduced the input statistics of the TI; akin to assessing the histogram and variogram reproduction in traditional semivariogram-based geostatistics. A number of metrics are presented to compare the input multiple point statistics of the TI with the statistics of the geostatistical realizations. These metrics are (1) first and second-order statistics, (2) trends, (3) the multiscale histogram, (4) the multiple point density function, and (5) the missing bins in the multiple point density function. A case study using MPS realizations is presented to demonstrate the proposed metrics; however, the metrics are not limited to specific MPS realizations. Comparisons could be made between any reference numerical analogue model and any simulated categorical variable model.     

RESIDUAL BILINEARIZATION.PART 1:THEORY AND ALGORITHMS

When using hyphenated methods in analytical chemistry,the data obtained for each sample are given asa matrix.When a regression equation is set up between an unknown sample (a matrix) and a calibrationset (a stack of matrices),the residual is a matrix R.The regression equation is usually solved by minimizing the sum of squares of R.If the sample containssome constituent not calibrated for,this approach is not valid.In this paper an algorithm is presentedwhich partitions R into one matrix of low rank corresponding to the unknown constituents,and onerandom noise matrix to which the least squares restrictions are applied.Properties and possibleapplications of the algorithm are also discussed.In Part 2 of this work an example from HPLC with diode array detection is presented and the resultsare compared with generalized rank annihilation factor analysis (GRAFA).     

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.