SIMPLE VALIDATORY TOOLS FOR JUDGING THE PREDICTIVE PERFORMANCE OF PARAFAC AND THREE-WAY PLS

The methods PARAFAC and three-way PLS are compared with respect to their ability to predictreversed-phase retention values.Special attention is paid to simple validatory tools,the meaning and useof which are explained.The simple validatory tools consist of percentages of explained variation in the training set and thosethat can be calculated with the use of markers.These markers are special(reference)solutes,the retentionvalues of which are used to gain information about a new object for which predictions are wanted.Different validatory tools can be calculated with the use of these marker retention values:percentagesof used variation and mean sum of squared residuals after applying the model to these marker retentionvalues.The validatory tools are evaluated on their power to estimate their test set counterparts:thepercentages of explained variation in the test set and mean sum of squared prediction errors in the test set.Two different data sets from reversed-phase chromatography are used to evaluate the validatory tools.The first data set has a high signal-to-noise ratio and is measured under the same measurementconditions.The second data set has a low signal-to-noise ratio and is measured under differentmeasurement conditions.Some of the simple validatory tools seem to have relevance to their test setcounterparts,even in the case of the second data set.     

ESTIMATION OF PREDICTION ERROR FOR SAMPLES WITHIN THE CALIBRATION RANGE

A modification of a technique proposed by Lorber and Kowalski for the estimation of prediction errorsis presented.The method is applied to five data sets.The results show that for some data sets theestimated prediction errors are close to the actual prediction errors for samples within the calibrationrange,while samples outside the calibration range must be background corrected before quantificationof the prediction error.     

USE OF THE KALMAN FILTER FOR MULTIVARIATE CALIBRATION IN A REAL SYSTEM AND ITS COMPARISON WITH CLS AND PURE COMPONENT CALIBRATION METHODS

The usefulness of the Kalman filter as an algorithm for calibration in a real system is shown. Results arecompared with classical least squares and pure component calibration. The prediction of four prioritypollutant chlorophenols in binary, ternary and quaternary mixtures was also carried out by Kalmanfiltering. The condition number, standard deviation and prediction error have been employed to choosethe most suitable wavelength range. Comparison of the standard error of prediction in the validation setshows significant differences between the evaluated chlorophenols, the best results being obtained withKalman multivariate calibration.     

THE CONSTRUCTION OF SIMULTANEOUS OPTIMAL EXPERIMENTAL DESIGNS FOR SEVERAL POLYNOMIALS IN THE CALIBRATION OF ANALYTICAL METHODS

In this paper a criterion is described for the construction of experimental designs for the evaluation ofcalibration models in analytical chemistry.The proposed criterion seeks a compromise between theD-optimal designs for estimating the parameters of different polynomial models.A computer algorithmis presented for a sequential construction of experimental designs using the optimality criterion.Theperformance of the optimality criterion and the computer algorithm is elaborated for the problem ofdiscrimination between a first-to a third-degree polynomial for the calibration of analytical methods.Anexperimental design consisting of replicate measurements at five distinct levels equally spaced over thecalibration range proved a good solution.     

BODY DIAGONALIZATION OF CORE MATRICES IN THREE-WAY PRINCIPAL COMPONENTS ANALYSIS:THEORETICAL BOUNDS AND SIMULATION

In contrast with conventional PCA,a direct superposition and joint interpretation of loading plots is notpossible in three-way PCA,since there may be data variance which is described by unequal componentsof different modes.The contributions to variance of all possible combinations of components aredescribed in the core matrix.Body diagonalization,which is achieved by appropriate rotation ofcomponent matrices,is an essential tool for simplifying the core matrix structure.The maximum degreeof body diagonality which may be obtained from such transformations is analysed from both themathematical and simulation viewpoints.It is shown that,at least in the average case,high degrees canbe expected,which makes the procedure reasonable for many practical applications.Furthermore,simulation as well as theoretical derivation show that the success of body diagonality depends on the so-called polarity of the core array.The methodology is illustrated by a three-way data example fromenvironmental chemistry.     

城镇体系等级结构的分形维数及其测算方法*

文章探讨了城镇体系等级结构的分形研究方法。首先,讨论了区域城镇规模分布的Zipf模型,并通过分形退化分析将其应用范围加以拓广,从而与非分形研究接口;第二,引进了分形结构因子,以此开创了城镇体系等级结构的FSF分析;第三,提出了表征城镇体系等级差异的差异度概念和度量方法。文章给出实例说明了各种方法的应用,并比较了三种方法的异同。     

THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS

By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression.     

SHORT COMMUNICATION A PROGRAM FOR THE SIMULTANEOUS POTENTIOMETRIC DETERMINATION OF PROTONATION CONSTANTS AND ELECTRODE CALIBRATION PARAMETERS

A program for the potentiometric determination of the protonation constants of mononuclear polyproticsubstances is described.A maximum of twelve parameters can be determined simultaneously,includingup to six protonation constants,four electrode calibration parameters,the protolysis constant of thesolvent and the titrant concentration.Optimization is carried out by using the non-simplifiedNewton-Raphson method,which is potentiated by the Marquardt algorithm and a distance speeding-upcoefficient.A direct search method is also used to improve the initial set of values.Variances arecalculated very accurately,since the real Hessian function is used.Statistical weights and ionic strengthcorrections are also considered,The program has been tested by using simulated titration curves ofpolyprotic acids with close constants.     

STATE POLICY AND URBAN SYSTEMS :THE CASE OF CHINA

Ｃｉｔｙｓｉｚｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｎａｔｉｏｎａｌｕｒｂａｎｓｙｓｔｅｍｓｈａｓａｔｔｒａｃｔｅｄｃｏｎｓｉｄｅｒａｂｌｅｒｅｓｅａｒｃｈｉｎｔｅｒｅｓｔ.Ｔｈｅｉｓｓｕｅｉｓａｌｓｏｃｒｉｔｉｃａｌｔｏｇｏｖｅｒｎｍｅｎｔｐｏｌｉｃｙａｓｉｔｉｓａｓｓｏｃｉａｔｅｄｗｉｔｈｐｏｐｕｌａｔｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎ,ｕｎｅｖｅｎｄｅｖｅｌｏｐｍｅｎｔ,ａｎｄｇｅｏｐｏｌｉｔｉｃｓ.Ｐｒｅｖｉｏｕｓｒｅｓｅａｒｃｈｅｆｆｏｒｔｈａｓｇｒｅａｔｌｙｅｎｈａｎｃｅｄｏｕｒｕｎｄｅｒｓｔａｎｄ…     

STANDARD ERRORS IN THE EIGENVALUES OF A CROSS-PRODUCT MATRIX:THEORY AND APPLICATIONS

New expressions are derived for the standard errors in the eigenvalues of a cross-product matrix by themethod of error propagation.Cross-product matrices frequently arise in multivariate data analysis,especially in principal component analysis (PCA).The derived standard errors account for the variabilityin the data as a result of measurement noise and are therefore essentially different from the standarderrors developed in multivariate statistics.Those standard errors were derived in order to account for thefinite number of observations on a fixed number of variables,the so-called sampling error.They can beused for making inferences about the population eigenvalues.Making inferences about the populationeigenvalues is often not the purposes of PCA in physical sciences,This is particularly true if themeasurements are performed on an analytical instrument that produces two-dimensional arrays for onechemical sample:the rows and columns of such a data matrix cannot be identified with observations onvariables at all.However,PCA can still be used as a general data reduction technique,but now the effectof measurement noise on the standard errors in the eigenvalues has to be considered.The consequencesfor significance testing of the eigenvalues as well as the usefulness for error estimates for scores andloadings of PCA,multiple linear regression (MLR) and the generalized rank annihilation method(GRAM) are discussed.The adequacy of the derived expressions is tested by Monte Carlo simulations.     

GEOGRAPHIC CATEGORIES OF SETTLEMENT AND THE 2000 CENSUS: A CHALLENGE FOR GEOGRAPHERS

Through a close examination of the case of Virginia v. Hicks—from Kevin Hicks's arrests for trespassing on streets near a Richmond, Virginia, public housing project in 1998 and 1999 to the unanimous Supreme Court decision upholding these arrests on the grounds that no harm was done to the First Amendment—this paper explores how the rights of private property are made, through the judicial process, to "trump" other kinds of rights and interests. It examines the implications of both dominant property practices and discourses and a more general judicial anti-urbanism for city life. The paper shows that one of the things at risk given the judiciary's love affair with private property rights is the right of some people simply to be present in public space. By implication, the paper argues that legal geographies need to examine more than just final court decisions (as is often the case), but also uncover the full legal history—the strange twists and turns—of the cases examined.     

RECONNAISSANCE SURVEYS OF CONTEMPORARY PERMAFROST ENVIRONMENTS IN CENTRAL ICELAND USING GEOELECTRICAL METHODS: IMPLICATIONS FOR PERMAFROST DEGRADATION AND SEDIMENT FLUXES

Four different sites in the highlands of central Iceland have been investigated for permafrost occurrence using two‐dimensional resistivity imaging. The results of the surveys indicate the presence of shallow permafrost of low to medium resistivity. The distribution pattern is spatially heterogeneous which is consistent with permafrost at the fringe of seasonal frost. These sites are likely to react rapidly to changes of the environmental boundary conditions, therefore future research should include monitoring for detecting the early impact of climate change on permafrost degradation. The extent to which periglacial morphodynamics and sediment fluxes are influenced by permafrost and/or seasonal frost and potential permafrost degradation is hard to determine. Hence, long‐term monitoring approaches for both permafrost and sediment dynamics are essential.     

PRINCIPLES FOR THE LOCATION OF SYNAGOGUES: SYMBOLISM AND FUNCTIONALISM IN A SPATIAL CONTEXT

Two traditional Jewish approaches to the location of synagogues can be found, one symbolic and one functional. The locational requirements are not identical; the symbolic approach deals with idealistic spatial status while the functional approach poses realistic locational demands. This spatio-locational conflict reflects a problematic situation on both theoretical and practical levels.     

PRINCIPLES FOR THE LOCATION OF SYNAGOGUES: SYMBOLISM AND FUNCTIONALISM IN A SPATIAL CONTEXT

Two traditional Jewish approaches to the location of synagogues can be found, one symbolic and one functional. The locational requirements are not identical; the symbolic approach deals with idealistic spatial status while the functional approach poses realistic locational demands. This spatio-locational conflict reflects a problematic situation on both theoretical and practical levels.     

EDAPHIC LIMITATION OF A BRAZILIAN RAINFOREST PALM: THE ROLE OF ENERGY ALLOCATION AND COMPETITION FOR SUNLIGHT

Tropical forest palms are often associated with specific soil conditions, yet the ecological role of edaphic limitation in Palmae has seldom been considered. In the Atlantic Coastal Forest Biome of eastern Bahia, Brazil, the piassava palm (Attalea funifera) inhabits coastal podzolic soils but not nearby latosols. This paper examines the role of changing edaphic conditions and access to sunlight in the restriction of this species to tropical podzols.     

南极陨石研究的启示Ι:早期太阳星云连续化学分馏作用的岩石化学证据

球粒陨石金属相的 Ir、Os、Co等亲铁元素的浓度随氧化程度的升高而显著增大 ,其浓度以及铁纹石 Co含量和橄榄石 Fa值均反映了球粒陨石的氧化 -还原程度具有连续变化的特征。根据铁纹石 Co含量、橄榄石 Fa值、低 Ca辉石 Fs值、金属相的 Ir、Os、Co浓度以及其他球粒陨石分类参数 ,可能存在介于 E与 H、H与 L、L与 L L以及 L L与 C之间的球粒陨石过渡型 ,即E/H、H/L、L/L L和 LL/C化学群 ,从而将原有的 9个球粒陨石化学群增加到 1 3个。球粒陨石氧化 -还原程度的变化特征以及球粒陨石过渡型的发现都表明早期太阳星云的化学分馏作用具有连续变化的特点。