ThreeMode Abstracts, Part X
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INDEX
Xa  Xb 
Xc  Xd 
Xe  Xf 
Xg  Xh 
Xi  Xj 
Xk  Xl 
Xm  Xn 
Xo  Xp 
Xq  Xr 
Xs  Xt 
Xu  Xv 
Xw  Xx 
Xy  Xz 


Xia, A. L., Wu, H. L., Fang, D. M., Ding, Y. J., Hu, L. Q., & Yu, R. Q. (2005).
Alternating penalty trilinear decomposition algorithm for secondorder
calibration with application to interferencefree analysis of
excitationemission matrix fluorescence data.
Journal of Chemometrics, 19, 6576.
A new method, alternating penalty trilinear decomposition (APTLD), is
developed for the decomposition of threeway data arrays. By utilizing the
alternating least squares principle and alternating penalty constraints to
minimize three different alternating penalty errors simultaneously, the
intrinsic profiles are found. The APTLD algorithm can avoid the twofactor
degeneracy problem and relieve the slow convergence problem, which is
difficult to handle for the traditional parallel factor analysis (PARAFAC)
algorithm. It retains the secondorder advantage of quantification for
analytes of interest even in the presence of potentially unknown
interferents. In additions, it is insensitive to the estimated component
number, thus avoiding the difficulty of determining a correct component
number for the model, which is intrinsic in the PARAFAC algorithm. The
results of treating one simulated and one real excitationemission
spectral data set showed that the proposed algorithm performs well as long
as the model dimensionality chosen is not less than the actual number of
components. Furthermore, the performance of the APTLD algorithm sometimes
surpasses that of the PARAFAC algorithm in the prediction of concentration
profiles even if the component number chosen is the same as the actual
number of underlying factors in real samples.

Xia, A. L., Wu, H. L., Fang, D. M., Ding, Y. J., Hu, L. Q., & Yu, R. Q.
Determination of daunomycin in human plasma and urine by using an
interferencefree analysis of excitationemission matrix fluorescence
data with secondorder calibration.
Analytical Sciences, 22, 11891195.
Daunorubicin (DNR) is a significant antineoplastic antibiotic, which is
usually applied to a chemotherapy of acute lymphatic and myelogenous
leukaemia. Unfortunately, cardiotoxicity research in animals has
indicated that DNR is cardiotoxic. Therefore, it is important to
quantify DNR in biological fluids. A new algorithm, the alternating
fitting residue (AFR) method, and the traditional parallel factor
analysis (PARAFAC) have been utilized to directly determine DNR in
human plasma and urine. These methodologies fully exploit the
secondorder advantage of the employed threeway fluorescence data,
allowing the analyte concentrations to be quantified even in the
presence of unknown fluorescent interferents. Furthermore, in contrast
to PARAFAC, more satisfactory results were gained with AFR.

Xia,A. L., Wu, H. L., Li, S. F., Zhu, S. H., Zhang, Y., Han, Q. J., & Yu, R. Q. (2003).
Study of the interactions of berberine and daunorubicin with DNA using
alternating penalty trilinear decomposition algorithm combined with
excitationemission matrix fluorescence data.
Talanta, 73, 606612.
Studies of interactions between drugs and DNA are very interesting and
significant not only in understanding the mechanism of interaction, but
also for guiding the design of new drugs. However, until recently,
mechanisms of interactions between drug molecules and DNA were still
relatively little known. It is necessary to introduce more simple methods
to investigate the mechanism of interaction. In this study, the
interactions of daunorubicin (DNR) or berberine (BER) with DNA and the
competitive interactions of DNR and BER with DNA have been studied by
alternating penalty trilinear decomposition algorithm (APTLD) combined
with excitationemission matrix fluorescence data. The excitation and
emission spectra as well as the relative concentrations of coexisting
species in different reaction and equilibrium mixtures can be directly
and conveniently obtained by the APTLD treatment. The results obtained
are valuable for providing a deeper insight into the interaction
mechanism of DNR and BER with DNA. It is proved that the fluorescence
spectrum of complex DNRDNA is different from that of DNR. Furthermore,
the present method provides a new way to search for a new nontoxic,
highly efficient fluorescent probe. For controversial interaction
mechanism of the drugs and DNA, it can provide a helpful verification.

Xian, B., Li, T. H., Kai, C., Cao, T. C., Huang, J. R., & Qi, Y. P. (2004).
A novel preprocessing algorithm for threeway HPLC data.
Journal of Mathematical Chemistry, 36,129138.
Orthogonal signal correction (OSC) was a data preprocessing algorithm. It
ensured that the filtered information was irrelevant to concentration data while using it
to filter the noise from the original data. This paper extended the OSC application range
from twoway data to threeway data. Two drug data sets, Enoxacin, Norfloxacin,
Ciprofloxacin and Betamethasone, cortisone acetate, prednisone acetate, showed that the
application of the OSC algorithm to threeway HPLC data was feasible and needed further
research.

Xiao, Y. D., Wei, L. H., Wang, J. T., Zhang, J. B., Lin, S. F., & Zhou, Z. H. (1999).
Study of 3Dquantitative structureactivity relationship on a set of 1,2,4triazole compounds.
Chemometrics and Intelligent Laboratory Systems, 45, 277280.
In this article, 3Dquantitative structure–activity relationship on a set of 1,2,4triazole
compounds is studied. A set of 16 derivatives of triazole that have different biological activities to wheat
black rust as inhibitors are characterized by molecular mechanics. The analysis result by PLS agrees with the
study of 2DQSAR, and it offers useful 3dimensional information for designing high activity compounds.

Xie, H. P., Jiang, J. H., Chu, X., Cui, H., Wu, H. L., Shen, G. L. & Yu, R. Q. (2002).
Competitive interaction of the antitumor drug daunorubicin and the fluorescence
probe ethidium bromide with DNA as studied by resolving trilinear fluorescence data:
the use of PARAFAC and its modification Analytical and Bioanalytical Chemistry,
373, 159162.
The competitive interaction with DNA of daunorubicin (DR), being present in the
clinical antitumor drug daunoblastina, and the fluorescence probe ethidium bromide
(EB) has been studied by parallelfactor analysis (PARAFAC) and fullrank parallelfactor
analysis (FRAPARAFAC) of a fluorescence excitationemission threeway data array.
The PARAFAC algorithm can furnish stable resolution results for the data array studied,
if the estimated number of chemical components is consistent with the real number.
The FRAPARAFAC algorithm is not sensitive to the estimated number of components of
the fluorescence data array if the estimated number is not less than the real number.
Both algorithms gave identical resolution for the three components concerned DR,
EB, and the complex EBDNA. Variations of the equilibrium concentrations of free DR,
EB, and the complex EBDNA were resolved by both algorithms. Experimental observation
confirms the hypothesis that DR is an intercalator of DNA and that the binding
interactions of DR and EB with DNA are a pair of parallel competitive intercalation
reactions on same base sites of DNA. The method exemplified by this study provides a
useful approach for studying competitive interactions of different drugs with DNA
in the presence of interferents.

Xie, H. P., Jiang, J. H., Long, N., Shen, G. L., Wu, H. L.& Yu, R. Q. (2003).
Estimation of chemical rank of a threeway array using a twomode subspace comparison
approach. Chemometrics and Intelligent Laboratory Systems, 66, 101115.
When two matrices are formed by unfolding a threeway array along two fullrank
modes and when two subspaces with the same size are constructed by taking the first
principal component vectors of the same mode space in these two unfolded matrices,
the principal components corresponding to the chemical species should behave
identically in both subspaces, while the components corresponding to the noise
contribution should behave differently in these two subspaces. Based on the difference
of the behavior of the chemical signal and noise components, the twomode subspace
comparison (TMSC) approach has been proposed to estimate the chemical rank of a
threeway array with two fullrank modes. Two outstanding features of the proposed
method have been demonstrated. It is robust to a very high degree of collinearity
between the spectra or chromatograms involved, or to a very high level of noise
contained in a threeway array. The method has been shown to be useful for the treatment
of threeway analytical data sets obtained by highperformance liquid chromatographydiode
array detector (HPLC)DAD and excitationemission fluorescence spectroscopy.
(C) 2003 Elsevier Science B.V. All rights reserved.

Xie, H. P., Chu, X., Jiang, J. H., Cui, H., Shen, G. L. & Yu, R. Q. (2003).
Competitive interactions of adriamycin and ethidium bromide with DNA as studied
by full rank parallel factor analysis of fluorescence threeway array data
Spectrochimica acta part amolecular and biomolecular spectroscopy, 59, 743749.**
The competitive interactions of adriamycin (AMC) and a fluorescence probe of ethidium
bromide (EB) with DNA have been studied by full rank parallel factor analysis (FRAPARAFAC)
of fluorescence excitationemission threeway data array. The excitation and emission
spectra as well as the equilibrium concentrations of coexisting species in different
reaction mixtures can be directly obtained by the FRAPARAFAC treatment. The concordance
of the resolved excitation and emission spectra of AMC, EB and EBDNA with The standard
spectra of these species confirmed the reliability of the equilibrium concentrations
of these components in the reaction mixtures studied. The results obtained are valuable
for providing a deeper insight into the competitive interaction mechanism of AMC and
EB with DNA. The conclusion was directly given out that the interaction of AMC with
DNA is the intercalating model. The FRAPARAFAC method as exemplified by the present
study provides an useful approach for studying the interaction of clinical drugs with
DNA in the presence of disturbance of drug assistants. (C) 2002 Elsevier Science B.V.
All rights reserved.

Xie, Y.L., BaezaBaeza, J.J., & RamisRamos, G. (1995).
Kinetic spectrophotometric resolution of binary mixtures using threeway partial
least squares. Chemometrics and Intelligent Laboratory Systems, 27, 211220.
Threeway partial least squares (PLS) was applied to kineticspectrophotometric
data. The coupling reaction of diazotized sulfanilamide with o, m
and pamino benzoic acid (ABA), and with orciprenaline (ORC), to give azodyes
was monitored. Three binary mixtures of substrates, i.e., oABA/ORC,
mABA/pABA and o ABA/mABA, with different values of
the rate constant ratio and spectra which overlapped seriously were studied. The
spectra of the mixtures were scanned with a 2 nm resolution every 30 s during ca.
15 min. The data sets contained from 30 x 36 to 30 x 48 timewavelength data. Nine
mixtures of each binary combination of substrates were used for calibration, thus
the threeway calibration data sets contained from 9 x 30 x 36 to 9 x 30 x 48
concentrationtimewavelength data. The twoway PLS modelling was constructed on
the basis of single wavelength kinetic curves, and the threeway PLS modelling was
applied to series of threeway data arrays consisting of a number of selected wavelengths
each (up to the whole spectra). The results based on threeway data arrays were
better than that of ordinary PLS, particularly with mixtures having both a low rate
constant ratio and small spectral differences.

Xie, Y.L., BaezaBaeza, J.J., & RamisRamos, G. (1996a).
Secondorder tensorial calibration for kinetic spectrophotometric determination.
Chemometrics and Intelligent Laboratory Systems, 32, 215232.
Kineticdiode array spectrophotometric detection,
as well as other multichannel techniques when used
in nonequilibrium conditions, constitute
secondorder instrumentation. The secondorder
response provided will be bilinear, under certain
conditions even trilinear, thus allowing the use
of the generalized rank annihilation method (GRAM)
and the trilinear decomposition method (TLD). Both
numerically simulated and experimental data were
used to evaluate the performance of these
calibration techniques. The conditions in which
the 'secondorder advantage' (the possibility of
quantifying the analytes in the presence of
unknown reactions or interferences) is preserved
were investigated. The coupling reaction of
diazotized sulfanilamide with p, o and mamino
benzoic acid, and with orciprenaline, to give
azodyes was monitored. Binary mixtures of these
substrates with different values of the rate
constant ratio, and with various degrees of
spectral overlap, were resolved. The advantages
and limitations of higherorder data analysis
techniques such as GRAM and TLD for the treatment
of secondorder kinetic data are discussed.

Xie, Y.L., BaezaBaeza, J. J., & RamisRamos, G. (1996b).
A compariative study of several chemometric methods applied to the treatment of twoway kineticspectral
data for mixture resolution.
Analytica Chimica Acta, 321, 7595.
A comparative study was conducted to investigate the performance of several
chemometric methods applied to the treatment of twoway kineticspectral data with the aim of
resolving mixtures. The methods involved are nonlinear least squares regression performed using
the Powell algorithm, the linear and extended Kalman filter, and partial least squares regression.
Both simulated and experimental data were processed. The coupling reaction of diazotized
sulfanilamide with arylamines to give azodyes was monitored spectrophotometrically. Binary mixtures
of the substrates with different values of the rate constant ratio and with varied degrees of
spectral overlap were resolved. The effects of several influence factors have been studied using
numeric simulation. The advantages and the limitations of each method have been evaluated.

Xie, Y.L., Hopke, P.K., & Paatero, P. (1998).
Positive matrix factorization applied to a curve
resolution problem.
Journal of Chemometrics, 12, 357364.
Positive matrix factorization (PMF) is a least
squares approach to factor analysis which was
originally developed for environmental data
analysis and has been applied to several problems
in resolving sources of environmental pollutants.
PMF has been used as both a twoway and threeway
data analysis tool. In this investigation,
threeway data arrays were used to explore the
ability of PMF in curve resolution. Pulsed
gradient spin echo (PGSE) nuclear magnetic
resonance (NMR) data were measured for spectral
mixtures where the concentrations of the
compounds decay exponentially. Threeway data
arrays were constructed by packing different
parts of the data from single experiments and
were analyzed with threeway PMF to obtain the
NMR spectra, decay profiles and the
selfdiffusion coefficients of constituents.

Xie, Y.L., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, S.M.
(1999a).
Identification of source nature and seasonal
variations of Arctic aerosol by positive matrix
factorization.
Journal of the Atmospheric Sciences, 56,, 249260.
Weeklong samples of airborne particulate matter
were obtained at Alert, Northwest Territories,
Canada, between 1980 and 1991. The concentrations
of 24 particulate constituents have some strong,
persistent seasonal variations that depend on the
transport from their sources. In order to explore
the nature of the cyclical variation of the
different processes that give rise to the
measured concentrations, the observations were
arranged into both a twoway matrix and a
threeway data array. For the latter the three
modes consist of chemical constituents, weeks
within a year, and years. The twoway bilinear
model and a threeway trilinear model were used
to fit the data and a new data analysis
technique, positive matrix factorization (PMF),
has been used to obtain the solutions. PMF
utilizes the error estimates of the observations
to provide an optimal pointwise scaling data
array far weighting, which enables it to handle
missing data, a common occurrence in
environmental measurements. It can also apply
nonnegative constraints to the factors. Five
factors have been obtained that reproduce the
data quite well for both twoway and threeway
analyses. Each factor represents a probable
source with a compositional profile and
distinctive seasonal variations. Specifically,
there are (i) an acid photochemical factor
typified by Br^{}, H^{+}, and
SO_{4}^{2} and characterized
by a concentration maximum around April, or
shortly after polar sunrise; (ii) a soil factor
representing by Si, Al, and Ca and having its
main seasonal maximum in September and October;
(iii) an anthropogenic factor dominated by SO_{4}^{2}
together with metallic species like Pb, Zn, V,
As, Sb, Se, In, etc., peaking from December to
April; (iv) a sea salt factor consisting mainly
of Cl, Na, and K with maximum concentrations
during the period from October to April: And (v)
a biogenic factor characterized by
methanesulfonate and having a primary maximum at
May and a secondary maximum in August. The
results obtained by both twoway and threeway
PMF analyses are generally consistent with one
another. However, there are differences because
of additional constraints on the solution imposed
by the threeway analysis. The results also help
to confirm the hypotheses regarding the origins
of the Arctic aerosol.

Xie, YL., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, SM.
(1999b).
Identification of source nature and seasonal variations of Arctic aerosol by the
multilinear engine. Atmospheric Environment, 33, 2549
2562.
The multilinear engine is introduced in this study to estimate a mixed 2way/3
way model for the Alert aerosol data. Five 2way and two 3way factors have been
found to provide the best fit and interpretation of the data. Each factor
represented probable source with a distinctive compositional profile and
seasonal variations. The results obtained are consistent with those obtained in
the previous study (Xie, 1999a) and agree
with the current understanding of the Arctic aerosol.

Xie, YL., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, SM. (1999c).
Locations and preferred pathways of possible sources of Arctic aerosol.
Atmospheric Environment, 33, 22292239.
In this investigation, potential source contribution function (PSCF) analysis
was applied to the source contributions derived from the ME (Multilinear Engine)
analysis by incorporating meteorological information in the form of 5d air
parcel back trajectories. The potential locations and/or the preferred pathways
of these possible sources were then determined by the PSCF analysis.

Xu, Q., & Liang, Y. (1999).
On the equivalence of window factor analysis and orthogonal projection resolution.
Chemometrics and Intelligent Laboratory Systems, 45, 335338.
Window factor analysis (WFA) and orthogonal projection resolution (OPR) are two factor analytical
techniques for extracting component concentration profiles from twoway evolutionary data. Both methods take
advantage of the fact that each component lies in a special region along the evolutionary axis. Theoretical
equations are derived to prove that WFA is equivalent to OPR, if errors are ignored.
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ThreeMode bibliography

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Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
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First version : 12/02/1997;