Wastewater dissolved organic matter (DOM) from different processing stages of a sewage treatment plant in Xiamen was characterized using fluorescence and absorption spectroscopy. Parallel factor analysis modeling of...Wastewater dissolved organic matter (DOM) from different processing stages of a sewage treatment plant in Xiamen was characterized using fluorescence and absorption spectroscopy. Parallel factor analysis modeling of excitation-emission matrix spectra revealed five fluorescent components occurring in sewage DOM: one protein-like (C1), three humic-like (C2, C4 and C5) and one xenobiotic-like (C3) components. During the aerated grit chamber and primary sedimentation tank stage, there was only a slight decrease in fluorescence intensity and the absorption coefficient at 350 nm (a 350 ). During the second aeration stage, high concentration of protein-like and short-wavelength-excited humic-like components were significantly degraded accompanied by significant loss of DOC (80%) and a 350 (30%), indicating that C1 and C2 were the dominant constituents of sewage DOM. As a result, long-wavelength- excited C4 and C5 became the dominant humic-like components and the DOM molecular size inferred from the variation of spectral slope S (300–650 nm) and specific absorption (a 280 /DOC) increased. Combination use of F max of C1 and the ratio of C1/C5, or a 350 may provide a quantitative indication for the relative amount of raw or treated sewage in aquatic environment.展开更多
The feasibility of using fluorescence excitation-emission matrix(EEM) along with parallel factor analysis(PARAFAC) and nonnegative least squares(NNLS) method for the differentiation of phytoplankton taxonomic groups w...The feasibility of using fluorescence excitation-emission matrix(EEM) along with parallel factor analysis(PARAFAC) and nonnegative least squares(NNLS) method for the differentiation of phytoplankton taxonomic groups was investigated. Forty-one phytoplankton species belonging to 28 genera of five divisions were studied. First, the PARAFAC model was applied to EEMs, and 15 fluorescence components were generated. Second, 15 fluorescence components were found to have a strong discriminating capability based on Bayesian discriminant analysis(BDA). Third, all spectra of the fluorescence component compositions for the 41 phytoplankton species were spectrographically sorted into 61 reference spectra using hierarchical cluster analysis(HCA), and then, the reference spectra were used to establish a database. Finally, the phytoplankton taxonomic groups was differentiated by the reference spectra database using the NNLS method. The five phytoplankton groups were differentiated with the correct discrimination ratios(CDRs) of 100% for single-species samples at the division level. The CDRs for the mixtures were above 91% for the dominant phytoplankton species and above 73% for the subdominant phytoplankton species. Sixteen of the 85 field samples collected from the Changjiang River estuary were analyzed by both HPLC-CHEMTAX and the fluorometric technique developed. The results of both methods reveal that Bacillariophyta was the dominant algal group in these 16 samples and that the subdominant algal groups comprised Dinophyta, Chlorophyta and Cryptophyta. The differentiation results by the fluorometric technique were in good agreement with those from HPLC-CHEMTAX. The results indicate that the fluorometric technique could differentiate algal taxonomic groups accurately at the division level.展开更多
Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with t...Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with the fluorescence regional integration(FRI),parallel factor(PARAFAC) analysis,and multi-order kinetic models.In the FRI analysis,fulvic-like and humic-like materials were the main constituents for both BH-FDOM and HF-FDOM.Four individual components were identified by use of PARAFAC analysis as humic-like components(C1),fulvic-like components(C2),protein-like components(C3) and unidentified components(C4).The maximum 3 DEEM fluorescence intensity of PARAFAC components C1-C3 decreased by about 60%,70% and 90%,respectively after photo-degradation.The multi-order kinetic model was acceptable to represent the photo-degradation of FDOM with correlation coefficient(Radj2)(0.963-0.998).The photo-degradation rate constants(kn) showed differences of three orders of magnitude,from 1.09 × 10-6 to 4.02 × 10-4 min-1,and half-life of multi-order model(T1/2n)ranged from 5.26 to 64.01 min.The decreased values of fluorescence index(FI) and biogenic index(BI),the fact that of percent fluorescence response parameter of Region I(PⅠ,n) showed the greatest change ratio,followed by percent fluorescence response parameter of Region II(PⅡ,n,while the largest decrease ratio was found for C3 components,and the lowest T1/2n was observed for C3,indicated preferential degradation of protein-like materials/components derived from biological sources during photodegradation.This research on the degradation of FDOM by 3 DEEM/FRI-PARAFAC would be beneficial to understanding the photo-degradation of FD OM in natural environments and accurately predicting the environmental behaviors of contaminants in the presence of FDOM.展开更多
High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a c...High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a commercial recommender system or the user-user interactions in a social network services system. The factorization of such an HDI matrix can embed the involved entities into the low-dimensional feature space for acquiring their principal representation, which is a vital task in various application scenes and is often established through the Latent Factor Analysis(LFA). Nevertheless, an HDI matrix can be huge when the corresponding application explodes to involve millions of users, items, or other interactive nodes. In this case, a parallel optimization algorithm is desired for raising the scalability and time efficiency of an LFA model. This paper provides a comprehensive review of the existing parallel optimization algorithms for the LFA model. Specifically, it performs: 1) discussion and summary of these algorithms based on computing architecture and mode, 2) empirical studies of representative models, and3) summary of the current challenges and future directions in this domain. This survey aims to offer an exhaustive review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization, thereby fostering further research in this field.展开更多
An in vivo three-dimensional fluorescence method for the determination of algae community structure was developed by parallel factor analysis (PARAFAC) and CHEMTAX. The PARAFAC model was applied to fluo-rescence exc...An in vivo three-dimensional fluorescence method for the determination of algae community structure was developed by parallel factor analysis (PARAFAC) and CHEMTAX. The PARAFAC model was applied to fluo-rescence excitation-emission matrix (EEM) of 60 algae species belonging to five divisions and 11 fluorescent components were identified according to the residual sum of squares and specificity of the composition profiles of fluorescent. By the 11 fluorescent components, the algae species at different growth stages were classified correctly at the division level using Bayesian discriminant analysis (BDA). Then the reference fluo-rescent component ratio matrix was constructed for CHEMTAX, and the EEM-PARAFAC-CHEMTAX method was developed to differentiate algae taxonomic groups. The correct discrimination ratios (CDRs) when the fluorometric method was used for single-species samples were 100% at the division level, except for Bacil-lariophyta with a CDR of 95.6%. The CDRs for the mixtures were above 94.0% for the dominant algae species and above 87.0% for the subdominant algae species. However, the CDRs of the subdominant algae species were too low to be unreliable when the relative abundance estimated was less than 15.0%. The fluorometric method was tested using the samples from the Jiaozhou Bay and the mesocosm experiments in the Xiaomai Island Bay in August 2007. The discrimination results of the dominant algae groups agreed with microscopy cell counts, as well as the subdominant algae groups of which the estimated relative abundance was above 15.0%. This technique would be of great aid when low-cost and rapid analysis is needed for samples in a large batch. The fluorometric technique has the ability to correctly identify dominant species with proper abundance both in vivo and in situ.展开更多
This paper links parallel factor(PARAFAC) analysis to the problem of nominal direction-of-arrival(DOA) estimation for coherently distributed(CD) sources and proposes a fast PARAFACbased algorithm by establishing...This paper links parallel factor(PARAFAC) analysis to the problem of nominal direction-of-arrival(DOA) estimation for coherently distributed(CD) sources and proposes a fast PARAFACbased algorithm by establishing the trilinear PARAFAC model.Relying on the uniqueness of the low-rank three-way array decomposition and the trilinear alternating least squares regression, the proposed algorithm achieves nominal DOA estimation and outperforms the conventional estimation of signal parameter via rotational technique CD(ESPRIT-CD) and propagator method CD(PM-CD)methods in terms of estimation accuracy. Furthermore, by means of the initialization via the propagator method, this paper accelerates the convergence procedure of the proposed algorithm with no estimation performance degradation. In addition, the proposed algorithm can be directly applied to the multiple-source scenario,where sources have different angular distribution shapes. Numerical simulation results corroborate the effectiveness and superiority of the proposed fast PARAFAC-based algorithm.展开更多
A spacecraft attitude estimation method based on electromagnetic vector sensors(EMVS)array is proposed,which employs the orthogonally constrained parallel factor(PARAFAC)algorithm and makes use of measurements of the ...A spacecraft attitude estimation method based on electromagnetic vector sensors(EMVS)array is proposed,which employs the orthogonally constrained parallel factor(PARAFAC)algorithm and makes use of measurements of the two-dimensional direction-of-arrival(2D-DOA)and polarization angles,aiming to address the issues of incomplete,asynchronous,and inaccurate third-party reference used for attitude estimation in spacecraft docking missions by employing the electromagnetic wave’s three-dimensional(3D)wave structure as a complete third-party reference.Comparative analysis with state-ofthe-art algorithms shows significant improvements in estimation accuracy and computational efficiency with this algorithm.Numerical simulations have verified the effectiveness and superiority of this method.A high-precision,reliable,and cost-effective method for rapid spacecraft attitude estimation is provided in this paper.展开更多
Treated wastewater(TWW)irrigation may harm soil and agricultural production.Adverse effects of TWW irrigation may be mitigated by changing irrigation water quality,e.g.,use of fresh water(FW),or management,e.g.,lower-...Treated wastewater(TWW)irrigation may harm soil and agricultural production.Adverse effects of TWW irrigation may be mitigated by changing irrigation water quality,e.g.,use of fresh water(FW),or management,e.g.,lower-frequency irrigation(LFI)with TWW.The influence of mitigation treatments on soil organic matter and water-extractable organic matter is unknown.To examine this influence,a study was conducted in an avocado orchard irrigated from 2009 with secondary TWW.Four parallel treatments were applied for six years(2016-2021),involving irrigation with FW,a 1:1 FW-TWW mixture,TWW at LFI(twice a week),and TWW irrigation three times a week as control.Soil samples from three depths were characterized for total organic and inorganic carbon and nitrogen and using Fourier-transform infrared spectra that were decomposed into components by nonnegative matrix factorization.Aqueous extracts of soil samples were characterized for dissolved organic carbon(DOC),inorganic carbon,and nitrogen concentrations,absorbance at254 nm(Abs254),and excitation-emission matrices of fluorescence that were decomposed into components by parallel factor analysis.The Abs254 and fluorescence of humic-like components in the soil extracts were the attributes most consistently responding to irrigation water quality.Irrigation with FW and a 1:1 FW-TWW mixture led to decreases in the concentrations of aromatic and humic-like constituents in the soil extracts compared with the control TWW irrigation.Changing soil irrigation management had no or little impact on those attributes compared with the control TWW irrigation.Results of the study support the use of optical properties related to the concentrations of ultraviolet-absorbing and light-emitting constituents in soil extracts,rather than the whole DOC concentration,as sensitive descriptors suitable for evaluating soil response in different agricultural scenarios.展开更多
Factor analysis is widely utilized to identify latent factors underlying the observed variables.This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of fa...Factor analysis is widely utilized to identify latent factors underlying the observed variables.This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of factors in factor analysis,the K1 rule,and parallel analysis,along with a more recently developed method,the bass-ackward method.We provide an in-depth exploration of these techniques,discussing their historical development,advantages,and limitations.Using a series of Monte Carlo simulations,we assess the efficacy of these methods in accurately determining the appropriate number of factors.Specifically,we examine two cessation criteria within the bass-ackward framework:BA-maxLoading and BA-cutoff.Our findings offer nuanced insights into the performance of these methods under various conditions,illuminating their respective advantages and potential pitfalls.To enhance accessibility,we create an online visualization tool tailored to the factor structures generated by the bass-ackward method.This research enriches the understanding of factor analysis methodology,assists researchers in method selection,and facilitates comprehensive interpretation of latent factor structures.展开更多
基金supported by the National Natural Science Foundation of China(No.40776041,40676046)the National High Technology Research and Development Program of China(No.2007AA091704)the Program for New Century Excellent Talents in Fujian Province University
摘要Wastewater dissolved organic matter (DOM) from different processing stages of a sewage treatment plant in Xiamen was characterized using fluorescence and absorption spectroscopy. Parallel factor analysis modeling of excitation-emission matrix spectra revealed five fluorescent components occurring in sewage DOM: one protein-like (C1), three humic-like (C2, C4 and C5) and one xenobiotic-like (C3) components. During the aerated grit chamber and primary sedimentation tank stage, there was only a slight decrease in fluorescence intensity and the absorption coefficient at 350 nm (a 350 ). During the second aeration stage, high concentration of protein-like and short-wavelength-excited humic-like components were significantly degraded accompanied by significant loss of DOC (80%) and a 350 (30%), indicating that C1 and C2 were the dominant constituents of sewage DOM. As a result, long-wavelength- excited C4 and C5 became the dominant humic-like components and the DOM molecular size inferred from the variation of spectral slope S (300–650 nm) and specific absorption (a 280 /DOC) increased. Combination use of F max of C1 and the ratio of C1/C5, or a 350 may provide a quantitative indication for the relative amount of raw or treated sewage in aquatic environment.
基金Supported by the National Natural Science Foundation of China(Nos.41376106,41176063)the Shandong Provincial Natural Science Foundation of China(No.ZR2013DM017)
摘要The feasibility of using fluorescence excitation-emission matrix(EEM) along with parallel factor analysis(PARAFAC) and nonnegative least squares(NNLS) method for the differentiation of phytoplankton taxonomic groups was investigated. Forty-one phytoplankton species belonging to 28 genera of five divisions were studied. First, the PARAFAC model was applied to EEMs, and 15 fluorescence components were generated. Second, 15 fluorescence components were found to have a strong discriminating capability based on Bayesian discriminant analysis(BDA). Third, all spectra of the fluorescence component compositions for the 41 phytoplankton species were spectrographically sorted into 61 reference spectra using hierarchical cluster analysis(HCA), and then, the reference spectra were used to establish a database. Finally, the phytoplankton taxonomic groups was differentiated by the reference spectra database using the NNLS method. The five phytoplankton groups were differentiated with the correct discrimination ratios(CDRs) of 100% for single-species samples at the division level. The CDRs for the mixtures were above 91% for the dominant phytoplankton species and above 73% for the subdominant phytoplankton species. Sixteen of the 85 field samples collected from the Changjiang River estuary were analyzed by both HPLC-CHEMTAX and the fluorometric technique developed. The results of both methods reveal that Bacillariophyta was the dominant algal group in these 16 samples and that the subdominant algal groups comprised Dinophyta, Chlorophyta and Cryptophyta. The differentiation results by the fluorometric technique were in good agreement with those from HPLC-CHEMTAX. The results indicate that the fluorometric technique could differentiate algal taxonomic groups accurately at the division level.
基金financially supported by the National Natural Science Foundation of China(No.41573130)BNU Interdisciplinary Research Foundation for First-Year Doctoral Candidates(No.BNUXKJC1802)
摘要Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with the fluorescence regional integration(FRI),parallel factor(PARAFAC) analysis,and multi-order kinetic models.In the FRI analysis,fulvic-like and humic-like materials were the main constituents for both BH-FDOM and HF-FDOM.Four individual components were identified by use of PARAFAC analysis as humic-like components(C1),fulvic-like components(C2),protein-like components(C3) and unidentified components(C4).The maximum 3 DEEM fluorescence intensity of PARAFAC components C1-C3 decreased by about 60%,70% and 90%,respectively after photo-degradation.The multi-order kinetic model was acceptable to represent the photo-degradation of FDOM with correlation coefficient(Radj2)(0.963-0.998).The photo-degradation rate constants(kn) showed differences of three orders of magnitude,from 1.09 × 10-6 to 4.02 × 10-4 min-1,and half-life of multi-order model(T1/2n)ranged from 5.26 to 64.01 min.The decreased values of fluorescence index(FI) and biogenic index(BI),the fact that of percent fluorescence response parameter of Region I(PⅠ,n) showed the greatest change ratio,followed by percent fluorescence response parameter of Region II(PⅡ,n,while the largest decrease ratio was found for C3 components,and the lowest T1/2n was observed for C3,indicated preferential degradation of protein-like materials/components derived from biological sources during photodegradation.This research on the degradation of FDOM by 3 DEEM/FRI-PARAFAC would be beneficial to understanding the photo-degradation of FD OM in natural environments and accurately predicting the environmental behaviors of contaminants in the presence of FDOM.
基金supported in part by the National Key Research and Development Program of China(2024YFF0908200)the National Natural Science Foundation of China(62302402,62272078)+1 种基金the Chongqing Natural Science Foundation(CSTB2024TIAD-KPX0018,CSTB2023NSCO-LZX006)the Southwest University Graduate Research Innovation Project(SWUB24050)
摘要High-dimensional and incomplete(HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a commercial recommender system or the user-user interactions in a social network services system. The factorization of such an HDI matrix can embed the involved entities into the low-dimensional feature space for acquiring their principal representation, which is a vital task in various application scenes and is often established through the Latent Factor Analysis(LFA). Nevertheless, an HDI matrix can be huge when the corresponding application explodes to involve millions of users, items, or other interactive nodes. In this case, a parallel optimization algorithm is desired for raising the scalability and time efficiency of an LFA model. This paper provides a comprehensive review of the existing parallel optimization algorithms for the LFA model. Specifically, it performs: 1) discussion and summary of these algorithms based on computing architecture and mode, 2) empirical studies of representative models, and3) summary of the current challenges and future directions in this domain. This survey aims to offer an exhaustive review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization, thereby fostering further research in this field.
基金The National Natural Science Foundation of China under contract Nos 41376106 and 41276069
摘要An in vivo three-dimensional fluorescence method for the determination of algae community structure was developed by parallel factor analysis (PARAFAC) and CHEMTAX. The PARAFAC model was applied to fluo-rescence excitation-emission matrix (EEM) of 60 algae species belonging to five divisions and 11 fluorescent components were identified according to the residual sum of squares and specificity of the composition profiles of fluorescent. By the 11 fluorescent components, the algae species at different growth stages were classified correctly at the division level using Bayesian discriminant analysis (BDA). Then the reference fluo-rescent component ratio matrix was constructed for CHEMTAX, and the EEM-PARAFAC-CHEMTAX method was developed to differentiate algae taxonomic groups. The correct discrimination ratios (CDRs) when the fluorometric method was used for single-species samples were 100% at the division level, except for Bacil-lariophyta with a CDR of 95.6%. The CDRs for the mixtures were above 94.0% for the dominant algae species and above 87.0% for the subdominant algae species. However, the CDRs of the subdominant algae species were too low to be unreliable when the relative abundance estimated was less than 15.0%. The fluorometric method was tested using the samples from the Jiaozhou Bay and the mesocosm experiments in the Xiaomai Island Bay in August 2007. The discrimination results of the dominant algae groups agreed with microscopy cell counts, as well as the subdominant algae groups of which the estimated relative abundance was above 15.0%. This technique would be of great aid when low-cost and rapid analysis is needed for samples in a large batch. The fluorometric technique has the ability to correctly identify dominant species with proper abundance both in vivo and in situ.
基金supported by the National Natural Science Foundation of China(6137116961601167)+2 种基金the Jiangsu Natural Science Foundation(BK20161489)the open research fund of State Key Laboratory of Millimeter Waves,Southeast University(K201826)the Fundamental Research Funds for the Central Universities(NE2017103)
摘要This paper links parallel factor(PARAFAC) analysis to the problem of nominal direction-of-arrival(DOA) estimation for coherently distributed(CD) sources and proposes a fast PARAFACbased algorithm by establishing the trilinear PARAFAC model.Relying on the uniqueness of the low-rank three-way array decomposition and the trilinear alternating least squares regression, the proposed algorithm achieves nominal DOA estimation and outperforms the conventional estimation of signal parameter via rotational technique CD(ESPRIT-CD) and propagator method CD(PM-CD)methods in terms of estimation accuracy. Furthermore, by means of the initialization via the propagator method, this paper accelerates the convergence procedure of the proposed algorithm with no estimation performance degradation. In addition, the proposed algorithm can be directly applied to the multiple-source scenario,where sources have different angular distribution shapes. Numerical simulation results corroborate the effectiveness and superiority of the proposed fast PARAFAC-based algorithm.
摘要A spacecraft attitude estimation method based on electromagnetic vector sensors(EMVS)array is proposed,which employs the orthogonally constrained parallel factor(PARAFAC)algorithm and makes use of measurements of the two-dimensional direction-of-arrival(2D-DOA)and polarization angles,aiming to address the issues of incomplete,asynchronous,and inaccurate third-party reference used for attitude estimation in spacecraft docking missions by employing the electromagnetic wave’s three-dimensional(3D)wave structure as a complete third-party reference.Comparative analysis with state-ofthe-art algorithms shows significant improvements in estimation accuracy and computational efficiency with this algorithm.Numerical simulations have verified the effectiveness and superiority of this method.A high-precision,reliable,and cost-effective method for rapid spacecraft attitude estimation is provided in this paper.
基金supported by a grant from the Chief Scientist,the Ministry of Agriculture and Rural Development,Israel(No.21-16-004)by the Plants Production&Marketing Board(Avocado Growers Branch)of Israel。
摘要Treated wastewater(TWW)irrigation may harm soil and agricultural production.Adverse effects of TWW irrigation may be mitigated by changing irrigation water quality,e.g.,use of fresh water(FW),or management,e.g.,lower-frequency irrigation(LFI)with TWW.The influence of mitigation treatments on soil organic matter and water-extractable organic matter is unknown.To examine this influence,a study was conducted in an avocado orchard irrigated from 2009 with secondary TWW.Four parallel treatments were applied for six years(2016-2021),involving irrigation with FW,a 1:1 FW-TWW mixture,TWW at LFI(twice a week),and TWW irrigation three times a week as control.Soil samples from three depths were characterized for total organic and inorganic carbon and nitrogen and using Fourier-transform infrared spectra that were decomposed into components by nonnegative matrix factorization.Aqueous extracts of soil samples were characterized for dissolved organic carbon(DOC),inorganic carbon,and nitrogen concentrations,absorbance at254 nm(Abs254),and excitation-emission matrices of fluorescence that were decomposed into components by parallel factor analysis.The Abs254 and fluorescence of humic-like components in the soil extracts were the attributes most consistently responding to irrigation water quality.Irrigation with FW and a 1:1 FW-TWW mixture led to decreases in the concentrations of aromatic and humic-like constituents in the soil extracts compared with the control TWW irrigation.Changing soil irrigation management had no or little impact on those attributes compared with the control TWW irrigation.Results of the study support the use of optical properties related to the concentrations of ultraviolet-absorbing and light-emitting constituents in soil extracts,rather than the whole DOC concentration,as sensitive descriptors suitable for evaluating soil response in different agricultural scenarios.
基金supported by Grants from the Department of Education(R305D140037,R305D210023).
摘要Factor analysis is widely utilized to identify latent factors underlying the observed variables.This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of factors in factor analysis,the K1 rule,and parallel analysis,along with a more recently developed method,the bass-ackward method.We provide an in-depth exploration of these techniques,discussing their historical development,advantages,and limitations.Using a series of Monte Carlo simulations,we assess the efficacy of these methods in accurately determining the appropriate number of factors.Specifically,we examine two cessation criteria within the bass-ackward framework:BA-maxLoading and BA-cutoff.Our findings offer nuanced insights into the performance of these methods under various conditions,illuminating their respective advantages and potential pitfalls.To enhance accessibility,we create an online visualization tool tailored to the factor structures generated by the bass-ackward method.This research enriches the understanding of factor analysis methodology,assists researchers in method selection,and facilitates comprehensive interpretation of latent factor structures.