Waste Management 33 (2013) 1324–1331

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Waste Management

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A hybrid procedure for MSW generation forecasting at multiple time scalesin Xiamen City, China

Lilai Xu a,b,1, Peiqing Gao c,2, Shenghui Cui a,b,⇑, Chun Liu c,2

a Key Lab of Urban Environment and Health, Institute of Urban Environment, Chinese Academy of Sciences, 1799 Jimei Road, Xiamen 361021, Chinab Xiamen Key Lab of Urban Metabolism, Xiamen 361021, Chinac Xiamen City Appearance and Environmental Sanitation Management Office, 51 Hexiangxi Road, Xiamen 361004, China

a r t i c l e i n f o

Article history:Received 28 September 2012Accepted 11 February 2013Available online 11 March 2013

Keywords:MSW GenerationMultiple time scalesSARIMA modelGM (1,1)Grey relational analysis

0956-053X/$ - see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.wasman.2013.02.012

⇑ Corresponding author at: Key Lab of Urban EnvironUrban Environment, Chinese Academy of Sciences361021, China. Tel.: +86 592 6190957; fax: +86 592 6

E-mail addresses: llxu@iue.ac.cn (L. Xu), peiqinshcui@iue.ac.cn (S. Cui), xmhwlc@yahoo.com.cn (C. Li

1 Tel.: +86 592 6190664; fax: +86 592 6190977.2 Tel.: +86 592 2220607; fax: +86 592 2231808.

a b s t r a c t

Accurate forecasting of municipal solid waste (MSW) generation is crucial and fundamental for the plan-ning, operation and optimization of any MSW management system. Comprehensive information onwaste generation for month-scale, medium-term and long-term time scales is especially needed, consid-ering the necessity of MSW management upgrade facing many developing countries. Several existingmodels are available but of little use in forecasting MSW generation at multiple time scales. The goalof this study is to propose a hybrid model that combines the seasonal autoregressive integrated movingaverage (SARIMA) model and grey system theory to forecast MSW generation at multiple time scaleswithout needing to consider other variables such as demographics and socioeconomic factors. To demon-strate its applicability, a case study of Xiamen City, China was performed. Results show that the model isrobust enough to fit and forecast seasonal and annual dynamics of MSW generation at month-scale, med-ium- and long-term time scales with the desired accuracy. In the month-scale, MSW generation in Xia-men City will peak at 132.2 thousand tonnes in July 2015 – 1.5 times the volume in July 2010. In themedium term, annual MSW generation will increase to 1518.1 thousand tonnes by 2015 at an averagegrowth rate of 10%. In the long term, a large volume of MSW will be output annually and will increaseto 2486.3 thousand tonnes by 2020 – 2.5 times the value for 2010. The hybrid model proposed in thispaper can enable decision makers to develop integrated policies and measures for waste managementover the long term.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Increasing population levels, booming economies, rapid urban-ization and a rise in community living standards have greatlyaccelerated municipal solid waste (MSW) generation in developingcountries, especially in China (Zhu et al., 2009; Chen et al., 2010).With this increase in volume, as well as changes in composition,MSW problems have begun to pose serious threat to the urbanenvironment and to public health (Giusti, 2009; Pan et al., 2010),thereby threatening long-term sustainable development. China’sreported MSW generation has soared from 25.08 million tonnesto 158.05 million tonnes over the 1979–2010 period, with an an-nual growth rate of over 6% (National Bureau of Statistics, 2011),leading to the dilemma that almost two thirds of China’s cities

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ment and Health, Institute of, 1799 Jimei Road, Xiamen190977.

g15@yahoo.com.cn (P. Gao),u).

have become ‘‘garbage-besieged cities’’ – a problem that is spread-ing to rural areas. Accurate forecasts of MSW generation are crucialand fundamental, since the amount and composition of waste gen-erated comprise the basic information needed for the planning,operation and optimization of any MSW management system(Beigl et al., 2008). However, achieving the desired prediction accu-racy with regard to MSW generation trends facing many develop-ing countries is quite challenging, because MSW generationforecasting is a complex problem which includes identifying timeand spatial scales, influence factors and forecasting methods (Beiglet al., 2008).

There is a growing body of literature on MSW generation fore-casting. Since the early 1970s, several studies have been under-taken using different models, which can be generally classifiedinto four categories: a regression analysis model (Grossmanet al., 1974; Daskalopoulos et al., 1998; Sokka et al., 2007; Benitezet al., 2008; Rimaityte et al., 2012), a system dynamics model(Dyson and Chang, 2005; Zhang et al., 2007; Kollikkathara et al.,2010), an artificial intelligence model (Jalili and Noori, 2008; Nooriet al., 2009; Wang et al., 2010), and a time series model (Chen andChang, 2000; Navarro-Esbri et al., 2002; Li et al., 2003; Liu and Yu,

L. Xu et al. / Waste Management 33 (2013) 1324–1331 1325

2007). Among these models, regression analysis is widely used inMSW generation forecasting because of its mature theory and sim-ple algorithms; the system dynamics model can fully characterizethe dynamic properties in the process of solid waste generation;the artificial intelligence models, such as the support vector ma-chine and the artificial neural network, are commonly used be-cause of their high flexibility and recently proven predictionabilities. These three kinds of models, however, frequently applydemographic and socioeconomic factors that are difficult to iden-tify and quantify, in order to construct the model essentials (Chenand Chang, 2000; Dyson and Chang, 2005). While the time seriesmodel was introduced to cope with just such a problem, it, to-gether with the other three kinds of models, can only output futureinformation on MSW generation at a single time scale that is inad-equate to cope with the complexities currently facing MSW man-agement. As the upgrading of waste management methods –from landfill processing, energy recovery, and material recyclingto waste minimization – proceeds, more detailed information, overmultiple time scales (month-scale, medium- and long-term) willbe critical. In this paper, a pioneer study employed a seasonal auto-regressive integrated moving average (SARIMA) model along withgrey system theory, to build a hybrid model capable of forecastingMSW generation at multiple time scales, without consideringdemographic and socioeconomic factors, in Xiamen City, China.

The remainder of this paper is organized as follows. Section 2briefly introduces Xiamen City and the data source. The methodol-ogy used in the study is described in Section 3. The results of mod-eling and forecasting are presented and discussed in Section 4.Section 5 summarizes the main findings.

2. Study area and data

Xiamen City, with a population size of 3.53 million and an areaof 1573 square kilometers, is located on the southeast coast of Chi-na and is divided into six administrative districts. Fig. 1 illustratesthe geographic location of Xiamen City and its solid waste manage-ment facilities. Landfill capacity of East Solid Waste Disposal Cen-tre is 2500 tonnes/day, and treatment capacity of Houkeng

Fig. 1. Geographic location and solid waste

incinerator is 400 tonnes/day. However, Dongfu landfill has goneout of service. As one of the Special Economic Zones in China, abooming economy and urbanization have accelerated the produc-tion of MSW in the past three decades. According to existing re-ports, the amount of MSW generated in Xiamen City is morethan 2500 tonnes/day, posing tremendous pressure on MSW man-agement (Xiamen Municipal Bureau of Statistics, 2011). Hence acritical problem facing Xiamen City in the present and in the nearfuture is to determine if the collection, shipping, treatment anddisposal capacity is sufficient to handle the increasing volume ofsolid waste generation.

In this study, historical MSW generation data during the periodJanuary 2000–December 2010, with a total of 132 samples, wereobtained from the Xiamen Environmental Sanitation ManagementDepartment and the Yearbook of the Xiamen Special Economic Zone2011 published by the Xiamen Municipal Bureau of Statistics (Xia-men Municipal Bureau of Statistics, 2011). As illustrated in Fig. 2,the collected data exhibit strong seasonality and growth trends.The original time series was divided into two sets; the period fromJanuary 2000 to December 2009 was used to build the models, andthe period from January 2010 to December 2010 to verify the per-formance of models.

3. Methodology

In this paper, we combined the SARIMA model and grey systemtheory to analyze the future MSW generation of Xiamen at threetime scales: monthly MSW generation from 2011 to 2015, for themonth time scale; annual MSW generation from 2011 to 2015,for the medium-term time scale; and annual MSW generationinformation from 2016 to 2020, for the long-term time scale. Ingeneral, SARIMA model can only forecast future information within5 years while first-order and one-variable grey differential equa-tion model (GM (1,1)) is expert in long-term forecasting underthe condition of data scarcity, based on which procedure forMSW generation forecasting was proposed and presented inFig. 3. First, historical monthly data were used by the SARIMA mod-el to estimate and forecast the monthly MSW generation for the

management facilities of Xiamen City.

Fig. 2. Original monthly MSW generation series for Xiamen City (January-2000 to December-2010).

Fig. 3. Procedure for MSW generation forecasting in Xiamen City.

1326 L. Xu et al. / Waste Management 33 (2013) 1324–1331

month-scale, thereby allowing the corresponding annual informa-tion to be collected simultaneously, for the medium-term scale.Second, historical annual data were applied in GM (1,1) to predictthe annual information at both medium-term and long-term timescales. Third, grey relational analysis (GRA) was employed to deter-mine the accuracy of the annual forecast of the SARIMA model andthe GM (1,1) model by comparing the results with the observed se-quence. Consequently, weight coefficients of the two models werecomputed based on the grey rational grade. Finally, to eliminaterandom error caused by a single model and to strengthen the reli-ability of the forecast, the weighted average of the SARIMA modeland the GM (1,1) was generated as the end result, at the medium-term time scale.

3.1. SARIMA model

The autoregressive integrated moving average (ARIMA) model,first introduced by Box and Jenkins (1976), has achieved great suc-cess in both academic research and applications for forecastingtime series data (Box and Jenkins, 1976). Based on ARIMA, the sea-sonal ARIMA (SARIMA) model was developed to handle situationswhere seasonal and non-stationary behaviors were included(Tseng and Tzeng, 2002). The generalized form of the SARIMAmodel can be written as:

/pðLÞUPðLsÞð1� LÞdð1� LsÞDXt ¼ hqðLÞHQ ðLsÞmt; ð1Þ

/pðLÞ ¼ 1� /1L� /2L2 � � � � � /PLp; ð2Þ

UpðLsÞ ¼ 1�U1Ls �U2L2s � � � � �UPLPs; ð3Þ

hqðLÞ ¼ 1� h1L� h2L2 � � � � � hqLq; ð4Þ

HQ ðLsÞ ¼ 1�H1Ls �H2L2s � � � � �HQ LQs; ð5Þ

where d is the number of regular differences; D is the number ofseasonal differences; p, q, P, Q are integers; s is periodicity; L is

the backward shift operator; Xt denotes the observed value of thetime series data; and vt is the residuals.

3.2. Grey system theory

3.2.1. The GM (1,1) modelGrey system theory, originally proposed by Professor Deng in

1982, provides a good approach to investigating fuzzy issues(Deng, 1982). It has been extensively studied and applied for pre-diction, decision-making and grey relational analysis over the pastfew decades, especially for prediction (Kayacan et al., 2010; Liu andForrest, 2007). A grey system is a partially known and partially un-known system in which a large sample set is not easily availableand the information is poor, uncertain or incomplete (Deng,1989). An MSW generation system meets the characteristics of agrey system because the waste generation mechanism, as well asits driving factors, are not well defined or fully understood. In thispaper, a first-order and one-variable grey differential equationmodel GM (1,1) and grey relational analysis are employed to fore-cast MSW generation in Xiamen City. The basic principles of GM(1,1) are described as follows:

Assume that Xð0Þ ¼ xð0Þð1Þ; xð0Þð2Þ; � � � ; xð0ÞðnÞ� �

is a non-negativeseries of raw data. Its series of the first order accumulative gener-ation operation (AGO) is denoted as follows:

Xð1Þ ¼ xð1Þð1Þ; xð1Þð2Þ; � � � ; xð1ÞðnÞ� �

; xð1ÞðkÞ ¼Xk

i¼0

xðiÞ ðk

¼ 1;2; . . . ;nÞ ð6Þ

According to the whitened equation of GM (1,1) expressed as dx(1)/dt + ax(1) = u, the time response function of the whitened equationyields: x̂ð1Þðt þ 1Þ ¼ ðxð0Þð1Þ � u=aÞe�at þ u=a, where the systemparameters a, u can be determined by the least squares estimatemethod, and the restored values of raw data can then be obtainedas:

x̂ð0Þðt þ 1Þ ¼ x̂ð1Þðt þ 1Þ � x̂ð1ÞðtÞ: ð7Þ

L. Xu et al. / Waste Management 33 (2013) 1324–1331 1327

3.2.2. Grey relational analysisGRA is a method used to determine whether variables are cor-

related, and to quantify their correlation in terms of their geomet-rical similarity (Ma, 2010). A more similar trend is demonstratedby a closer relationship expressed by a grey relational grade. Sup-pose that x0 = (x0(1), x0(2), . . .,x0(m)) is the reference sequence andthat xi = (xi(1), xi(2), . . .,xi(m)), (i = 1,2, . . .,k) are the compared se-quences. The grey relational grade between the compared se-quence xi and the reference sequence x0 is defined as:

cðx0; xiÞ ¼1m

Xm

j¼1

cðx0ðjÞ; xiðjÞÞ; ð8Þ

cðx0ðjÞ; xiðjÞÞ ¼min

imin

jjx0ðjÞ � xiðjÞj þ qmax

imax

jjx0ðjÞ � xiðjÞj

jx0ðjÞ � xiðjÞj þ qmaxi

maxjjx0ðjÞ � xiðjÞj

;

ð9Þ

where q e (0,1), generally taken as 0.5, is the distinguishing coeffi-cient used to diminish the effect of a large absolute error.

4. Results and discussion

4.1. Month-scale forecasting

Three steps were involved in building the SARIMA model. First,the SARIMA structure was identified as SARIMA (3,1,2) (1,1,1)12

using an autocorrelation function (ACF) and a partial autocorrela-

Fig. 4. Inverse roots of autoregressive (AR) and moving average (MA) polynomials.

Fig. 5. SARIMA model fitting of monthly MSW

tion function (PACF). Second, the unknown parameters were esti-mated by the least squares method. Third, goodness of fit on theestimated residuals was tested. Results showed that the residualswere independent and identically distributed as normal randomvariables with a mean of 0 and a variance of d2, and that the inverseroots of /p(X) = 0 and hq(X) = 0 lay inside the unit circle (see Fig. 4),indicating that the SARIMA model as built is correct.

After the modeling process, a forecasting equation was obtainedas:

ð1� 0:59Lþ 0:5L2 þ 0:13L3Þð1þ 0:3L12Þð1� LÞ1ð1� L12Þ1LnXt

¼ ð1� 1:19Lþ 0:88L2Þð1� 0:87L12Þmt ð10Þ

As presented in Fig. 5, SARIMA (3,1,2) (1,1,1)12 is a good repre-sentation of the monthly MSW generation behavior, especially itsdemonstration of the characteristics of seasonal dynamics. To ver-ify the predictive performance of the built model, we compared theforecast value with observed data from January 2010 to December2010. As shown in Fig. 6, the trend of the forecast curve is basicallyconsistent with the observed curve. In addition, the mean absolutepercentage error (MAPE) value is 2.76% and the mean absolute er-ror (MAE) is 0.218, demonstrating that the built model is a fore-casting tool of satisfactory ability, so that it can be used toforecast the monthly MSW generation from 2011 to 2015.

As revealed in Fig. 7, MSW generation in Xiamen will increasewith seasonal fluctuations. The monthly minimum value will occurin February and the maximum will occur in July every year, a resultwhich accords with the actual situation because February is thecoldest month and July the hottest month in Xiamen City, and sev-eral studies have demonstrated that waste generation has a signif-icant positive relationship with temperature (Afon and Okewole,2007; Falahnezhad et al., 2011). By July 2015, MSW generation willpeak at 132.2 thousand tonnes – 1.5 times the value for July 2010.Based on this information at the month-scale obtained from theSARIMA (3,1,2) (1,1,1)12 model, the decision makers of XiamenCity should assess whether the treatment facilities and manage-ment strength are adequate to respond to the growth trend ofMSW, particularly the peak that will emerge in July 2015. More-over, the seasonal dynamic characteristics of MSW generationshould be fully taken into consideration when arranging and allo-cating management measures, thereby contributing to the optimaluse of limited management resources such as personnel, truck uti-lization and allotted funding (Matsuto and Tanaka, 1993). As forwaste management, it is not cost-effective to assign MSW manage-ment resources equally to every month, because of the dynamicvariation characteristics of waste generation. The month-scaleforecast of the proposed model can grasp such dynamics and givemonthly information on waste generation, based on which thedecision makers can plan and arrange waste management actionswith respect to collection, transportation, transfer, treatment andfinal disposal.

generation (May-2002 to December-2009).

Fig. 6. Comparison of observed and forecast data by the SARIMA model (January-2010 to December-2010).

Fig. 7. Extrapolated prediction for MSW generation for Xiamen City by the SARIMA model (January-2011 to December-2015).

Table 1Forecast results of MSW generation at the long-term time scale (104 tonnes).

Year 2016 2017 2018 2019 2020

MSW 172.00 188.60 206.80 226.75 248.63

1328 L. Xu et al. / Waste Management 33 (2013) 1324–1331

4.2. Long-term forecasting

In this study, we fitted the GM (1,1) model to historical annualMSW generation data from 2000 to 2009 using the software Mat-lab7.0. A forecasting equation was obtained as:

xðt þ 1Þ ¼ 447:753211 expð0:09;211 � tÞ � 412:153211: ð11Þ

By comparing the observed and forecast sequences (see Table 2),MAPE and MAE were calculated as 2.8% and 1.68%, indicating thatthe GM (1,1) built in this study is an excellent representation of the

Table 2Prediction for MSW generation by different models for medium-term time scale (104 tonn

Year Observed SARIMA AE APE (%) GM (1,1

2000 35.60 35.602001 40.02 43.202002 47.11 47.372003 54.88 55.01 0.13 0.2 51.942004 56.29 57.00 0.71 1.3 56.952005 60.85 59.48 1.37 2.3 62.452006 70.58 75.23 4.65 6.6 68.472007 77.36 76.01 1.35 1.7 75.082008 83.24 81.00 2.24 2.7 82.322009 87.42 85.80 1.62 1.9 90.272010 94.45 96.18 1.73 1.8 98.972011 103.49 108.522012 112.61 1192013 122.97 130.482014 133.67 143.072015 144.53 156.87

Note: AE presents absolute error; APE presents absolute percentage error.

MSW generation behavior of all the samples. We therefore appliedthe GM (1,1) built above in order to forecast MSW generation atthe medium-term and long-term time scales (see Tables 1 and2). In Fig. 8, the left section of the figure shows the accuracy ofthe model fitting and the right section presents the extrapolatedprediction for MSW generation in Xiamen City. Overall, the fore-cast curve shows exponential growth trends at both medium-termand long-term time scales. As listed in Table 1, a huge amount ofMSW will be generated annually and will increase to 2486.3 thou-sand tonnes by 2020 – 2.5 times that generated in 2010. Xi et al.(2008) forecasted MSW generation of Shenzhen City – one of Spe-cial Economic Zones in China like Xiamen – by system dynamicmodel, and results also shown rapid growth trend.

Values forecast by the GM (1,1) model at the long-term timescale provide decision makers with a basic scenario in which theincreasing trend of MSW generation will cause it to increase be-yond the handling capacity of MSW management and pose a great

es).

) AE APE (%) Combination AE APE (%)

0 03.18 7.90.26 0.62.94 5.4 53.20 1.68 3.10.66 1.2 56.97 0.68 1.21.60 2.6 61.23 0.38 0.62.11 3.0 71.24 0.66 0.92.28 2.9 75.46 1.90 2.50.92 1.1 81.78 1.46 1.82.85 3.3 88.44 1.02 1.23.84 4.1 97.83 2.70 2.9

106.46116.38127.40139.22151.81

Fig. 8. Forecast results of MSW generation by the GM (1,1) model.

Fig. 9. Forecast results of MSW generation by SARIMA, GM (1,1) and combined models at medium-term time scale.

L. Xu et al. / Waste Management 33 (2013) 1324–1331 1329

environmental load on Xiamen City if the rapid economic growthand urbanization continue while MSW regulation and strategiesmaintain the current state with neither processing breakthroughsnor emphasis on MSW minimization, reuse, recycling and recov-ery. A long-term forecast of the proposed model is needed espe-cially for government and waste management organizationswhen developing management strategies and policies, selectingappropriate technologies, scheduling landfill sites and planningthe capacities of incinerators (Navarro-Esbri et al., 2002). In addi-tion, this case study of Xiamen City has demonstrated that theGM (1,1) model is excellent for forecasting waste generation inthe long term, with the desired accuracy even under conditionsof data scarcity.

4.3. Medium-term forecasting

At the medium-term time scale, outputs from the SARIMA mod-el and GM (1,1) were integrated to obtain greater accuracy of MSWgeneration information based on the weighted average value. Theweight coefficients of the two models were determined in termsof their prediction accuracy computed by grey relational analysis.The results showed that the grey relational grade between the ob-served sequence and the SARIMA forecasted sequence was 0.5147,and that of the GM (1,1) model, 0.7349. Next, the weights from thetwo models were derived from the equation ki ¼ ci=c1 þ c2; andthe results were 0.41 and 0.59, from which the combined annualMSW generation information from 2011 to 2015 was obtained.

1330 L. Xu et al. / Waste Management 33 (2013) 1324–1331

According to Table 2, the MAPE and MAE of the combined modelswere calculated as 1.6% and 1.11%; both are less than those of theSARIMA (MAPE, 2.4%; MAE, 1.72%) and GM (1,1) models (MAPE,2.8%, MAE, 1.68%), indicating that the combined model is a compro-mise of the other two models and can eliminate the uncertainty of asingle forecasting method and enhance the reliability of the forecastinformation. Fig. 9 shows that all three models provide good repre-sentation of MSW generation, correlating closely with historicaldata and with all of the forecast curves displaying similar increasingtrends in the extrapolated prediction phrase. In terms of the com-bined model, annual MSW generation of Xiamen from 2011 to2015 will increase continuously and rapidly at an average annualgrowth rate of 10%. Chang et al. (2011) also forecasted MSW gener-ation of Xiamen City at medium-term, and concluded that MSWwould be 1682.6 thousand tonnes by 2015 with average annualgrowth rate of 11.14%. In light of the Twelfth Five-year Plan of Xiamen(2011–2015), these intrinsic factors influencing MSW generation,such as the level of economic growth and urbanization, will developat a relatively fast pace. GDP in 2015 will be double that of 2010, andthe urbanization level will increase from 80% to 85% during the per-iod 2010 to 2015. These levels account for the continuing rapidgrowth trend of MSW generation and demonstrate that the com-bined model is robust enough to predict the characteristics ofMSW generation as well. In practice, MSW generation informationobtained from the medium-term time scale can facilitate bettermedium-term waste management planning, which is the core ofwaste management planning systems – not only because it providesguidance for short-term planning but also because it drives theimplementation and deployment of long-term planning.

5. Conclusion

A hybrid model combining the SARIMA model and GM (1,1)was proposed in this analysis. As demonstrated by a case studyof Xiamen City, the hybrid model proposed is robust at forecastingMSW generation at multiple time scales without needing to con-sider variables such as demographic and socioeconomic factors.In the month-scale, monthly waste generation as well as seasonaldynamics are accurately depicted and forecast by the SARIMAmodel. From 2011 to 2015, the monthly minimum value of MSWgeneration will occur in February and the maximum in July. By July2015, MSW generation will peak at 132.2 thousand tonnes –1.5 times the value for July 2010. In the medium term, grey rela-tional analysis performs excellently in integrating the SARIMAmodel and GM (1,1) to yield a weighted average value of MSWgeneration, eliminating random errors caused by single-modelforecasting. According to the combined model, annual MSW gener-ation will increase continuously and rapidly to 1518.1 thousandtonnes by 2015 at an average growth rate of 10%. In the long term,GM (1,1) provides a basic scenario that a large volume of MSW willbe output annually and will increase to 2486.3 thousand tonnes by2020 – 2.5 times the value for 2010 – if Xiamen City maintains thecurrent momentum of development. The proposed model can pro-vide comprehensive information on waste generation at three timescales, enabling decision makers to develop integrated polices andmeasures for waste management over a longer period of time.Especially for developing countries, because total amount ofMSW will keep increasing motivated by rapid industrializationand increasing urban population. However, data unavailability isstill a primary problem facing many developing countries, estab-lishment of database for MSW must be received more attention.

Acknowledgements

The authors gratefully acknowledge financial support from theMinistry of Science and Technology of China (2011DFB91710),

the Science and Technology Project of Fujian Province, China(2010I0014) and the Science and Technology Project of XiamenCity, China (3502Z20101015 and 3502Z20111049).

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