a new chaos agent based approach in prediction of ...

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Farhad S. Gharehchopogh, Zahra A. Dizaji. A new chaos agent based approach in prediction of the road accidents with hybrid of PSO optimization and chaos optimization algorithms: a case study. International Journal of Academic Research Part A; 2014; 6(2), 108-115. DOI: 10.7813/2075-4124.2014/6-2/A.18 Library of Congress Classification: T58.5-58.64, TK7885-7895

A NEW CHAOS AGENT BASED APPROACH IN PREDICTION OF THE ROAD ACCIDENTS WITH HYBRID OF PSO OPTIMIZATION AND CHAOS OPTIMIZATION ALGORITHMS: A CASE STUDY Farhad Soleimanian Gharehchopogh, Zahra Asheghi Dizaji Department of Computer Engineering, Science and Research Branch, Islamic Azad University, West Azerbaijan (IRAN) E-mails: [email protected], [email protected] DOI: 10.7813/2075-4124.2014/6-2/A.18 Received: 12 Nov, 2013 Accepted: 24 Mar, 2014

ABSTRACT Nowadays, according to the increase of casualties in road accidents, providing solutions to explore and identify intricate relations between the factors involved in the accidents is essential. Considering the increasing rate of road accidents and consequently increase in information about the accidents, and presence of evident and latent dependencies among the influencing factors in road accidents using data mining techniques to identify the contribution of each factor involved in accidents and the relations between these factors are required. So we, in this paper, in order to achieve the optimal relationship between the factors involved in road accidents by type of accident(vehicle damage, injury, death) we have used the hybrid of Particle Swarm Optimization (PSO)algorithm and Chaos Optimization Algorithms (COA) (Tent map, Logistic Map, Lorenz attractor) as chaos factor. The main task of chaos factor is selecting the optimal values for the parameters of PSO algorithm from the values produced by three types of chaotic maps which each map presents 11 methods by combining PSO and COA. The results of the proposed method compared to the PSO algorithm and combination of PSO and COA reflect the improved performance of the PSO algorithm. Therefore based on the relations obtained from the proposed method, we have dealt with predicting road accidents which the results show 98 percent of accuracy in predictions. Key words: Particle Swarm Optimization, Chaos Optimization Algorithm, Prediction of Traffic Accidents, Data Mining 1. INTRODUCTION Road accidents annually take the life of many people around the world. So this is considered an important issue in all countries, especially in developing countries. Many factors seem to be involved in an accident. These factors can be classified in four groups [1]: environment around road factor, human factor, vehicle factor ,and road factor that each of the mentioned factors, in turn, seems to contribute to road accidents. Among the main elements of an accident, human is intelligent one, so that, in addition to its role as an agent, controlling three other factors role in incidence of accidents is also possible by him [2]. Considering the complexity of accidents and the involvement of multiple factors in its occurrence, using common and traditional methods to obtain a communication between effective factors in accident occurrence is difficult and in some cases is impossible. Therefore, to obtain optimal results using new methods such as data mining techniques are required. Nowadays, with the improvement in the results of collective intelligence algorithms to solve problems using this algorithms as data mining techniques is customary. One of these algorithms PSO algorithm that was introduced as a nondeterministic search method in 1995 by Eberhart and Kennedy [3]. The implementation of this algorithm compared with other mathematical algorithms, and evolutionary algorithms is easier and the results are better [3]. Due to the random nature of this algorithm, it has also convergence property. Therefore, the algorithm don't catch in premature convergence and reduced diversity during time, do some settings on the parameters are required. One of the ways that used to solve this problem is COA [4, 5]. COA can be as a kind of order in disorder, the main key of COA is understanding this point that we shouldn't search the order in a scale because a phenomenon in local scale is completely random and unpredictable that it will be in large-scale fully predictable. Chaotic systems are a kind of dynamic systems that they indicate sensitive behavior changes in the initial values so that their future behaviors aren't predictable. Chaotic systems behavior in appearance are random while they have discipline [6]. In this paper we explain the prediction of road accidents, based on kind of accident (damage, injury, death). Therefore, the algorithm don't catch in premature convergence and reduced diversity during time and could be create optimal results, and we should adapt the initialize of the parameters of this algorithm with chaos factor, and evaluate this results.

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To achieve to optimal results using available real data that indicates a relation between involved factors in accidents are required. Parameters used in this paper for the prediction of traffic accidents are: Kind of happened accident - The effective vehicle factor in accidents – Human factor in accidents – The total cause of accident Affecting defects of ways – Status of air Lighting -Road surface condition - The geometry status of the situation Vision obstacles in way - User kind of the accident scene - Climate - Type of lining in accident occurrence location - Shoulder Type of accident occurrence location Different parts of this paper are organized like: In section 2 reviews of works done in this subject, section 3 material and methods, section 4 proposed method, section 5 evaluate the proposed method and in section 6 conclusion and future work we've provided. 2. PREVIOUS WORKS Nowadays accident analysis in order to identify the affected factors and reduce the amount of damages has been considered by many researchers [7]. For predicting of the severity of occurred accidents, the comparison of algorithms classified as follows: Naive Bayesian classifier, AdaBoostM1 Meta classifier, PART Rule classifier, Decision Tree 48 classifier and Random Forest Tree classifier for classifying traffic accident records of the year 2008 produced by the transport department of government of Hong Kong. To finding the cause of accident and the severity of accident they did classified them into three different cases such as Accident, Casualty and Vehicle. The results of the comparison showed that the performance of Random Forest Tree classification algorithm is better than other methods. Juan de Ona and et al. in [8] used road accidents based on crash severity. To create decision tree (CART, C4.5) to classify. Obtained results showed that counts of generated rules by c4.5 algorithm is more than generated rules by CART algorithm. Also generated rules by CART have less training. But the problem that is important in creating decision tree is root node. The time we can analyze the whole rules of a database that chosen property for start node be different. One of the important subjects in road accidents is identify the main factor in severity of road accidents that researchers [9] to achieve this important affair used latent class cluster (LCC) algorithm to divide the accord accidents in Spain highway and by Bayesian networks to identify involved factors in severity of road accidents. Obtained results from this paper showed that combination of two LCC and Bayesian networks are more accurate than overall analysis of the accident data. Jianfeng Xi and et al. For the analyzing road accidents and to obtain the laws governing on happened accidents used PSO algorithm. In this research, to evaluate the results, has been used Delphi and Ttest model to applying the proposed method. Based on obtained results from this paper speed of analysis traffic accidents by using proposed algorithm is 10 times faster and the accuracy and stability of the provided methods is more than the usual accident analysis methods [10]. Mehmet Metin Kunt and et al. To predict the severity of road accidents using three methods: genetic algorithm (GA), Artificial Neural Network (ANN) with multilayer perceptron and pattern search (PS) in combination with a GA. In this research, three methods was used to evaluate and compare the three proposed methods: mean square error, mean absolute error and sum of squared errors. Results showed that the accuracy prediction of ANN model is more than the other two methods. And also specified relationships between the input parameters are better. On the other hand, advantages of using GA or combination of GA or PS model is that the coefficients of functions and relations are known [11].Neslihan Karsli and et al. ANN were employed to model traffic accidents that were developed based on input neurons of six models, that in this study the best model according to the akaike information criteria is selecting and statistical analysis was tested in a fault condition. It should be noted that this was a case study (in Turkey) [12]. Researchers [13] to impact of simultaneously investigate of human factors, road, vehicle, weather conditions and traffic (traffic volume and speed) the severity of traffic accidents on urban freeways began using ANNs. In this paper, after removing additional variables, 25 independent variables that have the greatest impact on output (based on mortality and injury) were selected.The results showed that the use of multilayer perceptron learning methods feed forward back propagation have better results. In [4], they began to solve the Traveling Salesman Problem with combining of PSO algorithm and COA algorithm. The results showed that the use of a somewhat COA algorithm is an exposure to prevent premature convergence to a local optimum. Hua Rong to find the optimal solution by combining two of PSO and COA algorithm used Tenet method. The results showed that the use of the Tent map as COA algorithm is more desirable than Logistic map, and its impact to prevent premature convergence is better than Logistic map [5]. 3. MATERIAL AND METHODS 3.1. Road Accidents Road accidents were the one of the most important causes of mortality and financial and human injuries, and its heavy social, cultural and economic phenomena strongly influenced human society. Unfortunately, in most cases, this important affair is ignored. In our country (Iran) this problem also become a disaster, so that Iran have been introduced in the top of countries that have most road traffic accidents that causes incidence and mortality. According to the annual report of World Health Organization in 2009, 12 million people were killed in road accidents, and more than 50 million people are injured. Taken estimation indicates that if one day any plan will not done to prevent accidents till next 20 years this statistics will grow to 65% [14]. Every day, in an average 3,000 people around the world die due to injuries from road traffics, Over 91% of deaths due to road traffic injury deaths occurs are in low and middle income countries. While there are only 48% of registered cars. Forecasts suggest is in coming years, in high-income countries, deaths from road accidents will be reduced but mainly in low-income countries and moderate increases. If no action is done until 2030, accepted that road accident become as the fifth cause of deaths that is equal to 2\4 million dead in year [14].Road accident not only exacts heavy burden on the

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national and international levels to the families but also exacts a heavy budget. Many families because of a lack of breadwinner and additional fees based on the individuals cares with disabilities that resulting from road traffic injuries, are extremely poor. But to prevent accident injuries minimal cost are needed [14]. Road accidents are investigated and solved incidents. Knowledge about the factors that have caused the accident is a valuable tool for predicting. If there be sufficient information and knowledge about road accidents, we can use science to analyze these data and affected factors and relationships between these factors in accident occurrence (damage, injury, death) and so then predict these accidents. At this stage after the identification and prediction of road accidents, can prevent one of the leading causes of accidents, especially fatal and damage crashes. Therefore, the rate of mortality and damages from road accidents can reduce. 3.2. PSO Algorithm PSO algorithm is an evolutionary algorithm for functional optimizing that is inspired by mass movement of birds that are looking for food. The problem that non-deterministic search algorithms are faced with is being in a local optimum and the global optimum is not available. In the first step of PSO algorithm for each particle, a random value is generated. Then, based on these values, the valuable value is calculated for each particle. However, if the value of valuable function does not have desired outcome, each particle is updated by using the following values:  Best position that particle has been able to reach it, this situation is called pbest and maintained.  Best position ever achieved by a particles population, this situation is called gbest and maintained.  The current position of each particle. These positions are displayed by , ( ) After finding the optimal values , speed and location of each particle is updated by using of equation (1) and (2). Then based on updated values until the value of valuable function reach to desired result or the number of steps don not finish, the cycle continues.

According to equation (1), this algorithm requires 5 variables (W, c , c , r , r ) that is a user-specified values and the values of these variables are highly effective in finding the optimal solution. w € [0.8, 1.2] is to represent the inertia weight [15], where 1 is the standard amount. [16] For local searches consider low value and for general searches high values. r , r : usually take place between [0,1]. c and c € [0, 2] represents are learning coefficients for pbest and gbest.The sum of these two numbers is not more than 4. [17]. Decrease of c and increase of c , will cause to move towards the optimum particles, so then the search space becomes smaller and by decrease of c and increase of c , movement filed of particle get larger. In many papers is provided several methods for improving the convergence rate.    

By increasing Inertia weight with time pass [19.18] using fuzzy method for initializing Inertia weight [20] initializing random inertia weight in the range [1,0] [21] the random inertia weight in the range of [1,0.5][22]

3.3. Chaos Optimization Algorithm COA for the first time in late of 1890 was introduced by Henri Poincaré. Chaos in a non-periodic long-term behavior in a deterministic system that shows highly dependent to the initial condition [23]. Chaotic Systems are nonlinear dynamic systems which are highly sensitive to their initial conditions. Small changes in initial conditions in such systems will cause changes in the future. Chaotic systems behavior are seemingly random. Chaotic systems are seemingly random behavior. However, there is no need to a random element to create of chaos behavior, and certain dynamical systems can also show chaos behavior. Since description of discrete dynamical systems in time perform with the aid of repetition maps, In this kind of systems a relationship as x = f(x ) exists between the points that system chooses where these parts together come to form a circuit. Therefore the purpose of mapping, a relation is a function from F: R → R where R is the set of real points by which the orbit o(x ) of the point x0 (belonging to the set of integers R) is defined in the group of points o(x ) = (x , f (x ), f (x ), … ) [23]. First-order state equation with consideringx = fn(x ), the equation is expressed to x = f(x )we can Classify mappings based on linearity to Lorentz and tent mapping and based on non-linearity to logistic mapping and hennon mapping. Mappings that used in this paper are as follows:

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 Logistic map [23]: the most popular non-linear mapping, which has been studied, Logistic map is a onedimensional mapping that is given by the following equation: Equation(3)xn+1 =axn +(1-xn )  Lorenz attractor [23]: Equation(4)xn+1 =

2xn , 0 ≤xn ≤

1 2

1 ≤x ≤1 2 n  Tent map [23]: this mapping is similar to the Lorentz mapping with this distinction that is benefit from variable parameter that changes in range. 1 rxn , 0 ≤xn ≤ 2 Equation(5)xn+1 = 1 r-rxn , ≤xn ≤1 2 2-2xn ,

COA has many applications, the most important ones are these applications: weather forecasts, management, economics, computer science, natural science, medicine, pharmaceuticals. 3.4. PSO and Chaos Chaotic models are the one of nonlinear models that are able to create very complex behaviors with certain assumptions. Thus, this theory can be used for improving the convergence speed and to optimize the PSO algorithm. Methods that obtained from combining of PSO and COA algorithm are classified as [19]: CEPSO1: amount of c variable where is updated by COA algorithm that indicates in equation (6) Equation(6)v , (t + 1) = wv , (t) + CM r (t) pbest , (t) − x , (t) + c r (t) gbest (t) − x , (t) CEPSO2: amount of c variable where is updated by COA algorithm that indicates in equation (7) Equation(7)v , (t + 1) = wv , (t) + c r (t) pbest , (t) − x , (t) + CM r (t) gbest (t) − x , (t) CEPSO3: amount of c and c variable where is updated by COA algorithm that indicates in equation (8) Equation(8)v , (t + 1) = wv , (t) + CM r (t) pbest , (t) − x , (t) + CM r (t) gbest (t) − x , (t) CEPSO4: amount of r , variable where is updated by COA algorithm that indicates in equation (9) Equation(9)v , (t + 1) = wv , (t) + c CM (t) pbest , (t) − x , (t) + c r (t) gbest (t) − x , (t) CEPSO5: amount of r

,

variable where is updated by COA algorithm that indicates in equation (10)

Equation(10)v , (t + 1) = wv , (t) + c r (t) pbest , (t) − x , (t) + c CM (t) gbest (t) − x , (t) CEPSO6: amount of r , and r , and variable where is updated by COA algorithm that indicates in equation (11) Equation(11)v , (t + 1) = wv , (t) + c CM (t) pbest , (t) − x , (t) + c CM (t) gbest (t) − x , (t) CEPSO7: amount of r , and r , and w variable where is updated by COA algorithm that indicates in equation (12) Equation(12)v , (t + 1) = CM v , (t) + c CM (t) pbest , (t) − x , (t) + c CM (t) gbest (t) − x , (t) CEPSO8: amount of w variable where is updated by COA algorithm that indicates in equation (13) Equation(13)v , (t + 1) = CM v , (t) + c r (t) pbest , (t) − x , (t) + c r (t) gbest (t) − x , (t) CEPSO9: amount of c and w variable where is updated by COA algorithm that indicates in equation (14) Equation(14)v , (t + 1) = CM v , (t) + CM r (t) pbest , (t) − x , (t) + c r (t) gbest (t) − x , (t) CEPSO10: amount of c and w variable where is updated by COA algorithm that indicates in equation (15) Equation(15)v , (t + 1) = CM v , (t) + c r (t) pbest , (t) − x , (t) + CM r (t) gbest (t) − x , (t) CEPSO11: amount of c and c and w variable where is updated by COA algorithm that indicates in equation (16) Equation(16)v , (t + 1) = CM v , (t) + CM r (t) pbest , (t) − x , (t) + CM r (t) gbest (t) − x , (t) 4. PROPOSED METHOD The combination of PSO and COA algorithm (Logistic map, Tent map, Lorenz attractor) led to 33 based on formulas presented in section 3.4. Now the question that arises is the selecting one of these methods as updating parameters in equation (1).In this paper, we used chaos factor to solve the problem. In fact the task of chaos factor in each irritation is selecting best method from 33 available methods. Implementation of the proposed methods is to be each particle for first time is generating set of rules based on available information and kind of road accidents. In fact, these rules represent the relationship between the involved factors in road accidents based on type of it. Generated rules by each particle through valuable function will be evaluated in comparison

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with random values with available facts (training data), If desired results are not achieved or the number of iterations aren't completed, values of each particle (rules)in next steps is based on pbest (the best values of the involved factors in accidents compared with training data on the particle itself),gbest(the best values of the involved factors in accidents compared with training data among all particles) the current position of each particle (current rules) and Some parameters are selected by chaos factor become up to date. Chaos agent in every stage of forecast, selected best method from production methods (combination of PSO and COA) then update parameter values with selected method. Performance process of this algorithm is shown in figure (1).

Fig. 1. Proposed Method

According to presented method achieves after repeating optimal Solutions (relationship between involved factors in kind of accidents). In fact, with access to this communication, we can predict road accidents. Finally, by using the rules, data sample tests were examined and the percentage of error is determined. Performance process of these predictions with assuming that the collected data have been processed and extra data have been omitted, are shown in Table 1. Table 1. Simulated proposed Pseudo-code 1-Ds=read data from dataset 2-Train_ds=get many random record for training 3-Exam_ds=get many random record for examining 4-Use pso algorithm and chaos agent for train with trainds 4.1. set the swarm size. Initialize the velocity and the position of each particle randomly. 4.2. for each j, evaluate the fitness value of xj and update the individual best position pbest if better fitness is found. 4.3. Find the new best position of the whole swarm. Update the swarm best position gbest if the fitness of the new best position is better than that of the previous swarm. 4.4. If the stopping criterion is satisfied, then stop. 4.5. develop new value for c1, c2, r1,r2,w with chaos agent 4.5.1. get best method of combine 11 method with COA 4.6. For each particle, update the position and the velocity according (1) and (2). Go to step 2. 5- Result= Evaluated according to the rules 6- Review and evaluate result

5. RESULTS EVALUATION The investigated data in this paper, the accident occurring at the axis of West Azerbaijan is in time ranges of the 6 months of 2011. This data is received from department of transportation and terminals of West Azerbaijan province in the form of 114 com forms, it should be noted that the data has been used in the paper [2]. After perform operation before processing data, we used PSO algorithm and chaos factor to extract behaviors and

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relationships between relationships, the results of combination of PSO algorithm and COA algorithms based on 6 to 16 formulas from 724 counts that from this 724, 579 episode are training data and 149 episode are experimental data that shown in table2. As it is represented in Table 2, Outcome of the combination of COA algorithm and PSO algorithm, it has better performance when we use tent mapping as COA algorithm than we use Logistic map optimization and Lorenz attractor optimization algorithm. Also according to the results of the parameters adaptation based on CEPSO9, CEPSO11 it can be say that, the combination with COA algorithm don't always improves performance of PSO algorithm. Table 2. Obtained results from PSO algorithm and COA algorithm

Logistic Map Lorenz Attractor Tent Map

T F T F T F

CEPSO1

CEPSO2

CEPSO3

CEPSO4

CEPSO5

CEPSO6

CEPSO7

CEPSO8

CEPSO9

CEPSO10

CEPSO11

0.96 0.04 0.97 0.03 0.98 0.02

0.96 0.04 0.97 0.03 0.98 0.02

0.86 0.14 0.94 0.06 0.97 0.03

0.97 0.03 0.976 0.024 0.98 0.02

0.96 0.04 0.969 0.031 0.97 0.03

0.969 0.031 0.967 0.024 0.976 0.024

0.88 0.12 0.969 0.031 0.97 0.03

0.84 0.16 0.96 0.04 0.97 0.03

0.65 0.35 0.66 0.34 0.67 0.33

0.67 0.33 0.88 0.12 0.96 0.04

0.66 0.34 0.61 0.39 0.61 0.39

Performance of combination of PSO algorithm with three algorithms of COA (Logistic, Lorenz, and Tent) have shown in figure (2-3). According to figure (2), the percentage of correct predictions of each combined COA algorithm with PSO algorithm can show the improve performance of combined PSO algorithm can be expressed as follows:  Combination with tent map  Combination with Lorenz attractor  Combination with tent map Except that when the PSO algorithm based on Logistic map is combined with CEPSO11 method have better performance than combination with Lorenz attractor and tent map. Figure (3) illustrates the percentage of false predictions of each combined COA algorithm with PSO algorithm. According to the presented charts in Figures (2) and (3), can be said that obtained results from the combination of (PSO & Logistic map) based on 6 to 16 formulas is more steady than (PSO & Lorenz attractor) combination and (PSO &Tent).

Fig. 2. The combination of COA and PSO algorithms to predict traffic accidents( truth)

Fig. 3. The combination of COA and PSO algorithms to predict traffic accidents (fault)

As Figure (4) indicates that using the chaos factor except the time when are used from CEPSO11 and CEPSO9 methods as updated formulas in different mappings that cause to PSO algorithm have better performance.

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Fig. 4. The combination of COA and PSO algorithms to predict traffic accidents

According to in each iteration, the optimal values for update is selecting by chaos factor, Therefore, the performance of this algorithm is better than (PSO & Logistic map) combination and (PSO & Lorenz attractor) and (PSO & Tent map) combination, that Figure(5) also indicates it.

Fig. 5. comparison of PSO algorithm and chaos factor with combination of PSO and COA for predicting road accidents

The results of applying the presented method (PSO & Chaos Agent) and comparison it with (PSO & COA) methods and PSO have shown in Table (3). Table3. Comparison of presented method with PSO

PSO Propos ed Method

T F T

CEPSO1 0.89 0.11 0.98

CEPSO2 0.89 0.11 0.98

CEPSO3 0.89 0.11 0.97

CEPSO4 0.89 0.11 0.98

CEPSO5 0.89 0.11 0.97

CEPSO6 0.89 0.11 0.976

CEPSO7 0.89 0.11 0.97

CEPSO8 0.89 0.11 0.97

CEPSO9 0.89 0.11 0.67

CEPSO10 0.89 0.11 0.96

CEPSO11 0.89 0.11 0.66

F

0.02

0.02

0.03

0.02

0.03

0.024

0.03

0.03

0.33

0.04

0.34

6. CONCLUSIONS AND FUTURE WORKS For perform accurate prediction of road accidents we need to find optimal relationships among the affected factors in road accidents. Therefore in this paper to find involved factors in accident occurrence and the relationships between these factors and parameters of PSO algorithm for optimization with COA algorithms (Tent map, Logistic map, Lorenz attractor) that adopted as chaos factor. Note that in each iteration, the optimal combination is selected by the chaos factor, Therefore, when the parameters of PSO algorithm that are initialized by chaos factor, obtained results will improve. According to performed simulations on input data (724 counts of accidents occurring are at the axis of West Azerbaijan province in Iran).Using MATLAB tool to outcomes of predict based on the type of road accidents by PSO algorithm and chaos factor get 0.083 percent better than classic PSO algorithm. Therefore, based on these results, the combination of PSO algorithm and chaos factor can be used in future applications and statistical programs used for various data mining. ACKNOWLEDGEMENTS We take this opportunity to thank staff members of West Azerbaijan Transportation and Terminals Organization for the valuable datasets presented by them in their respective fields. We grateful for their cooperation during the period of our research. REFERENCES 1. John Richardson,” Accident Related Factors”, traffic accident causation in Europe (TRACE), Project No. 027763, Europe, V3: September 2009. 2. Farhad Soleimanian Gharehchopogh, Zahra Asheghi Dizaji, and Zahra Aghighi,” Evaluation of Particle Swarm Optimization Algorithm in Prediction of the Car Accidents on the Roads: A Case Study”, International Journal on Computational Sciences & Applications (IJCSA), 3(4): 1-12(2013). 3. Bilal Alatas, Erhan Akin, A. BedriOzer,”Chaos embedded particle swarm optimization algorithms”, Chaos, Solutions and Fractals, 40:1715–1734, (2007).

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