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Journal of Advanced Transportation
Volume 2017, Article ID 9754508, 14 pages
Research Article

A Novel Trip Coverage Index for Transit Accessibility Assessment Using Mobile Phone Data

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China

Correspondence should be addressed to Xiqun (Michael) Chen; nc.ude.ujz@nuqixnehc

Received 30 November 2016; Accepted 18 January 2017; Published 13 February 2017

Academic Editor: Xiaoyue Liu

Copyright © 2017 Zhengyi Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Transit accessibility is an important measure on the service performance of transit systems. To assess whether the public transit service is well accessible for trips of specific origins, destinations, and origin-destination (OD) pairs, a novel measure, the Trip Coverage Index (TCI), is proposed in this paper. TCI considers both the transit trip coverage and spatial distribution of individual travel demands. Massive trips between cellular base stations are estimated by using over four-million mobile phone users. An easy-to-implement method is also developed to extract the transit information and driving routes for millions of requests. Then the trip coverage of each OD pair is calculated. For demonstrative purposes, TCI is applied to the transit network of Hangzhou, China. The results show that TCI represents the better transit trip coverage and provides a more powerful assessment tool of transit quality of service. Since the calculation is based on trips of all modes, but not only the transit trips, TCI offers an overall accessibility for the transit system performance. It enables decision makers to assess transit accessibility in a finer-grained manner on the individual trip level and can be well transformed to measure transit services of other cities.

1. Introduction

Public transportation plays an important role in solving traffic problems in urban cities. It is well recognized among transportation planners that transit accessibility is an important measure of the service performance. The Transit Capacity and Quality of Service Manual summarized spatial, temporal, information, and capacity availability factors of public transit systems [1]. A major concern in the public transit sector has been the adequate assessment of access to transit services. Measures of transit accessibility are important in assessing existing transit services, allocating investments, and making decisions on the land development [2]. Transit accessibility has been one of the key indicators of transit planning, performance evaluation, and quantification of the level of service. Transit system planners design the layout of transit lines and stops to improve accessibility and enhance the transit attractiveness. One of the recent research concerns is the extent to which public transit systems enable the less privileged population of privately nonmotorized travelers to access the systems more conveniently, efficiently, and comfortably [3]. To achieve this objective, the first question we need to answer is: How to assess accessibility of public transit for trips in a network with spatially and temporally nonuniform travel demands?

As shown in Table 1, modeling public transit accessibility has attracted numerous research efforts in the past decades, primarily including the evaluation of the spatial coverage [46], temporal coverage [710], and trip coverage [1113]. Since passengers’ departure time varied according to their own need, Owen and Levinson calculated continuously in time for the evaluation of transit systems rather than at a single of a few departure times [14]. On the other hand, more and more research combined the spatial coverage and temporal coverage to assess transit accessibility. For instance, Mavoa et al. combined public transit, walking accessibility index, and transit frequency to calculate accessibility at the parcel level [15]. Mamun et al. combined the spatial coverage, temporal coverage, and trip coverage to measure public transit performance [16]. El-Geneidy et al. incorporated both travel time and transit fares to determine whether people residing in socially disadvantaged neighborhoods [17].

Table 1: Summary of transit accessibility measures.

Based on the literature review it is evident that most assessment models belong to the physical location-based proximity analysis, while few studies take into account the transit coverage of individual travels in a real-world large-scale network; most of the existing transit accessibility measures account for the spatial and temporal coverage, while very few studies consider the trip coverage; the accessibility metrics produced by most existing tools are therefore static in the sense that they describe the transit system but consider less the temporal variability of individual travel demands. To assess whether the public transit service is well accessible for trips of specific origins, destinations, and origin-destination (OD) pairs, a public transit accessibility measure coping with the trip coverage is needed to provide a more reasonable assessment of transit quality of service.

There are some reasons for the gap of the previous studies. In the past, multiple sources of data required to evaluate transit accessibility considering individual travel demands are difficult to collect and consequently extensive efforts are required in order to obtain the useful data. In particular, it is difficult to measure real-world travel demands due to the small amount of household survey data in the past. In addition, many surveys are zone based and unable to describe individual travel behavior. In some cases, public transit operational data (e.g., stops, routes, schedules, frequencies, and hours of operation) may be hard to access and data fusion could become uneasy due to their inconsistent formats in the time scale and data particle size [18].

Fortunately, the recent advent of data collection technologies, for example, mobile phone signaling data and automated vehicle location, has shifted a data-poor environment to a data-rich environment and offered opportunities to conduct comprehensive transit system performance evaluation. For example, cell phone signaling data have emerged to be a widely used resource to measure both individual travel behavior and network demand, for example, individual human mobility patterns [19, 20], estimation of OD matrices [21], and OD trip purposes [22]. On the other hand, more and more web map service data become readily available for public use, for example, Google Maps APIs [23], Baidu Map API [24], and AMAP Open Platform [25], which can provide massive on-demand transit trip planning services in real time. Ma and Wang developed a data-driven platform for online transit performance monitoring using automated fare collection and automated vehicle location [26]. Ma et al. developed a series of data mining methods to identify the spatiotemporal commuting patterns of public transit riders using one-month transit smart card data [27]. Therefore, new accessibility indicators taking into account individual trips will definitely provide a more powerful tool.

This paper is aimed at presenting a new public transit quality of service measure, the Trip Coverage Index (TCI), which takes into account both the trip coverage for transit systems and the spatial distribution of heterogeneous and dynamic individual travel demands. The TCI provides a quantitative measure of transit accessibility on the basis of massive trips collected from mobile phone data. The transit accessibility information is extracted from the Baidu Map with the Python code implementation, for example, the access to transit facilities, transit routes (shortest in time/length and alternatives), transit on-vehicle time, and OD connectivity. The novel measure of transit service performance fills the research gap that the conventional spatial coverage index does not consider the coverage to individual trips or the percentage of travel demands that can be served by the transit systems.

The rest of the paper is organized as follows: Section 2 presents the methodological approach to the trip coverage analysis, which is different from the conventional spatial coverage of transit services. In Section 3, an illustrative and tractable numerical example is employed to present how to calculate TCI and compare it with the conventional measure of spatial coverage. Section 4 shows the field data utilized in this paper and presents results of a real-world city-wide case study that applies TCI to the transit network of Hangzhou, China. Finally, Section 5 concludes the paper and outlooks the future research.

2. Methodology

In this part, we first propose a new method to acquire the transit route information for millions of trips determined from the mobile phone data automatically based on online map and programing; then a new public transit quality of service measure (TCI) is proposed considering the access to transit facilities, transit routes information, driving routes information, and OD connectivity. The development of the proposed TCI requires several steps and the framework is shown in Figure 1. The first step is to acquire travel flows between cellular base stations using mobile phone data. Second, the information of transit services and driving routes between each OD pair is then extracted by accessing the online map service for millions of times. Third, the transit trip coverage from base station m to base station is estimated based on the data retrieved from the online map. Fourth, TCI from Zone to Zone is estimated using the transit trip coverage and travel demand between the base stations. Each of the key procedures of the transit accessibility assessment will be presented in the following sections.

Figure 1: Estimation framework of TCI.
2.1. Trip Estimation

In this section, we introduce the mobile phone data and present the methods used to determine trips from the mobile phone data.

2.1.1. Mobile Phone Signing Data

The dataset used in this study consists of two tables in the database: one is the base station table and the other is the anonymous table of mobile phone records. The mobile phone record is generated when a device connects to the cellular network in any of the following cases:(i)when the phone makes or receives a call;(ii)when the phone sends or receives a message;(iii)when the phone is switched on or off;(iv)when the user moves from one base station to another; or(v)when the system sends the periodic location update request on the phone, for example, 2 h.

The mobile phone signaling data contain Call Details Records (CDR), which were previously utilized to estimate OD demands in numerous related studies [1922]. Each record of the mobile phone signaling data contains an anonymous user ID, base station ID, and timestamp at the instance of the phone communication with the base station. The base station table contains the base station ID, longitude, and latitude. There are more than 52 thousand of base stations in the urban area of Hangzhou, China. The average covering radius of each base station is less than 100 m.

2.1.2. Determining Trips

In order to infer trips from the mobile phone signaling data, the first step is to filter out noise resulting from one base station to another. The call balancing is conducted by the mobile service provider, which creates the appearance of false movements, and distinguishes users’ stay locations. Once the stay locations are determined, we evaluate the trips as paths between a user’s consecutive locations. To achieve this, we estimate the trips by employing the method of using mobile phone traces data [20]. The estimation is carried out as follows:(i)Each mobile phone signaling record is characterized by a position expressed by latitude, longitude, and a timestamp for the th observation of a given anonymous user .(ii)Then the signaling records are connected into a sequence of records according to their time series.(iii)If the signaling record series satisfy the criteria, (I) ; (II) , which mean a user should stay in an area with the radius (set as 200 m) over a certain time interval (set as 30 min). Then the points are fused together by selecting the point with the longest stay time as the stay location.(iv)We evaluate paths between a user’s stay locations at consecutive points, and the stay locations are assumed to be trip origins or destinations.

2.2. Extracting Transit Routes from an Online Map
2.2.1. Online Map Service

Calculating the trip coverage indicators requires a database with transit data such as the transit network, road network, operational transit information, and bus stops. Based on those data, we know how many transit lines serve the trips from base station m to n and how large the distance is from base station m to n by transit line l and other associated information. Some literatures collected data based on Google Transit or GTFS (General Transit Feed Specification), a supplemental service to Google maps [3, 9, 18]. In those studies, the public transit network in a GIS format and the road network data were required, however, which were difficult to acquire as the data might be from different sources and difficult to use since the data must share the same coordinate, scale, context, and so forth [18].

More and more online map services provide path navigation in China, for example, Baidu Map and AMAP. If the user selects the transportation mode, enters the origin and destination, and chooses a departure time on the map website, it will return the route planning information including the trip distance, trip time, and suggested routes from the origin to destination. Some online map services provide open resources to developers, which are mostly in the form of the Application Programming Interface (API). The API is a set of predefined user applications and the operating system’s function, by means of which programmers can easily achieve the underlying operating system feature development or packages. Launched in April, 2010, Baidu Map API [24] not only includes the basic interface to build maps, but also provides information such as local search, route planning, and other data services, through which we can acquire the route information of trips. However, since it needs to search the transit route information for millions of trips completed by over 4 million mobile phone users for a week in Hangzhou, it is impossible to manually acquire such huge information.

As shown in Figure 2, we propose a new method to acquire the transit route information for millions of trips automatically. The trip database stores millions of trips on a local computer server (each trip includes origin/destination geolocations and departure and arrival time). The Python code extracts one piece of trip data and makes an API request to the Baidu Map server via HTTP for the transit route data and the server will return data in the form of XML or JSON after it queries the back-end database. After that we call JSON parsing functions [28] and store the result to the database.

Figure 2: Web scraping of transit information.
2.2.2. Transit Routes Data

The response of the transit route information from the Baidu Map API contains fruitful information and we just extract the useful information for assessing transit accessibility, for example, the taxi route information and bus route information. An example of response is shown in Table 2. The status code indicates whether the online service returns valid results, 0 means a correct record, and 1 means invalid information. The taxi route information includes the taxi distance of the trip, taxi travel time, and monetary costs. The bus route information is much more complicated. There may be several suggested bus schemes per trip and several segments per bus scheme. In addition, the segment_type code means the travel model (e.g., 5 for walking, 3 for bus).

Table 2: A sample of the transit route information from the Baidu Map API.

Generally, there are three segments per scheme in a direct transit route without transfer, which means that the trip distance from origin base station to destination base station by taking transit line consists of the access distance by walking, in-vehicle distance by bus, and egress distance by walking, given by

2.3. Trip Coverage Index

The conventional evaluation criterion for the transit service includes the transit spatial coverage area, which is usually estimated using the buffer area covered by the transit route or by the area within a walking distance threshold of a transit stop or transit route [1]. The walking distance threshold is modified for various features, for example, the percent elderly in the population and street connectivity [29]. It is commonly accepted by transit planners and researchers that bus transit users are willing to walk up to 1/4 mile (400 m) to reach their nearest transit stop [3033]. The government agencies and researchers of China use 500 m as the buffer radius to evaluate the transit serving area [34, 35]. The sensitivity of the walking distance threshold will be analyzed in Section 4. In the context of transit, a traveler may transfer from one bus route to anther and continue to reach his/her destination. According to Modesti and Sciomachen [36], more than two times of transfers in a transit trip are generally intolerable for transit users, such that two transfers can be chosen as the maximum value allowed per trip.

Based on the aforementioned idea, this paper presents the binary connectivity parameter () to indicate whether two regions are connected by transit services. Here we only consider walking to reach the transit station and other options such as bike, park, and ride have not been considered. For any trip from base station to , if there exists a transit line that connects the two regions; both the access and egress distances are smaller than the preselected walking distance threshold; and the transfer count is less than the transfer tolerance threshold N, then the binary connectivity parameter is 1; and 0, otherwise. The binary connectivity parameter is given by

The research concern is the extent of the efficiency and attractiveness of the public transport system compared to private cars. As is known to all, there are many factors that may influence the travel mode choice such as travel time, transit distance, transit fare car parking fare, and weather. However, this paper is not concerned with individual travel mode choice behavior but provides the trip-level assessment of transit accessibility, so we just take into account the travel time and travel distance. On the other hand, the developed index (i.e., TCI) is applied to assess accessibility of public transit for all trips, not only those currently or likely to be using transit and no matter whether he/she owns cars or not. Instead, they can rent a car or take a taxi to reach the destination for those have no access to personal car. Therefore, the trip coverage from base station to served by the transit line , that is, , is measured by the ratio of the driving distance to the transit distance from base station to by transit line and the ratio of the total travel time by driving to the total travel time by transit line , given by where the weighting factor can be determined according to the preference on travel distance or travel time by decision makers. The default value is 0.5.

Considering there may be serval transit lines or no transit lines serving the trip, we select the maximum value between 0 and multiplied by the binary connectivity parameter as the trip coverage score for the OD pair in the network, given by where the trip coverage score takes into account the OD pairwise transit accessibility which is rarely considered by previous studies.

There are some short trips, of which the distance is shorter than the walking distance threshold. In other words, it is unnecessary to take bus for this trip. So when calculating TCI, we only consider the trips with a distance longer than twice of the service access distance threshold, that is, 1,000 m.

The spatial relationship between TAZs and base stations (BSs) can be obtained by the ArcGIS spatial analysis toolbox. The TAZ-BS membership table can be obtained, which is the foundation of calculating TCI from TAZ to . TCI from TAZ to is defined as the weighted average trip coverage score () by the travel demand, given by

TCI can be used to quantify the coverages of origin TAZ and destination TAZ , given by

3. An Illustrative Numerical Example

This section provides a tractable numerical example to illustrate the application of TCI to the assessment of transit accessibility. As shown in Figure 3, we consider a road network of four zones served by three transit lines, and each line has four stops. The dashed circles represent 500-meter buffers around each transit stop.

Figure 3: An illustrative road and transit networks.

Table 3 shows the travel demands between base stations and the trip coverage results for the trips. Columns 4 and 5 of Table 3 show which TAZs base stations and belong to, respectively. Column 6 provides the number of transit lines serving the OD pair. Columns 7–13 present the transit route information which can be obtained from the online map for a real-world network. The binary connectivity parameter for each transit line estimated by (2) is shown in Column 14.

Table 3: Trip coverage calculation.

The illustrative numerical example helps understand the difference between the proposed measure and the conventional spatial coverage measure. There are two lines and two bus stops serving BS1, while there is only one transit line and one bus stop serving BS2. At the same time, there are two bus lines serving trips of BS1–5 and only one bus line serving trips of BS2–5. It is reasonable to expect a higher level of transit coverage for BS1–5 than that of BS2–5. However, for trips of BS1–5, of both line 1 and line 2 (see Column 11 in bold in Table 3) exceed the preselected distance threshold (500 m), and the binary connectivity parameters for both lines are zero, which means no buses can offer services to trips of BS1–5 given the stop buffer distance threshold.

Column 15 shows the trip coverage of different OD pairs, that is, estimated by (3)-(4). For BS1–6, is calculated as follows and other OD pairs can be calculated in the same way:

Table 3 shows that driving distances of BS1–3 and BS2–5 have the same value of 1400 m, but the transit route distance of BS1–3 is longer than that of BS2–5, which means the transit route of BS1–3 makes a detour and the connectivity level is lower than that of BS2–5 (see Columns 7, 13, and 15 in bold in Table 3). This situation is embodied in the calculation of .

Finally, TCI from TAZ to should incorporate the trip coverage with the travel demand of the trip. TCI for TAZ 1 to 4 can be calculated according to (5) and the results are shown in Table 4.

Table 4: TCI and travel demand (in brackets).

The for TAZ 1 as the origin can be calculated by

Similarly, other and can be obtained. Results of the trip coverage as well as the travel demand of each OD pair are shown in Table 4. It has been realized that the trips in the opposite direction have the same trip coverage scores as Table 3, for example, trips of BS1–6 and BS6–1 (see italic rows in Table 3) and trips of BS1–3 and BS3–1. This is because the bus lines are set two ways in this numerical example. However, the zone-to-zone TCIs in the opposite directions show different scores, for example, TCI1,4 and TCI4,1 highlighted in Table 4. Recalling the contents indicated by asterisk of Table 3, we find that the demands from Zone 1 to Zone 4 and from Zone 4 to Zone 1 are different in opposite directions, which means the transit system covering more travel demands has a higher value of TCI.

TCI also offers a way to quantify the transit service level of OD pairs that require a transfer between transit lines. Equation (3) can be improved by considering the transfer distance and transfer travel time , given by

The spatial coverage is the proportion of the area served by transit stops, which can be calculated by the Transit Capacity and Quality of Service Manual [1]. This method uses a buffer (set as 500 m) around each stop to define the spatial coverage of bus services. Table 5 shows the zonal data of the spatial coverage calculations and the corresponding TCI results. The buffer area for each stop is calculated using the ArcGIS toolbox and the overlapped buffers are calculated only once. The results show that the spatial coverage of Zone 1 is much higher than that of Zone 2, while the TCI of Zone 1 is lower than that of Zone 2, which are highlighted in Table 5.

Table 5: Zonal data of spatial coverage and TCI.

4. Case Study

4.1. Study Area and Data

In this section, TCI is applied to a case study in Hangzhou, China, to assess the transit accessibility. Hangzhou is the capital and most populous city of Zhejiang Province, China. As shown in Figure 4, the study area contains the Shangcheng District, Xiacheng District, Jianggan District, Binjiang District, Xihu District, Gongshu District, and part of Xiaoshan District. The study area is 955 km2, and it contains 540 TAZs with 4.43 million residents. As shown in Figure 4, there are 912 transit lines and 18,508 transit stops in the transit network of Hangzhou.

Figure 4: Layout of transit and the average base station coverage radius in terms of TAZs in Hangzhou, China.

The mobile phone signaling data used in this study consist of two tables, that is, the base station table and the anonymous mobile phone records table collected from 4.17 million mobile phone users in Hangzhou over one month between August and September, 2015. The position accuracy of a trip is determined by the coverage radius of base stations. There are 41,823 base stations in the 540 TAZs, and the average BS coverage radius for each TAZ is shown in Figure 4. Results show that the average coverage radius of 90% base stations is less than 100 m. The remaining 10% are distributed in less populated areas such as the mountainous and wetland areas shown in Figure 4.

The study time periods are AM peak hours (7:00–9:00) and PM peak hours (17:00–19:00). After processing the mobile phone signaling data using the method proposed in Section 2.1, we obtain 2,816,910 trips in AM peak hours and 2,756,187 trips in PM peak hours on September 8, 2015, a regular working day. The desire lines of trips are shown in Figure 5. The average trip distance is 5.68 km and more than 50% of the trips are less than 3 km.

Figure 5: Desire lines of OD trips during the AM peak hours.

We also obtain spatial and temporal distributions of the population density using the trip information, for example, origin, destination, and timestamp. As shown in Figure 6, the population distribution is dispersed before 7:00 and after 20:00 and is aggregating during working hours. These observations are consistent with the daily experience.

Figure 6: Spatiotemporal distributions of population density using mobile phone signaling data (September 8, 2015).
4.2. Results

Combining both the mobile phone data and transit information extracted from the online map service, we are able to calculate the TCI for different time of day. The analytical results are as follows: the distribution of in the AM peak hours and PM peak hours are shown in Figures 7(a)-7(b). We can see a totally different picture of in the AM peak hours as compared to that in PM peak hours, which indicates that some of the vary during different periods while the transit routes and departure interval are the same, which is similar to the findings of [37]. Based on those pictures, we should have different principles and strategies in terms of deploying our bus-related resources and services. Most of the in the AM peak hours are higher than those in the PM hours according to Figure 7(c) and the outliers show that of some TAZs significantly vary with time periods and different travel demands. Transit operators should reschedule transit routes in a dynamic manner to be more consistent with travel demands.

Figure 7: Distributions of TCI of TAZs during peak hours ( = 1000 m, = 0.5).

As shown in Figure 8, results are compared with the spatial transit coverage during the AM and PM peak hours, respectively. of TAZs is a skewed distribution, and most of the is lower than 0.5, which means the transit system provides a poor coverage for the travel demand, while the spatial transit coverage calculated by the buffer method shows higher scores in both peak hours, which means most of the population can access to the bus stops in the walking threshold. The comparison between and the spatial transit coverage shows the bus stops which can be accessed in the walking threshold may not lead travelers to their destinations by transit services.

Figure 8: Comparison of with the spatial transit coverage during AM and PM peak hours ( = 1000 m, = 0.5).

In order to further explore the sensitivity of the walking distance threshold, acceptable times of transfer, and the weighting factor , we summarize the statistics of TCI in terms of these factors in Figure 9. As shown in Figure 9(a), as the walking distance threshold rises from 500 m to 900 m, the TCI of whole network rises significantly; then it slows down after the walking distance threshold is longer than 900 m, which means that transit operators could gain more trip coverage by improving bus services for those travel demands that the walking distance is under 900 m.

Figure 9: Sensitivity analysis for transit network.

As the acceptable transfer times increase from 0 to 2, the TCI increases both during the AM peak hours and PM peak hours, which is comparable with experience. The results suggest that increasing the transit route crossings would provide a better transit service.

We also explore the interaction between the weighting factorα and TCI. The larger value ofα is, the more weight of travel distance is considered in the TCI. Figure 9(c) shows that TCI increases with in all transfer scenarios, which means TCI is sensitive to ratio of the bus travel time and the driving time. So we should promote the travel time reliability of buses to provide a better transit service.

5. Conclusions

In this paper, the novel TCI is proposed for measuring transit connectivity and accessibility. It is built on the existing transit service measures and allows us to analyze the transit connectivity and accessibility for massive trips between the origin and destination, as well as the transit coverage from or to a TAZ. This paper is among the first attempts considering the connectivity of trips from point to point and real-world complicated travel demand in a large-scale urban area. The TCI developed in this paper provides the capability to quantify the level of accessibility of the transit system and vary the assessment of transit accessibility with the temporal and spatial change of travel demands.

This paper also presents an easy-to-implement method to acquire the transit route information for millions of trips based on the online map. Since the data is acquired automatically using computer programming, it is possible to easily construct the data repository and analyze large public transit networks.

TCI can be applied to all trips, not only those currently or likely to be using transit, such that TCI is demonstrated as an overall measure of transit accessibility and can be used to measure how the transit system reaches its target, which is to provide services for more potential users.

Through the case study of Hangzhou, we find that fluctuations in the travel demand in different time periods make TCI distributing diversely across the city, which means transit operators should reschedule transit routes in a dynamic way to be consistent with travel demands. The sensitivity analysis is performed to determine how the walking distance threshold, times of transfer, and the weighting factor would impact the network-wide TCI. The results can provide operators targeted measures to improve transit services.


:Service access distance threshold
:Distance from base station to by car
:Travel time from base station to by car
:Total distance from base station to by transit
:Transfer count from base station to by transit
:Total travel time from base station to by transit
:Access distance from base station to by transit
:Egress distance from base station to by transit
:Origin traffic analysis zone (TAZ)
:Destination TAZ
:Transit line
:Origin base station
:Destination base station
:Travel demand from base station to
:Travel demand from TAZ to
:Trip coverage from base station to by transit
:Trip coverage from base station to
:Trip coverage index from TAZ to
:Trip coverage index of origin TAZ
:Trip coverage index of destination TAZ
:Trip coverage index of a transit network
:Binary connectivity parameter, 1 if a transit line connects the trip from to with and smaller than ; 0 otherwise.

Competing Interests

The authors declare that they have no competing interests.


This research is financially supported by Zhejiang Provincial Natural Science Foundation of China under Grant no. LR17E080002, National Natural Science Foundation of China under Grant nos. 51508505, 51338008, and 51278454, and Hangzhou Municipal Science and Technology Commission under Grant no. 20142013A57. Mr. Yanlei Cui helped in processing some of the data used in this paper, and his assistance is gratefully acknowledged.


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