The economic assessment of the impacts of storm surges and sea-level rise in coastal cities requires high-level information on the damage and protection costs associated with varying flood heights. We provide a systematically and consistently calculated dataset of macroscale damage and protection cost curves for the 600 largest European coastal cities opening the perspective for a wide range of applications. Offering the first comprehensive dataset to include the costs of dike protection, we provide the underpinning information to run comparative assessments of costs and benefits of coastal adaptation. Aggregate cost curves for coastal flooding at the city-level are commonly regarded as by-products of impact assessments and are generally not published as a standalone dataset. Hence, our work also aims at initiating a more critical discussion on the availability and derivation of cost curves. Such relations take the form of damage cost curves and are used by researchers as an essential ingredient for the estimation of economic loss due to sea-level rise and the associated intensification of storm surges3. In a wider sense, they constitute the starting point for the appraisal of the benefits of adaptation in light of climate change4. Despite their pivotal role in the workflow leading to economic assessments of coastal impacts and adaptation, academic literature has put little scrutiny on the derivation of cost curves or their comparison.Establishing the relation between economic loss and flood height is a crucial step in the elaboration of flood-damage assessments in coastal zones, be it at global5.Mainly seen as a by-product of the impact assessment itself, damage cost curves are generally not published as a standalone dataset. At the case-study scale, damage cost curves are rarely derived in a consistent manner, with regard to the data sources for assets at risk and the employed cost methodology. These factors severely limit the comparability of cost results and renders the synthesis of knowledge embedded in such curves a daunting task. In order to advance the comparability of forthcoming impact assessments of coastal flooding, and to initialize a more critical discussion on the availability and development of cost curves, this work releases a consistently derived set of macroscale damage and protection cost curves for the 600 largest European coastal cities. We employ the term macroscale to indicate that the curves are obtained for the entity of the city, and also to differentiate our cost curves from depth-damage functions for single elements at risk 6, the data and processes chosen for the elaboration of the cost curves must, on the one hand, contain a certain degree of spatial detail to capture the city/landscape specificities that play an important role in shaping the magnitude of the impacts. On the other hand, it is mandatory for the objectives of this work - comparability and transferability - that data retains a certain level of universality in order to be generically available. The balancing of these two opposing premises shaped to a large extent the primary data choices made in this study.Given the local character of damages and adaptation8. The use of land-use information guarantees that our main object of analysis is the built-up city itself and not a less consistent approximation based on regional political or socio-economic consideration. Regarding hydrological modeling, we make use of a high resolution digital elevation model for Europe for determining areas at risk from flooding. To generate inundation maps, we employ a simple though commonly used static-inundation model that only accounts for hydraulic connectivity. Because we are interested in determining the rise of direct monetary damage with increasing flood height, we raise the flood height in small incremental steps up to a maximum of 12 m. This range was chosen to cover potential extreme sea levels both under current and future conditions9.Our approach differs from previous studies estimating potential damage from coastal flooding by employing land-use information as the basis to approximate the location of assets, rather than using population coupled with GDP per capita, as found in similar studies10–12, the existence of a consistent database of damage cost curves at city-scale will unlock new potential for the systematic analysis of coastal damage from sea-level rise in cities.The benefits of the damage cost curves to the scientific community are manifold. At the foremost, the comparability between alternative cost curves for different cities will be improved. The large number and size range of cities investigated makes room for further quantitative insights on the characteristics of cost curves. Because the provided cost curves embed in themselves a measure of asset vulnerability they only require information of typical or expected flood events for a given city in order for damage assessments to be performed. As regional and global datasets on sea-level rise and storm surges become available at increasing resolutionsUnique to this work is the evaluation of the protection needs of urban land within a city at increasing levels of coastal flooding. The protection cost curves describe the relation between the construction cost of coastal protection (whose costs are approximated by those of building dikes) and the designated protection height. The curves provided allow to contextualize the adaptation efforts expected in each city, while at the same time providing impact researchers with the underpinning information to run comparative assessments of costs and benefits of coastal adaptation.In this study, we derive macroscale damage and protection cost curves for European coastal cities. The cost curves are a product of combining information about the orography and land cover of a city and merging these with statistical information on land use and its associated monetary value.It is relevant to underline that only European cities are considered, given the availability of some datasets and the restrictions imposed, namely a consistent classification of land cover and land use. 13–15. Following this approach, we make use of the EU-DEM16 to model hypothetical inundation at the European coast at a horizontal resolution of 25 m  have received much attention in flood modeling and have been established as an important data source for large-scale damage assessments25 m see .17, we estimate areas that are hydraulically connected with the sea at a given sea level. A flood-fill algorithm using 8 nearest neighbors18 determines grid cells that are flooded at a presumed flood height. For each of these, we store the corresponding inundation depths. The whole procedure is repeated for flood heights between 0 m and 12 m in steps of 0.5 m. An example for the inundated area and the corresponding inundation depths is given in Employing a static inundation scheme20 to the CORINE 2012 Land-Cover dataset21 , which define the maximum distance between connected cells and the specific land-cover classes included . From these coastal clusters, the 600 largest (by area) are selected for further investigation. A breakup of the number of selected clusters per country is given in It should be noted, that the clusters do not correspond to administrative boundaries but represent connected areas of urban land cover. Hence, it is possible that the algorithm combines adjacent cities within one urban cluster. For instance, our analysis provides a joint cluster for the so-called Flemish Diamond, an urban agglomeration comprising the major cities of Antwerp, Ghent, Louvain, and Brussels. In two cases (i.e. the Flemish Diamond and Manchester/Liverpool) we provide further sub-clusters that relate to separate cities, each of which individually qualifies as coastal cluster according to the above criteria.For the following steps, the cluster boundaries are used as a mask to extract the corresponding land cover and inundation information. We give an example of the results for the city of Copenhagen in 24 (LUCAS). Specifically, we statistically relate observed land use and CORINE land-cover classes over all geo-referenced observation within the LUCAS data. Finally, every land-cover class is allocated the average fraction of the land-use classes. So far, the clusters boundaries define the location of assets at risk. However, the estimation of damage cost requires information about the quantity and the economic value of these assets (exposure). We estimate exposure on the basis of the economic value of land use. For this purposes a statistical mapping between land-cover and land-use classes is required. The mapping is created from raw data of the 2015 Land Use/Cover Area Frame Statistical Surveyconsidered share, i. e. the fraction of a cluster cell that can be attributed to the considered land uses, are given in For this study, we limit the considered land uses to the classes residential, commercial, industrial, road transport, and agriculture, as well as unused land cf.  and disret al.26, who provide country-specific data for five different land-use classes. For each country, the data contain land-use specific values for the average maximum damage per m2. These values are used to calibrate relative damage functions that were derived at the European level for the considered land use25. For the example of Germany, we show the inflation-adjusted average maximum damage in Microscale depth-damage functions are used to convert the grid-based information on inundation depth and land use to monetary damage. The depth-damage functions are adapted from publications by Huizinga 25 relates the average maximum damage per land use to the economic output of a country measured in terms of GDP per capita using Purchasing Power Standards (PPS) for the year 2004. In the lack of a more recent land-use valuation, we adjust monetary estimates to 2016 price levels by using historic inflation rates based on the consumer price index26. For most countries the inflation rates were obtained from Eurostat27, for Albania and Montenegro from the Worldbank28.Huizingadi for a land-cover class i as a weighted sum of the corresponding damage functions dj for land-use classes j,h denotes the inundation depth and the weight wi∧j represents the observed frequency of finding both i and j attributed to the same grid cell. The weight is taken from the statistical mapping between land cover and land use shown in Switching from land use to land cover data, we infer the microscale damage function 2 for a hypothetical 2 m flood in Copenhagen are shown in Knowing the land-cover class and the inundation depth for each grid cell, we can use Equation 29. Precisely,D is the total damage in the considered cluster at flood height x. The index n runs over all grid cells in the cluster and di(n) is the microscale damage function for the corresponding land-cover class in cell n. The inundation depth hx,n is obtained from the inundation model in Step I and is dependent on the overall flood height x and the location of grid cell n. Following this approach, we obtain the flood damages for all 600 urban clusters at all flood heights In this step, we combine the information on the urban cluster with the modeled inundation data and the microscale damage functions. For each urban cluster the monetary damage at a specific flood height is given by the sum over the damages for each of the inundated grid cellsurban protection course (UPC). The novel terminology has been chosen deliberately to stress the hypothetical nature of this product and its dependence on the urban cluster. The UPC can be understood as the entirety of all flood defense measures, whether they are dikes, sea walls or any other artificial construction.Using the results of Steps I and IV we determine the protection needs for a given urban cluster in terms of an In order to obtain the UPC, we need to identify grid cells, where the construction of a flood defense structure is theoretically required to avert the potential damage at a given flood height. First, we extract the outline of the city cluster by finding those cluster cells that belong to the cluster and are adjacent (in the sense of the 8 nearest neighbors) to the surrounding land, whereby the surrounding land excludes grid cells that are entirely enclosed by the city cluster (i.e. holes). Second, cells on the outline are identified as part of the UPC if they suffered a potential flood damage during Step IV.The required height of the protective structure at an identified UPC cell is defined as the difference between the cell's elevation and the considered flood height. The required length of the protective structure is given by the edge length of the cell itself. An example for an UPC in the city of Copenhagen at 2 m protection height is given in It is important to distinguish between the UPC, which is a purely hypothetical protection course around an urban cluster, and existing or planned flood protection which typically protect wider areas. Crucially, the UPC shall not be misunderstood as a basis for engineering decisions on coastal defense measures due to its known limitations, e. g. of the underlying DEM and the simplicity of the hydrostatic approach. A critical discussion of the UPC is included in the Technical Validation section, where we also compare the UPC and existing protection measures for the city of Hamburg.30–32. We employ unit costs for dike construction (cost of constructing or raising a dike per unit length and height)31 as a general cost proxy for the UPC. Protection costs are obtained by applying the unit cost to the product of protection height and length of each grid cell and summing over all grid cells belonging to the UPC. Repeating this process for every protection height 31 that reflect the high uncertainty32 of empirical dike construction costs.Since the UPC represents a compilation of potentially several different flood defense measures, its construction costs can only be estimated approximately. Since empirical costs estimates for coastal defense measures are only sporadically available on case study level, construction costs are commonly assessed via a unit-cost approach25. Subsequently, regional protection costs were inflation-adjusted to 2016 price levels26 analogous to the damage estimates in Step IV.Analogous to the preparation of the damage costs, we stratified the protection costs for the different European countries by calculating the difference in Purchasing Power StandardsAll data products were computed using Matlab R2014a. For computational efficiency, the Matlab functions for generating the city clusters and the inundation maps were coded in C and compiled with the Microsoft Windows SDK 7.1 C Compiler. Raster data were prepared either directly in Matlab or by using the Geospatial Data Abstraction Library 2.2.1 (GDAL). Any maps were generated with QGIS, version 2.18.In the Supplementary Information we provide a stand-alone example of the Matlab codes and data to generate the damage and protection cost curves for the Copenhagen urban cluster. Further codes are specific to our computational architecture and can be made available upon request.All data products that were derived and described in this work are publicly available at the PANGAEA repository [Data Citation 1] under the Creative Commons Attribution 3.0 Unported license. In detail, [Data Citation 1] provides four distinct datasets:2.[Data Citation 2] provides binary masks for each coastal city cluster derived from CORINE land-cover and EU-DEM data. The dataset comprises individual raster files (GeoTIFF) for the 600 largest clusters, as well as additional files for the 8 sub-clusters of the Flemish Diamond and Manchester/Liverpool megaclusters. The archive further contains auxiliary metadata, namely: The name and geographical coordinates of the clusters, as well as the area of the clusters in km[Data Citation 3] provides the direct monetary damage (million € in 2016) for each of the considered city clusters at flood heights varying from 0 to 12 m in 0. 5 m steps. Although existing flood protection is not considered, we propose an approach to take into account the impact of flood protection in the Usage Notes section.[Data Citation 4] provides lower bound cost estimates (million € in 2016) for potential protection at each of the considered city clusters. Costs are absolute figures for the construction of the UPC at design flood heights varying from 0 to 12 m in 0. 5 m steps. Note that existing flood protection is not considered in the cost estimates, but may still be incorporated based on simple assumptions (cf. Usage Notes).Analogous to [Data Citation 4], [Data Citation 5] provides upper bound cost estimates (million € in 2016) for potential protection at each of the considered city clusters.In the following, we provide a detailed account of each of the individual datasets.In [Data Citation 2] derived cluster masks are provided for each of the 600 largest urban clusters located at the European coast. The spatial distribution of the clusters is shown in Within the 600 clusters there are two which comprise two or more major cities. These are the Flemish Diamond of Brussels, Antwerp, Ghent, and Louvain, as well as the cluster of Manchester/Liverpool. These were disaggregated into 8 subclusters that are provided alongside the original clusters. All further results are available for both the original clusters and the disaggregated coastal sub-clusters.While the employed damage functions account for the predominant land use in urban areas, not all land use could be accounted for. We find that our method can attribute an average of 82% of the cluster area to accountable land use. Other land uses are not considered due to the unavailability of value estimates and damage functions. When considering the affected values (exposure) at a hypothetical 5 m flood height, the total exposure accumulated within the coastal clusters equates to more than half of the total urban exposure within Europe. In numbers, we find that 58% of the total exposure are due to the top 600 clusters.[Data Citation 3] provides estimated cost curves for direct monetary damage for each of the 600 clusters as well as the 8 subclusters. The curves for the largest 100 clusters are shown in Overall, the majority of curves exhibit a moderately convex (e.g. London), or slightly sigmoid (e.g. Copenhagen) behavior over the entire range from 0 to 12 m. As for the example of Bristol, cities that are mostly located on elevated grounds exhibit a strongly convex damage cost curve with no saturation for the flood heights considered.For [Data Citation 4] and [Data Citation 5] approximate protection cost curves were estimated for each of the 600 clusters as well as the 8 subclusters. We obtained a lower and an upper bound of protection costs for each city, which result from applying the lower and upper unit cost figures, respectively (cf. Step VI in the Methods section). Analogous to the damage cost curves, we show the protection cost curves (upper bound) for the 100 largest clusters in The feasibility of a technical validation is limited given that the damage and protection cost curves can only provide a characterization of potential cost under the assumption of no existing protection. Even if existing protection levels were modeled, empirical cost estimates at the city level remain scarce and may not be consistent in terms of the considered city areas and asset values. In order to address these limits, we focus our validation on three different aspects. First, we undertake a critical discussion of the caveats implicit in the data and the model choices of this work. Second, we identify comparable damage cost curves for 17 coastal cities in the scientific literature and compare these against our estimates. Third, we discuss the characteristics of the UPC against existing protection on the example of Hamburg.33. As population data is collected on the administrative level, the apparent choice is to simply rely on those definitions. Administrative boundaries, however, in general disagree with the common sense spatial extent of cities, so that definitions of metro-regions aim for consistent density and commuting thresholds34.The definition of city boundaries is a long-standing problem in any field studying citiesSince damages primarily arise from urban infrastructure, we employ a physical city definition which closely matches asset exposure and potential damage proxies. According to our definition, cities are spatial clusters of urban land cover, i. e. any two neighboring urban grid-cells belong to the same city cluster.22, we employ a systematic and reproducible procedure to extract city boundaries from land-cover data. Since land-cover data is also the source of our damage proxy, our approach assures consistency between the city boundaries and the estimated monetary damage.By following the EEA's definition of urban morphological zones18, continental and global assessments need to approximate asset values using economic information with a comparably coarser resolution. Economic proxies for asset exposure (e.g. GDP per capita) are typically downscaled using more detailed geographical information. For this purpose, recent studies have employed remote sensing data for population35, land use35, land cover36, or night light37 information.Given the large number of city clusters considered and the continental scope of analysis, approximating the economic value of assets at risk is bounded by a number of caveats. Unlike local studies in which asset value is available at the building level25. Where country averages are not available, European values are scaled to the country level by the ratio of national over European GDP per capita in Purchasing Power Standards, thus reflecting the differences in economic output25. This procedure results in monetary estimates that are homogeneous for each country.Fundamentally, our study is based on the average maximum damage for each land use per country35, these national estimates do not differentiate between relatively poor or wealthy regions or between more rural or strongly urbanized settlements. While some population-based studies have employed a factor of 2.8 to approximate asset values from national GDP per capita8, others have used a factor of 5 to account for increased affluence in cities35. The higher factor for cities can be motivated from the fact that GDP scales super-linearly with the size of the population38. If sub-national estimates of GDP per capita are available for a given city, the damage cost curves provided here could simply be rescaled by the ratio of city GDP over national GDP.As with similar studiesIn our approach the maximum damage of a grid cell is dependent on land use and local GDP per capita but independent of population density. This is a major difference to population-based approaches where total assets are assumed to be proportional to the local population. This aspect has two main consequences. On the one hand, our approach could overestimate potential damage in low-density areas. Due to the high 100 m resolution of the underlying CORINE data, we believe this to be a minor effect. On the other hand, studies based on population and GDP per capita may fail to accommodate for high-rise buildings in city centers, which are typically less affected by flood damage in relation to their total economic value. They may also systematically undervalue industrial and commercial sites which are not resolved explicitly. In contrast, our approach identifies and evaluates different types of built-up areas by land use and, thus, yields a more accurate spatial distribution of damages. Moreover, the use of land use can in principle be more appealing to spatial planners and adaptation practitioners.It should be noted that the allocation of average fractions of land use to the CORINE land-cover data could be a source of error for individual damage cost curves. Locally, the composition of land use per CORINE cell could be different from the statistical average. Generally, this random error is expected to become less significant at higher flood heights where more and more cells are affected, and it should be negligible for a large-scale assessment on the national or European scale.2 for different land uses, but they comply with the general shape of damage functions at the building level. While the maximum damage value per land use is broken down for each country according to its GPD in terms of Purchasing Power Parity25, the shape of the depth-damage functions remains homogeneous across Europe. This implies that damage effects stemming from country and behavioral-specific features are not captured. For example, differences in construction materials39 and the existence of an underground floor40 significantly influence the shape of the relative damage function. Furthermore, the existence of flood-adapted use and adapted interior fitting are reported to have a significant effect in shaping damages41 and hence the modification of the relative damage function.Despite the existence of a considerable amount of functions relating flood depth and relative damage at the building-level their overall shape is remarkably similar—a sub-linear rise of damage for the initial flood depths followed by a slow deceleration of damage and saturation for high flood depths. The microscale depth-damage functions used in this work  apply to9.Inundation maps produced are a explicit spatial representations of hypothetical flood events and thus define both the extent of the flooded area as well as the water height (inundation depth) at each individual point. Conventional approaches range from simple static inundation schemes to computationally demanding dynamic inundation modeling8. The comparison of different inundation schemes shows that static models may overestimate the flooded area9. The overestimation is due to the fact that static inundation schemes assume infinite water volume for immediate discharge during the flood event, disregarding limitations due to terrain roughness, narrow or constricted openings, and flow velocity in general.Static inundation schemes, sometimes also called bathtub models, are often used for large-scale flood damage assessment, where computational time becomes a limited resource42. However, since LiDAR data is not consistently and often not freely available, large-scale flood damage assessment relies on satellite based observations.The choice of the DEM and its resolution has a substantial effect on the accuracy of inundation models. In this context, many studies have demonstrated the benefit of using airborne light detection and ranging (LiDAR) data, which offers high horizontal resolution and vertical accuracy, as well as the capacity to separate bare-earth from built structures and vegetation8, whose general utility as a source of global terrain data has been noted42. Comparative studies show significant differences between SRTM and LiDAR for inundation mapping14, but also indicate that the differences may be within the accuracy that is typically associated with large-scale flood studies13.Recent large-scale studies have employed the shuttle radar topography mission (SRTM) DEM23, which is largely SRTM based and would thus be expected to provide similar accuracy. A first study comparing SRTM and EU-DEM products for flood modeling did not find significant differences15. However, since all elevation data were averaged to the same resolution as SRTM, the benefit of the higher resolution of the EU-DEM was not assessed.This study employs the EU-DEMEmpirical cost estimates are scarce and generally not available for the entirety of flood defense measures around a specific city. Hence, a direct validation of protection cost against reported figures is not feasible and, as a consequence, we discuss the costing and the location of flood defenses separately.31. Derived from actual project data, the unit cost include material and construction costs, as well as the costs for design, taxes, and fees31. Strictly, the unit-cost approach only applies to the incremental cost of raising dikes, such that absolute cost figures are potentially unsubstantiated. However, the unit-cost approach is supported by the finding that empirical costs for Canadian and Dutch dikes can be approximated by linear cost functions32.In our work we employ empirical estimates of protection cost that reflect the costs per 1 m increase in dike height31 we compute a range of €67.1 million to €259.0 million per m height and km width. These values are a factor 5 to 12 greater than the unit costs for sea dykes in urban areas, which have been estimated at €15.5 million and €22.4 million in ref. Costs for protection measures other than dykes are not considered in this work. Estuaries and in particular harbor cities require adaptable storm surge barriers, such as flood gates, in order to allow passage and water exchange at ordinary water levels. The construction costs of storm surge barriers are significantly higher than those for sea dykes. Based on empirical estimates for the construction costs of flood barriersUnder the unit-cost assumption, the shape of the estimated protection cost curves is determined solely by the length and height of the required flood protection. This information is provided by the UPC, which is based on the the city cluster that defines the urban land cover attributable to the city. As such, the UPC can be compared to the existing protection measures deployed within the city. However, the actual protection measures and the UPC differ in their objective. For consistency with our damage estimation, the UPC was designed to protect those urban areas which would otherwise suffer damage. As such, the UPC does not reflect economic considerations or protection needs beyond city cluster boundaries. In contrast, the processes leading to actual protection are very complex and might involve a local political discourse and constitute a compromise between economic and social aspects. The implicit decision process likely considers the city and its surroundings such that the protection in place potentially deviates from the UPC.32 and the specific assumptions of the UPC, it becomes evident that the monetary estimates of the protection costs should be considered as indicative. However, courtesy to the consistent approach, the estimates are well suited for differential analysis of protection costs across different cities.Given the high variance in empirical protection costsWhile being of great value for risk assessment, macroscale damage curves are typically being considered as an intermediate result of the damage assessment and often not published. This fact unnecessarily hampers the comparability and accessibility of flood risk assessments and hinders the validation of such curves.8 comparable to the one presented, both in regard to the number of cities considered and methodological homogeneity. This other study undertakes a risk assessment for the 136 major coastal cities worldwide. There is an overlap with our study for 17 urban agglomeration within Europe. The supplementary material to ref. We consider only one study2.If available, one would prioritize the comparison of the damage cost curves in this work with those derived from case-study investigations. We do so for the city of Copenhagen, where a monetary damage curve has been disclosed8. Despite the use of distinct datasets and methodology for asset estimates in the included studies , which provides the difference between the mean sea level and the reference geoid45.All cost curves are derived from EU-DEM data and relate to the vertical datum specified by the European Vertical Reverence System 2000 (EVRS2000) with quasi-geoid EGG08 ref. . Note thThe damage and protection cost curves can be the starting point for an economic assessment of coastal flooding impacts and adaptation at the city scale. Together with information on the height of floods at different return periods, they allow for the comparability of the risk from flooding in different cities.46 to empirical or modeled flood-gauge data11. From the distribution, it is possible to infer the return periods of floods at certain height, or vice versa, to obtain the estimated flood height for a given return period.A common approach to obtain the distribution of extreme sea levels is to apply extreme value statistics3. Specifically,The damage cost curve can be employed to transform the distribution of (extreme) sea levels to the distribution of damage costPD and PX are the cumulative distribution functions of the damage d and the extreme sea levels x, respectively, and D−1 represents the inverse of the damage cost curve.where 8 we did not consider existing protection in the cost curves. However, given information on existing protection levels (in terms of protection height or return period), the damage and protection costs curves can be manipulated to reflect the effects of existing protection.Since information on existing coastal defense measures are hardly available consistently for any locationz,z do not cause any damage. Evidently, such a stylized approach falls short of considering the risk of protection failure (e.g. dike breach) and could understate the monetary risk from flood events below the design flood height of the flood defense measure. In order to overcome this limitation, fragility curves47 could be employed to model the probability of e.g. dike breaches or wave over-topping.The simplest approach to incorporate existing protection into the damage cost curve would be a truncation of damage cost at the design flood height P' can be directly inferred from the protection cost curves,P of the already built coastal protection up to flood height z is simply subtracted from the total cost at protection height ω. The feasibility of this approach hinges on the assumptions made in this work, namely the unit-cost of dike construction and the predetermined protection course at the city cluster boundary. Since the unit-cost approach should be most reliable for the case of dike raise, we recommend to consider only protection cost increments between well-defined protection levels (e. g. upgrading protection levels from a 100-year to a 1000-year return period).Similarly, the calculation of the cost of raising or upgrading existing protection The damage cost curves provided in this work reflect the socioeconomic conditions of the reference period. This poses no problem if the damage assessment is targeted at the isolated effect of changes in the hazard (e. g. sea level rise or changing storm climates). In contrast, socioeconomic scenarios cannot be considered without making certain changes to the employed damage cost curves. In the following, we argue on the feasibility of adjusting for economic development as well as urban growth and provide some hints how this could be achieved on the basis of the data provided.8. In our work and in similar studies  and the accumulated asset valueg the damage cost curves could be multiplied by a factor (1+g).The adjustment for future growth of the urban clusters is less obvious and only possible under certain assumptions. In our view, land-use changes  or spatially explicit growth patterns cannot be adjusted for, since these result in specific non-linear transformations of the damage cost curve. However, we suggest that for large-scale assessment urban growth could be considered in a more general statistical manner. In order to motivate this hypothesis, we have computed the number of urban cells in Europe that would be affected at 1 m increments of flood height on the basis of three different time slices of the CORINE data, namely for the years 2000, 2006, and 2012. The results shown in Unfortunately, the protection cost curves provided in this work cannot be adjusted in a similar way. Here, the consideration of urban growth would require a reconstruction of the UPC and recalculation of the protection cost curve, since the UPC is crucially dependent on the geographical pattern of the cluster.How to cite this article: Prahl, B. F. et al. Damage and protection cost curves for coastal floods within the 600 largest European cities. Sci. Data 5:180034 doi: 10.1038/sdata.2018.34 (2018).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Attribute-based encryption (ABE) is a popular cryptographic technology to protect the security of users’ data in cloud computing. In order to reduce its decryption cost, outsourcing the decryption of ciphertexts is an available method, which enables users to outsource a large number of decryption operations to the cloud service provider. To guarantee the correctness of transformed ciphertexts computed by the cloud server via the outsourced decryption, it is necessary to check the correctness of the outsourced decryption to ensure security for the data of users. Recently, Li et al. proposed a full verifiability of the outsourced decryption of ABE scheme (ABE-VOD) for the authorized users and unauthorized users, which can simultaneously check the correctness of the transformed ciphertext for both them. However, in this paper we show that their ABE-VOD scheme cannot obtain the results which they had shown, such as finding out all invalid ciphertexts, and checking the correctness of the transformed ciphertext for the authorized user via checking it for the unauthorized user. We first construct some invalid ciphertexts which can pass the validity checking in the decryption algorithm. That means their “verify-then-decrypt” skill is unavailable. Next, we show that the method to check the validity of the outsourced decryption for the authorized users via checking it for the unauthorized users is not always correct. That is to say, there exist some invalid ciphertexts which can pass the validity checking for the unauthorized user, but cannot pass the validity checking for the authorized user. Recently, cloud computing has become a very fascinating computing paradigm, in which storage and computation have moved away from terminal devices to the remote side. There are many novel applications in this area, such as outsourcing computation ,2 and ouThe notion of ABE was first introduced by Sahai and Waters . There aIn order to reduce the decryption time and the computation cost, Green et al.  proposedRecently, Li et al.  proposedIn cloud computing, the ABE-OD scheme cannot ensure the correctness of the ciphertext or the transformed ciphertext for cloud server being untrusted. The untrusted server may send a wrong transformed ciphertext to the users for saving computing cost or it may have suffered from malicious attack which also produces the incorrect ciphertext or transformed ciphertext. In order to ensure the correctness of the ciphertext or the transformed ciphertext, the ABE-VOD schemes were proposed in ,12,13,15However, we firstly show that the validity verification method in decryption algorithm of the ABE-VOD scheme put forth by Li et al.  cannot aThe rest of this paper is organized as follows. The system model of the ABE-VOD and some basic mathematic knowledge are introduced in In the section, we will recall the definition of ABE-VOD and some basic mathematic knowledge in .The ABE-VOD Scheme consists of seven algorithms: Setup, KeyGen, Encrypt, Decrypt, GenTKSetupKeyGenM and two access structures EncryptS satisfies the access policy M if the ciphertext is valid; otherwise, the client outputs DecryptGenTKTransformS satisfies the access policy M if the ciphertext is valid; otherwise, outputs DecryptBilinearity: For any Non-degeneracy: There are elements Computability: For any elements Let G1×G1→G2 , which se will be using the modified Weil [The concrete bilinear pairings ied Weil  or Tate ied Weil  on some Definition 1.. That is to say, the Decrypt algorithm outputs a corresponding plaintext of some ciphertext if and only if the ciphertext is valid, or the DecryptThen, the ABE-VOD scheme can simultaneously check the correctness of the transformed ciphertext for the authorized users and unauthorized users by using “verifying-then-decrypt” method to guarantee the correctness of the transformed ciphertext.In general, the goal of the verification formulas of the decryption algorithm are to check the correctness of ciphertext. However, the decryption algorithm of ABE-VOD scheme proposed by Li et al. only checks validity of a part of ciphertext, but not checks whether the output of the decryption algorithm for some ciphertext is the original plaintext . In the subsection, we show that there exist some ciphertexts which are verified by the decryption algorithm, but its output isn’t the original plaintext.As analysis in , the cipThe adversary takes as input a random message A, The adversary first picks up a random string Set Set The ciphertext M since the adversary picks two distinct random numbers Obviously, the ciphertext S satisfies the access policy If Let It is clear that the equalityM since However, S satisfies the access policy If Let For the same reason above, the equalityR since However, Thus, the decryption algorithm of the ABE-VOD scheme proposed by Li et al. for both the authorized client and the unauthorized client cannot check the validity of all ciphertexts. I.e., there exist some invalid ciphertexts which can pass the validity checking. Furthermore, their ABE-VOD scheme cannot check the validity of the outsourcing computation by checking the correctness of the corresponding ciphertext since the output of both the Decrypt algorithm and DecryptSince verifying the correctness of the outsourced decryption for unauthorized clients is very important, Li et al. considered the following scenario. The authorized user wants to, but is not able to, process some pending businesses when the time or position of the authorized client is limited. He/she needs someone to help him/her to verify whether a pending business is correctly processed and does not want the latter to know anything about the content of the business. Thus Li et al. proposed the ABE-VOD scheme which could utilize an unauthorized client to help him/her to verify the correctness of the transformed ciphertext. We construct the following ciphertext which can pass the correctness checking for an unauthorized client but it is not a valid ciphertext for the authorized client.The adversary takes as input a random message The adversary first picks a random string For each row Set Set The ciphertext S satisfies the access policy It is clear that if S satisfies the access policy R for the unauthorized client. The equationsR correctly. Especially, when the untrusted server honestly runs the TransformHowever, if Thus, the ABE-VOD scheme cannot verify the correctness of the ciphertext or the transformed ciphertext for the authorized user via verifying it for the unauthorized user.We have showed that the decryption algorithm cannot satisfy two functionalities, checking the correctness of all ciphertexts and “full verifiable” above. Next, we will explain the reason and possibly reasonable method.On one hand, the construction of the above ABE-VOD scheme utilized ABE-OD scheme proposed by Green et al.  and shorOn the other hand, from the unauthorized client’s view, ction in  cannot cIn this paper, we showed that the validity verification method in decryption algorithm of the ABE-VOD scheme put forth by Li et al. cannot always check the validity of all ciphertexts. There exist some invalid ciphertexts which can pass the validity checking and the “verify-then-decrypt” skill used in  is unava


In this paper, an adaptive collaborative Gaussian Mixture Probability Hypothesis Density (ACo-GMPHD) filter is proposed for multi-target tracking with automatic track extraction. Based on the evolutionary difference between the persistent targets and the birth targets, the measurements are adaptively partitioned into two parts, persistent and birth measurement sets, for updating the persistent and birth target Probability Hypothesis Density, respectively. Furthermore, the collaboration mechanism of multiple probability hypothesis density (PHDs) is established, where tracks can be automatically extracted. Simulation results reveal that the proposed filter yields considerable computational savings in processing requirements and significant improvement in tracking accuracy. In multi-target tracking (MTT) in clutters, the correspondence between the targets and the measurements is unknown, while the target number is unknown and even time-varying. The objective of MTT is to recursively estimate the target number and target states from a sequence of noisy and cluttered measurement sets ,2.One common approach for multi-target tracking is the combination of state estimation and data association, along with track initialization and termination . In factAnother approach is to apply random finite sets (RFSs) to represent the collection of individual targets and measurements, and hence recast the MTT problem as the Bayesian estimation problem based on finite set statistics so as to avoid data association risk . HoweverHowever, there are still two important but open issues about PHD:The first is that the computational burden is still too intensive in many actual applications, especially in the case of dense clutters and intensive targets. One possible solution is to discern the measurement originality based on tracking gating ,16. NeveThe second issue is that additional track extraction is needed because the standard PHD only outputs the track points without the corresponding track identities. But the presented track extraction algorithm ,18 is toIn this paper, we present an adaptive collaborative GMPHD (ACo-GMPHD) filter with the capability for automatic track extraction for fast multi-target tracking in dense clutter. In the ACo-GMPHD, the persistent and birth target PHDs are updated respectively based on the corresponding measurement subsets, instead of based on all measurements, so that the computational complexity is expected to be reduced. Meanwhile, the collaboration mechanism among these PHDs regarding measurement utilization is adaptively established to avoid decision risks triggered by measurement partitions. In addition, permanent tracks and temporary tracks can be automatically extracted from the persistent and birth target PHDs. Simulations show that the proposed ACo-GMPHD greatly reduces the computational cost and significantly improves the track extraction, compared with the well-known GMPHD filter.The remainder of this work is organized as follows. In an MTT scenario, targets appear and disappear randomly. A new target appears in the surveillance region either by spontaneous birth or by spawning from an existing target. The number of the newly-born targets is assumed to be Poisson-distribution. A target may disappear at the next instant. Here, j-th measurement, and Denote tated in :(3)Xk=[In the PHD filter, the following common assumptions  are madeA.1: each target state evolves and generates one measurement independently;A.2: any clutter is Poisson distributed and independent of target-originated measurements;A.3: the predicted multi-target RFS is Poisson distributed and independent.Given the posterior intensity Lemma 1.If the multi-target PHD at timeis represented as the sum of multiple PHDs with each PHD having the following Gaussian mixture form :withthen the predicted PHD will bewithwhereandis the predicted mean;is the predicted covariance.Lemma 2.Given the predicted PHDand the measurements, the updated PHD  is:withwhereRemark 1.As shown in the PHD recursions specified by Lemmas 1–2, the output from the PHD filter provides a multimodal density from which we need to estimate the states of the targets at each time, while it does not output target tracks. Moreover, the persistent target PHD and birth target PHD are jointly processed indifferently. In fact, the birth PHD reflects the nature of the birth target and is used for capturing newborn targets while the persistent PHD is updated for track maintenance of the surviving targets. Utilizing their difference is expected to further improve both tracking performance and calculation efficiency. Furthermore, all measurements  are utilized to update the PHD, and hence most computational resources are wasted. These facts motivated us to establish the adaptive multi-PHD filter framework with track extraction and adaptive processing via both adaptive measurement partition and multi-PHD collaboration.Remark 2.One may wonder whether the measurement partition in the ACo-GMPHD filter introduces several decision risks. In fact, the measurements away from the confidence region have little contribution to the persistent targets, and hence the weight of the Gaussian components would not be underestimated in updating the persistent PHD. In other words, the partition of the measurements has nothing to do with updating the persistent targets in setting the large-confidence region. For the birth target, when the confidence region is large, the birth measurements may be possibly partitioned into the persistent measurements, which may lead to missing the birth target. Here the measurement which does not contribute to the update of the persistent PHDs will be introduced into the birth measurement set, which can avoid the birth target missing. In general, adaptive measurement partition is effective as shown in the later simulation.i-th persistent PHD and the i-th pre-persistent PHD; Given the persistent PHD set According to Lemma 1, the predicted persistent PHD is:According to reference , we chooAccording to Lemma 1, the predicted birth PHD is:As the integral of the PHD equals the expectation of the target number in the surveillance region, the PHD should be updated by using the target-oriented measurements instead of all the measurements. Different kinds of PHDs such as the persistent PHD and the birth PHD should be updated based on the different measurement sets. Thus, we partitioned the measurement space through utilizing the information of the Gaussian terms.The innovation covariances of the persistent and pre-persistent PHDs are:The shortest Mahalanobis distance between a real measurement If  freedom , where nThe birth measurement set According to Lemma 2, the persistent PHD is updated based on the persistent measurement set The corresponding measurement weight of the persistent measurement is:The measurement set for updating the birth PHDs is defined as:The integrals of the persistent and pre-persistent PHDs are:Denote the persistent PHD index set by For any birth PHD, its prediction is:According to Lemma 2, the birth PHDs are updated using the birth measurements Then the weight of the birth measurement and the integral of the birth PHD are calculated as:Denote If a birth PHD If a pre-persistent PHD A persistent PHD with a large enough large weight, for example M-by-M identity matrix; and Here we adopt the strategy previously described in reference  as folloeference ; IM is aAt different times, the Gaussian terms with the same label represent the same target. The output track information at time Remark 3.The analysis for the complexity of the ACo-GMPHD is an open issue due to the measurement partition is random. In principle, the ACo-GMPHD and the standard GM-PHD have the similar process flowchart and hence their calculation burden is similar. Differing from the standard GM-PHD, the ACo-GMPHD partitions all measurements into smaller sets and separately processes them. Since the computational complexity of the standard GM-PHD increases exponentially with respect to the number of the related measurements, the ACo-GMPHD is expected to be more cost-efficient, which coincides with the simulation result.To verify the systematic performance of the ACo-GMPHD filter, we compared it with the standard GMPHD filter which utilizes a priori birth target intensity and the GMPHD-I filter  via an MThe detailed scenario parameters are given in Priori birth target intensity We used a performance evaluation metric called the optimal subpattern assignment (OSPA) distance, which is specialized for the MTT filter accuracy test . We seleWe ran 100 Monte Carlo (MC) trials for each filter to obtain the OSPA distance and the averaged computational cost, and obtained the track-valued estimates in one MC trial. In addition, we validated the performance of each filter in the case of different clutter densities.the ACo-GMPHD does not utilize a priori information of the birth target. At the moment that a target appears, the clutter and birth target measurements are hardly distinguishable without the support of the subsequent measurements. Thus, the birth target measurements may be treated as the clutter, and hence possibly leads to a delay in the cardinality estimation, as shown in the GMPHD-I also does not utilize a priori information of the birth target. However, due to the absence of adaptation and collaboration compared with the ACo-GMPHD, the GMPHD-I is the worst regarding the OSPA measure.As shown in Furthermore, we present the time-averaged OSPA versus the clutter density in For each time step, the averaged computation time (ACT) is shown in In this paper, we proposed the ACo-GMPHD filter with automatic track extraction, which was shown to be satisfactory for multi-target tracking. It costs less computational time and has better OSPA, except for some undesirable peaks at the moment of birth targets appear. Hence, one possible avenue for future research is to introduce priori information about birth targets, which would be helpful in order to better discern the target and the clutter, and hence more effectively reduce the corresponding OSPA peaks. Additionally, the threshold at the step of PHDs management was considered as constant in the proposed filter, and a possible future research study is to adaptively choose the threshold under some optimal performance index.


A major feature of health care systems is substantial variation in health care quality across hospitals. The quality of stroke care widely varies across NHS hospitals. We investigate factors that may explain variations in health care quality using measures of quality of stroke care. We combine NHS trust data from the National Sentinel Stroke Audit with other data sets from the Office for National Statistics, NHS and census data to capture hospitals’ human and physical assets and organisational characteristics. We employ a class of non-parametric methods to explore the complex structure of the data and a set of correlated random effects models to identify key determinants of the quality of stroke care. The organisational quality of the process of stroke care appears as a fundamental driver of clinical quality of stroke care. There are rich complementarities amongst drivers of quality of stroke care. The findings strengthen previous research on managerial and organisational determinants of health care quality. A central observation of the health care systems is the existence of substantial heterogeneity in the quality of health care services across hospitals. The quality of health care measured along dimensions such as mortality or the process of care for medical conditions such as cancer, stroke and pneumonia varies widely across hospitals , 42. FigIt is evident that the quality of the process of stroke care varies across hospitals. The figure also reveals a notable positive shift in the distribution of the quality of stroke care over the years. Notwithstanding this, variations remain, with some hospitals still performing above the median quality whereas others are performing below the median quality. Mooney  and RuddHospitals are major providers of health care services and account for a major expenditure of the overall health care budget. Any effort at reducing the heterogeneity and enhancing the quality of care across hospitals can bring substantial benefits to society. Such efforts demand understanding why some hospitals perform better than other hospitals, providing a higher quality of care.The literature on the drivers of hospital quality is vast, offering a rich list of explanations for the observed heterogeneity in the quality of care. We borrow a theoretical framework from the economic literature on productivity  to shapeStarting with the empirical literature on the internal drivers of hospital performance, a series of papers studies impacts of hospital size, physical assets, human capital and information technology on the quality of health care. Raerty et al.  and NeedAn emerging finding in the literature is that the above factors do not fully account for the observed heterogeneity. Variations in care measured in mortality for disease conditions or the process of care measures persist even after controlling for case mix, human capital , information technology, hospital characteristics such as bed size, teaching status or foundational trust status, cost–contributing factors, post-operative complications and statistical noise , 47, 68.The finding has led researchers to turn attention towards management practices and organisational factors. Bloom et al.  collect Another substantial body of literature examines the role of external factors in shaping hospital performance. A key result in this literature is that competition, provided prices are regulated, has a positive impact on health care quality. NHS hospitals in more competitive regions provide higher health care quality compared to hospitals located in regions where there is less competition . In the This study seeks to contribute to the literature in health economics that argues for the impact of management practices and organisational factors in driving hospital performance and the quality of clinical care, where by organisational factors we also mean organisation of resources , 75. BuiOur emphasis on the organisation of resources and management practices is by no means new. A substantial body of literature, as mentioned above, has already documented evidence on the possible impact of organisational and management factors in driving hospital performance. The literature, however, has so far mainly sought to identify factors that drive the quality of care and has paid little systematic attention to possible interactions among the factors driving hospital performance. This is partly because the theory is silent on complex interactions that may exist among key variables driving performance and partly because common econometric techniques are not equipped to reveal interactive structures based on the data alone. The theory, though, emphasises the importance of complementarity among assets and skills that drive productivity and, in our case, health care quality. In other words, it points to the importance of critical interactions among factors driving quality, not simply the mere presence or absence of the factors or the level of the factors . We aim Research hypothesis: Variations in the organisation and management of resources involved in the process of hospital services such as stroke care partly drive variations in the clinical quality of the services (stroke care). Moreover, it is the joint presence of complementary resources and management practices that critically affects the quality of the clinical process of the services (stroke care).To assess this hypothesis, we put together a wide panel data set on a rich list of candidate variables that could possibly drive hospital quality in stroke care for which the organisation of resources and management of the process of care matter critically. The panel spans from year 2004–2010. To our knowledge the only significant policy change that took place during this period is the introduction of Department of Health’s National Stroke Strategy implemented in England in December 2007. We appropriately account for this change in our analysis in order to capture the potential impact this policy may have on the quality of stroke care in English hospitals. As our measure of quality, we employ an index that captures the quality of the process of stroke care as opposed to an outcome measure. Process of care measures illuminate the complicated process of delivering health care and describe the specific actions associated with health care delivery. It describes the care that patients actually receive and assesses the extent to which hospitals perform health care processes to achieve the desired aims. An important advantage of process measures over outcomes is that it does not suffer from the case-mix adjustment bias , 22. OutWe combine our measure of the clinical quality of stroke care with a measure of the organisational quality of the process of care and other data drawn from several sources. We will employ a new class of unbiased panel regression tree estimator from the machine learning literature to study the data. A reason behind the choice of the method is the intuitive interpretability of the results. The non-parametric method can reveal potential interactions among the variables, which could offer valuable information about the processes that drive variations in quality of stroke care across NHS hospitals. We use an out of sample prediction error estimator to calculate the predictive accuracy of the models.Our results point to the significant role of organisational features of the process of stroke care in driving the clinical quality of the process of stroke care. Including a composite measure of organisational design for the provision of stroke care improves the predictive accuracy of the models. The predictive results are robust to the inclusion of year as an additional variable to capture trends in the data. Using year as an additional predictor, our measure of organisational design for the provision of stroke care still has a significant predictive role in that it reduces both the in-sample and out-of-sample prediction error rate. Furthermore, the results of the unbiased panel regression tree estimator are consistent with our benchmark linear mixed effects model. The coefficients in the linear mixed effects model are consistent with the variables entering in the tree models. Specifically, the coefficient of the organisation score is substantial and statistically significant. The results are robust to the inclusion of fixed hospital and year effects. The key result also remains unchanged when we rescale the clinical and organisational measures of quality by taking out the within-hospital means of the variables to eliminate potential hospital-specific unobserved time-invariant factors.Our findings are consistent with the theories from the organisational economics and productivity literature when extended to the health care setting. The results are particularly in line with the findings of Bloom and Van Reenen , Bloom eThe rest of the article is organised as follows. "The study has gathered hospital and regional level panel data from several administrative sources. Our two key variables include composite measures of the clinical and organisational quality of the process of stroke care. We obtain the data on these measures from the Royal College of Physician’s National Sentinel Stroke Audit from 2004 to 2010 where the data have been collected at the hospital level. The Royal College of Physicians carried out rounds of the National Sentinel Stroke Audit (NSSA) in every 2-year cycle from 1998 to 2010. The NSSA monitored the progress of stroke care in England, Wales and Northern Ireland. Between 1998 and 2010, the NSSA achieved 100% voluntary participation of hospitals, collecting data on more than 60,000 patients from England, Wales and Northern Ireland. The focus of the audit was centred on two components: clinical and organisational. The former measured the clinical quality of the process of stroke care whereas the latter measured the organisational quality of stroke care. NSSA was eventually replaced by Sentinel Stroke National Audit Programme (SSNAP). As a result of the replacement, some of the questions used to construct the organisational and clinical components of the NSSA data underwent changes, making it difficult to combine the data from the two audits. For consistency, we have restricted the sample to the NSSA data that are in public domain and left the SSNAP data for a separate research. The audit data have been used for research studies, for instance, in Bray et al.  and McNahttps://www.rcplondon.ac.uk/.In assessing the quality of the process of care for stroke, the NSSA collected data on the practice of a set of clinical standards relating to patients hospitalised with a primary diagnosis of stroke with the ICD10 codes of I61 , I63  or I64 . Data were collected on 8697, 13,625, 11,369 and 11,353 patients respectively for the years 2004, 2006, 2008 and 2010 across the NHS trusts or hospitals in England, Wales and Northern Ireland. The clinical standards reflect scientifically based practices that are set by the National Institute for Health and Clinical Excellence (NICE). The clinical standards are organised into six domains of the process of stroke care, including initial patient assessment, multidisciplinary assessment, screening and functional assessment, care planning, communication with patients and carers, and acute care. Table Stroke is a medical emergency that requires immediate medical intervention as the benefits are critically time dependent. To achieve this, a high level of coordination is required between various steps of care from the onset of stroke to rehabilitation. And this is only feasible if relevant complementary resources are in place and stroke specialists and trained staff collaborate with each other in a multidisciplinary and timely manner. To capture the organisational quality of the process of stroke care, the audit included a set of questions on the availability of stroke units, neurovascular facilities, TIA clinics and specialist stroke teams and their features, on whether the hospital provided education and engaged in clinical research, and on whether the hospital sought patient’s views and had produced reports within the last 12 months. The audit further collected data on average waiting time for scanning. Table https://www.rcplondon.ac.uk/ and in https://www.rcplondon.ac.uk/projects/national-sentinel-stroke-audit.Over the years 2006–2010, the NSSA organisational audit went through changes in the form of inclusion of new and exclusion of old questions to collect data on a hospital’s organisational quality for stroke care. Despite the changes, a significant number of questions within the above domains remained the same. Particularly, the questionnaires used to collect data between 2006 and 2008 organisational audits were very similar or overlapping. We expect any impact of the organisational component on quality of stroke care to be slow. To capture these delayed effects we use 1-year lagged values of predictors when predicting the quality of stroke care instead of considering contemporaneous information. This leaves us with 2006 and 2008 organisational scores. Given the strong resemblance between 2006 and 2008 audits, we do not expect that the changes in the audits would distort our analysis. Further information on the data, questionnaire proforma and the method for constructing the composite organisational measure are available at In addition to an aggregate measure, we supplement the analysis using disaggregated measures or factors of stroke organisation that are common across 2006 and 2008 and are listed in Table Table We add several explanatory variables to our data to control for other factors that may affect health care quality. We add Teaching and Foundation Trust (FT) status for each hospital. Teaching hospitals tend to treat patients with the most severe and complex illnesses and have a higher chance of learning how to deal with complex cases. This may lead to a higher quality of care. Conversely, teaching hospitals can introduce a delay in the treatment process due to consultants’ role in training medical students .Foundation trust hospitals are non-profit public organisations that enjoy greater managerial and financial autonomy from the central government control. FT hospitals are allowed to retain their surpluses, which they can invest in staff salaries or capital equipment. They are also allowed to borrow money to improve services. Hospitals with FT status are likely to have higher quality of care for stroke. Farrar et al.  find thaLarger NHS hospitals can lead to higher quality of care because of economies of scale and the “volume-outcome” hypothesis. Or, they might lead to lower quality of care due to diseconomies of scale from the greater complexity of their organisational structure. A number of studies include hospital size measured by the number of hospital beds among factors affecting hospital quality , 62, 65.A rich literature highlights the importance of adequate specialists and neurologists in the prevention and management of stroke patients and improved stroke outcomes of care , 74, 78.A number of studies have found a positive relationship between nurse staffing and health care quality. Fine et al.  study thStudies have also documented considerable regional variations in health care quality , 45, 71.While the main objective of this article is to determine what predicts the quality of hospital care, our aim is to portray any predictor-response relationship in a simple, easy-to-understand and intuitive way. We are interested in making meaningful sense of how several predictors may be involved in complex interactions with one another when helping to explain quality. For example, we would like to understand whether the standard of care at hospitals that are located in a wealthy area and have a low nurse-to-bed ratio is different from the quality of care offered in hospitals with a higher nurse-to-bed ratio situated in a relatively lower income region. Traditional parametric methods such as regression models do not always offer straightforward interpretation of such intricate interplay of variables. We, therefore, resort to a class of non-parametric techniques, commonly known in machine learning literature as regression trees, that serve the purpose well. The tree mechanism involves recursively partitioning the predictor space into a number of small regions based on simple rules and then using the mean or median of the realised values  of observations  belonging to a region as the predicted value for a new observation that falls in that particular region. Most importantly, the splitting decision rules, order of importance of selected predictors and their interactions are summarised in a visually attractive and intuitive way. To our knowledge, this is one of the very few studies in health economics that exploit regression trees with an aim to find drivers of quality of care.Several tree growing algorithms are proposed in the statistics and machine learning literature. The most widely used are ‘CART’  and ‘C4.t (years) i and time period t, Since we observe a number of hospitals over several years the data used in our study are longitudinal or panel. Such a data structure requires careful accounting of possible variations across subjects that cannot be captured by observed predictors and also autocorrelation across observations from the same subject. If we observe subjects  f, which may well be non-linear. It is only over the last decade that developments have been made in generalising trees for panel data applications. This article uses a method called an unbiased random effect expectation maximisation (RE-EM) tree, only recently developed in Fu and Simono [f by using a tree method and the other estimating unobserved heterogeneities We seek to apply flexible tree-based methods for approximating the unknown relationship d Simono . Unlike d Simono , which rd Simono  and is, As any non-parametric estimator, regression trees are subject to over-fitting. To achieve an optimal trade-off between the bias and variance (over-fitting), we rely on the out-of-sample predictive accuracy of the model, estimated using cross validation. We select the regression tree model with the lowest prediction error to identify variables that potentially contribute to the quality of stroke care.By adopting the regression tree method, we complement the dominant tradition in econometrics, where the emphasis is on parameter estimation and statistical significance testing. There are no coefficients in regression trees. Instead, the idea is whether the variable of interest or the interactions implied by the background domain-specific information or theory appear in the tree that best predicts the outcome variable.Our methodological stance comes close to the seminal work of Milton Friedman  and the We employ an unbiased random regression tree estimator for panel data to develop a series of predictive models to identify key predictors of the quality of the process of stroke care in NHS hospitals. In building the tree models, we rely on the literature to decide on potential explanatory variables that may drive the quality of the process of stroke care across hospitals. Some of the potential control variables are highly correlated. The panel regression tree estimator arbitrarily selects from among highly correlated variables to build a model . To gainAmong the variables measuring physical capital, the variables operating theatres and day case theatres are highly correlated (0.88). We a priori exclude the number of operating theatres from the base model. The correlation among nurses, general medicine group (gmg) staff, science and allied professionals staff exceeds the threshold of 0.75. We keep nurses in the base model, partly because this choice will lead to models with overall lower out-of-sample prediction error. The number of nurses in a hospital is highly correlated with the number of beds. We replace nurses with the nurse-to-bed ratio in order to be able to identify possible distinct effects of physical capital  and non-specialist human capital. Among the regional health and socio-economic variables, the weekly median wage and inequality are highly correlated (0.845). We exclude inequality from the base models. Also, stroke mortality and the all-age standardised mortality ratio (SMR) are highly correlated (0.87). We keep stroke mortality.We consider four unbiased regression tree models to gain insights into the structure of the data. The first three models regress the measure of the quality of the clinical process of stroke care on the individual variables that capture organisational features of the process of stroke services and relevant control variables. The fourth regression tree model replaces the individual variables with the composite measure of organisational quality of the process of stroke care to better capture possible complementarity.We next compare the results of the unbiased REEM-Tree with linear mixed effects models (LME) to check the robustness of the results. We rely on the in-sample and out-of-sample predictive performance of the models to select a model from among the trees that best fits the data.Recall we categorised possible drivers of the quality of stroke care into internal and external drivers of hospital performance. Internal drivers refer to factors such as physical assets, human capital, the structure of decisions and the internal organisation of the hospital. External drivers refer to regional health and socio-economic features. We start with a model of internal drivers and next adds variables capturing potential external drivers. Our underlying methodological principle is that if any of these factors drive the quality of stroke care, variables measuring the factors will appear in a model that best predicts the quality of stroke care . With thModel 1:Scorebeds + day case theatres + nurses + neurology + neurophysiology + neurosurgeons + teaching + ft + ASU + RSU + CSU + SUTC + Specialist + ESD + NeuroClinic + PatientViews + Report.score measures the quality of the clinical process of stroke care. Table The dependent variable Adding the variables representing potential external drivers of quality will give rise to our second model:Model 2:Scorebeds + day case theatres + nurses + neurology + neurophysiology + neurosurgeons + teaching hospital + foundation trust + ASU + RSU + CSU + SUTC + Specialist + ESD + NeuroClinic + PatientViews + Report + stroke admissions + stroke mortality + median wage + no qualifications.From the tree results in Fig. Overall, the model points to several results. To begin with, the model reveals variations in the quality of stroke care across regions, consistent with the findings in Grimaud et al. . An explFigure Model 3:Scorebeds + day case theatres + nurses + neurology + neurophysiology + neurosurgeons + teaching hospital + ft + ASU + RSU + CSU + SUTC + Specialist + ESD + NeuroClinic + PatientViews + Report + stroke admissions + stroke mortality + median wage + no qualifications + yr2010.In Fig. A fundamental insight of economic theory is the critical complementarity among diverse elements that shape the organisation of the firm and its performance . In Fig.Model 4:Scorebeds + day case theatres + nurses + neurology + neurophysiology + neurosurgery + teaching + ft + admissions + stroke mortality + median wage + no qualifications + organisation score + yr2010.Figure k-fold out-of-sample-predictive performance measures for the unbiased tree models. Consistent with the in-sample fit measures, the final model yields the lowest out-of-sample prediction error among the models—(8.531) and (8.268) respectively.Table Figure The regression trees presented above do not take care of hospital fixed effects features. In the absence of strong theory, one requires alternative techniques to capture possible causal connections. We build a series of linear panel data models to investigate whether the coefficients of the variables appearing in the trees are statistically significant and whether the coefficient estimates are robust to the inclusion of hospital individual fixed effects. Further, we report whether the results are robust to the choice of alternative measures of physical capital, human capital and regional factors. We also consider replacing our human capital variables with relevant ratios.s and t, We first check the empirical validity of the patterns observed in trees by comparing them to a class of linear mixed effects models (LME). The LME results come quite close to traditional random-effects results. Both assume that mentclass2pt{minimmentclass2pt{minimWe assess the robustness of the four models introduced earlier. In each case, we consider two LME models: (1) a model with all the variables entering the corresponding tree and (2) a model with the within-group means of the time-varying variables to capture fixed effects.Table The Hausman test indicates the presence of fixed effects. Table In the above, we did not separate hospital fixed effects from time fixed effects. Testing for hospital and time effects, there is strong evidence for the presence of time effects, which is consistent with the observed pattern in Fig. Further, the nurse-to-bed ratio variable appears statistically significant in the first two models, with a positive sign across all the models, suggesting complementarity between the number of nurses and beds. The coefficient for beds, as a measure of hospital size, has a negative sign across the models and is significant only in the first model. The measures indicating external factors are statistically significant in one form or another. The number of neurosurgeons per region is statistically and positively significant in the second model and weekly median wage in the third model. The variable stroke mortality is statistically significant in both models—suggesting that in areas where stroke mortality increased over time the quality of the process of stroke care has improved too. It is possible that extra resources are devoted to the process of stroke care in areas with high stroke mortality, leading to a higher correlation between stroke mortality and the clinical quality of stroke care.To further support the robustness of our key results, we rescale the measures of the quality of the clinical and organisation of the process of stroke care by taking out the within-hospital means of the variables, while including the control variables in their level form. Table The fact that the organisational quality of the process of stroke care appears among critical drivers of the clinical quality of stroke care raises a deeper question as to what factors drive organisational quality. Our sample is inadequate for fully shedding light on the subject. Nonetheless, we have regressed the composite measure of organisational quality on several theoretically plausible drivers of organisational quality. Columns 1 and 2 in Table The results from the traditional econometric approaches corroborate the findings from the unbiased REEM-Trees. All the analyses indicate the importance of the organisational quality of stroke care in determining the clinical quality of stroke care. The tree models point to critical interactions among various variables driving stroke care quality. It is a complex interaction among hospital resources that shapes quality. Our key results are robust to the use of ratio variables or alternative measures of human or physical capital left out in constructing the trees because of the high correlation. Our results are not driven by hospitals in London. Excluding data relating to London’s hospitals will not change our results, as shown in Table A feature of the health care systems is substantial variation in health care quality across hospitals. This study has focused on the quality of the process of stroke care as an indicator of the overall quality of NHS hospitals. Drawing on the literature, we conjectured several explanations for the observed cross-hospital heterogeneity and tested their predictive implications using a short panel spanning 2004 to 2010. Both the parametric and non-parametric methods identify several features of the organisation of stroke care as key predictors of hospital quality. Presences of specialist stroke teams, well-equipped stroke units and neurovascular clinics have all been found to improve the quality of stroke care and the improvements range between 2 to 5 points in a quality score measured on a 0–100 scale. When a composite score as a summary of such organisation of care has been used separately it consistently appeared to be a significantly important driver of quality. The result persists when potential confounders/variables are controlled for and is particularly robust to the inclusion of a time trend, which accounted for a major policy change during the study period. The non-parametric methods identify the measure of organisation score as the key predictor of hospital quality. The result persists when potential confounders/variables are controlled for and is particularly robust to the inclusion of a time trend. The result supports an emerging literature that emphasises the critical role of organisation of resources in productivity. The non-parametric methods also reveal critical interactions among potential determinants of the quality of the process of stroke care.Several limitations offer scope for further research. The predictive results narrow down candidate hypotheses on the sources of hospital heterogeneity but are only indicative of the causal impact of organisational factors on the quality of stroke care; they do not establish causation. A thorough analysis will consider further control variables such as stroke admissions, examine alternative measures of quality and attempt to obtain a more comprehensive measure of organisation quality. As another limitation, our study does not control for clinical networks. Under these clinical networks, hospitals combine and integrate resources with other hospitals in the networks to provide high quality of care to the patients. As mentioned in , for exa


This paper presents a novel method of seamline determination for remote sensing image mosaicking. A two-level optimization strategy is applied to determine the seamline. Object-level optimization is executed firstly. Background regions (BRs) and obvious regions (ORs) are extracted based on the results of parametric kernel graph cuts (PKGC) segmentation. The global cost map which consists of color difference, a multi-scale morphological gradient (MSMG) constraint, and texture difference is weighted by BRs. Finally, the seamline is determined in the weighted cost from the start point to the end point. Dijkstra’s shortest path algorithm is adopted for pixel-level optimization to determine the positions of seamline. Meanwhile, a new seamline optimization strategy is proposed for image mosaicking with multi-image overlapping regions. The experimental results show the better performance than the conventional method based on mean-shift segmentation. Seamlines based on the proposed method bypass the obvious objects and take less time in execution. This new method is efficient and superior for seamline determination in remote sensing image mosaicking. A large remote sensing image with a wide field of view and high resolution is often required for many applications, such as map-making, disaster management, and military reconnaissance ,2. HowevSince Milgram  proposedMany of the methods described above considered seamline detection as an energy optimization, characterizing the difference between input images in overlapping regions by constructing a special energy function (cost). Image information should be contained in the cost comprehensively, e.g., the color, the gradient, the texture feature and the edge strength, and then find the optimal solution through different optimization algorithms, such as dynamic programming, Dijkstra’s algorithm , snake mPan et al.  proposedIn this paper, a novel method for seamline determination is presented based on a parametric kernel graph cuts (PKGC) segmentation algorithm  for remoConsidering the integrity of the mosaicking image, the seamline should pass through flat areas of texture, such as rivers and meadows, bypassing the obvious objects, such as buildings. Therefore, we can set the background regions (BRs) and obvious regions (ORs) with an image segmentation method. The seamline prefers to pass through BRs and round ORs.The corresponding relation of the overlap area of the input images will be determined after pretreatment and registration for input images . Then thSegmentation by PKGC: The PKGC algorithm borrows from the idea of kernel k-means, and a kernel function The kernel graph cuts model needs to set Then, substitution of Equation (3) into Equation (1) results in the expression:Clearly, the solution of Equation (4) depends only on the regional parameters Determining BRs: The image can be segmented into the foreground obvious objects regions and the background regions. Two input images are segmented using the PKGC algorithm independently. The BRs determine the intersection of the segmentation results of the left image and the right image. The remaining regions of overlapping area are regarded as ORs, i.e., the union of the segmentation results.I be the overlapping region of the input left image We consider the following steps to construct a more accurate energy function. Firstly, calculate the global energy function Color difference is the most common energy function in seamline detection for image mosaicking. We calculate the difference in the HSV  color space instead of the common RGB space. The color difference In the image morphological processing, the structural element is a common tool for image feature extraction and the structural element with different shapes can extract different image features. Furthermore, changing the size of the element can be extended to the multi-scale space . The graFirstly, construct the multi-scale element:Then the gradient feature According to the above definition, the maximum and minimum gray value of the local image region can be obtained by dilation and erosion operators, respectively. The morphological gradient is defined as the difference of the dilation and erosion, which can extract the local information effectively. Meanwhile, we can obtain more comprehensive information by changing the scale and angle of the linear structural element. The large scale indicates the gradient information within long distances, while the gradient information with short distances is indicated by the small scale. Angle 0° indicates the horizontal gradient information, and angle 90° indicates the vertical gradient information.MSMG.m is the number of angle Finally, gradients of all scales and all angles are integrated into the multi-scale morphological gradient The MSMG constraint In this paper, we calculate the image entropy of the 3 × 3 neighborhood of the pixel to represent the local texture features of the image. We iterate through all pixels using the entropy filter of size 3 in the implementation. Image entropy is the measure of data randomness in an image’s gray histogram, which is calculated by:The global cost Then we weight The purpose of the pixel-level optimization is to optimize the location of the seamline in the local area. As shown in Dijkstra’s algorithm is a global optimization technique to find the shortest path between the two nodes in the graph. Each pixel in the overlapping region is regard as one node which has eight neighbor nodes. As shown in We introduce the method of seamline determination in a two-image overlapping region and can obtain a panoramic image with a wide field of view and high resolution by mosaicking a set of images using this method. As shown in The method we proposed was implemented by C++ (VC 10.0) and Matlab (2012b), combined. A desktop computer with an Intel Core i5 CPU at 3.2 GHz and 4 GB of memory was used. Experiments were conducted using three sets of orthoimages. In order to improve the efficiency, we built one pyramid level that was built by a reduction factor of three with a 3 × 3 average filter. Five sets of experiments were carried out to verify the effectiveness and superiority of our method.An image segmentation comparison was performed for Image Set 1 to verify the advantages of the BRs obtained by the PKGC segmentation we introduced in The results of image segmentation are displayed in In order to verify the rationality of the energy function proposed in For Image Set 1 and 2, we determined the seamline using Chon’s method , Li’s meIn order to test the performance of suppressing noise, we detected seamlines in the images perturbed with Gaussian noise and Gamma noise. The mosaicking dataset is captured by an aerial digital camera integrated in the airborne photoelectric platform. We use the unmanned aerial vehicle (UAV)-equipped airborne photoelectric platform to take images by whisk broom for a ground area. We mosaic this dataset by the pixel fusion method, two-image overlap seamlines, and the multi-image overlap seamlines method. The proposed method is effective and excellent to determine seamlines for remote sensing image mosaicking. However, there is still room for improvement in this method. When the size of the objects is too small and the color is very close to the background, such as black cars in the shadow of buildings, they cannot be extracted. Moreover, although the time-consumption is greatly reduced compared with other methods, it is not sufficient for real-time processing. These issues will be solved in future research.We proposed a novel method to determine the seamline based on PKGC segmentation and the combined cost for remote sensing image mosaicking. In this method, we segment the input images by the PKGC algorithm and determine the BRs and ORs based on the result of segmentation firstly. Then the global cost containing the color difference, MSMG constraint, and texture difference is weighted by BRs. Finally, the seamline is determined in the weighted cost from the start point to the end point. Dijkstra’s shortest path algorithm is used to optimize the seamline at the pixel level. The BRs can automatically be obtained by PKGC segmentation in this method. Furthermore, the combined cost can indicate the image information accurately. The new method for multi-image seamline detection can effectively resolve the problems in multi-image mosaicking. Experimental results demonstrate the effectiveness and superiority of the proposed method. Seamlines go within roads or grass and successfully bypass the obvious objects. The performance of the proposed method is much better and faster than Pan’s method. Moreover, this method is particularly suitable for images with objects of larger size. The proposed method is effective and shows potential for remote sensing image mosaicking. The mosaicking image based on the seamlines using the proposed method can satisfy the requirements of both field of view and resolution.