dataesr/scientific-paragraphs-categorization huggingface dataset:
Clinical relevance By reducing the information from all domains into a single CQI, the areas for specific improvement may be obscured. Among the different types of composites, the opportunity-based and the all-or-none are the most frequently recommended for the quality of care assessment. 59, 60 Since the two methods, while associated,  61  provide different approaches, both types of CQI have been maintained in the updated version. The main CQI is an opportunity-based score, where all domains are represented and have the same weight (except in patients with LVEF < _40% in whom two additional items are required, giving more weight to the secondary prevention domain). This design has the advantage of increasing the number of items, which may vary according to the patient characteristics and the database used.
First, we show that the union of simple and nonsemisimple Jones-Wenzl idempotents dominates the category TL. Then, we exhibit explicit morphisms that ensure fullness of F TL. In Section 7, we list additional relations satisfied by generating morphisms of TL in the quotient TL = TL/ ker F TL , which will be useful in future works. It remains an open question to understand whether these relations provide a complete presentation of TL, in the sense that they generate the kernel of F TL. However, it seems likely that further relations, generalizing equation (57) to the case r m 2r -2, will be needed. Acknowledgments. This work was supported by JSPS Fellowship for Research in Japan, ID PE18705.
The objective of this study was to define the French population groups for PHM per hospital group. Methods: A database study based on DRG (acute care, post-acute and rehabilitation, psychiatry and home care) from the French National Hospitals Database was conducted. Data included all hospital stays from 1 January 2016 to 31 December 2017. The main outcome of this study was to create mutually exclusive territories that would reflect an accurate national healthcare service consumption. A six-step method was implemented using automated analysis reviewed manually by national experts. Results: In total, 2840 healthcare facilities, 5571 geographical zones and 31,441,506 hospital stays were identified and collated from the database. In total, 132 GHTs were included and there were 72 zones (1. 3%) allocated to a different GHTs.
Methods We aimed to define territories by utilizing healthcare services consumption, attributing a given area to a territory if the providers of that territory provided the majority of healthcare services. We did not focus on a single disease or a specific type of population but chose to capture total healthcare consumption from private and public hospitals. Ambulatory care providers who are located inside these areas would be also considered for the population, even though it was technically challenging to link ambulatory and hospital's services consumption. However, since ambulatory care providers cover a much smaller footprint that hospital providers and since ambulatory and hospital providers would be linked through a shared PHM approach, we did not consider this as an issue. A retrospective study of healthcare services utilization was conducted based on Diagnosis-related Groups (DRG, acute care, post-acute and rehabilitation, psychiatry and home care), through the national PMSI (programme de médicalisation des systèmes d'information) database.
This database records all hospitals stays and provides detailed, if anonymized, information on the patients, including their area of residence through a geographical code (Code GEO PMSI). Therefore, hospital utilization is linked with an area of residence. The database contains utilization data for all types of hospitals (public, private for profit, private non for profit) and all types of hospitalization (short stay, rehabilitation, psychiatry and hospital at home)  [13]. The population attribution to the GHTs was created in a prospective approach where the attribution of a population for the coming years was based on the patient service use from previous years  [14]. All hospital stays recorded in the database between 1 January 2016 and 31 December 2017 were included in the study. Hospital stays were anonymous and a single patient could have different hospital stays within the period of the study.
Hospital stays were included in the study if a corresponding geographical code and at least one diagnosis code was available. The geographical codes used in the database are linked to "communes" (counties), the smallest administrative area in France. There are 5571 "Geo PMSI" geographical codes, and 132 GHTs. There are 34,968 "communes" in France, therefore a Geo PMSI code may include multiple communes. Grouping of communes inside a single Geo PMSI code happens only in the case of communes with less than 1000 residents. The main study outcome was to create mutually exclusive territories that would reflect accurate healthcare service consumption regardless of the provider type or the type within which the services were provided. In addition to the GHTs, supra-GHTs were defined to include as well private hospital services not included in the scope of a GHT, however located within the same territory.
These supra-GHT are the aera where our PHM approach would be deployed. The residents of these area are the residents towards whom healthcare providers are accountable whether they utilize healthcare services or not. Statistical analysis was conducted in a stepwise approach comprising of three consecutives steps. The first step allocated all hospital stays of resident patients within a geographical code to the GHT which provided the majority of stays for the residents of the geographical code. The allocation was made based on two methods: firstly, the number of absolute hospital stays (séjour) in acute hospitals and secondly the number of hospital days adjusted to the mean daily cost of a full hospital day per type of activity (short stay, rehabilitation, psychiatry and hospital at home). All daily costs were extracted from the national database.
This stage makes it possible to adjust the boundaries of the GHT territories while taking into account the private healthcare activity. The same method of homogenization of consumption between types of activities was used. A second round of expert advice was then used for consistency of results and consistency of territories. According to French legislation, this study did not require patient consent. An authorization from the French Data Protection Authority (CNIL) was obtained (no. 715016) have access to the French national hospital database.
Results In total, 2840 healthcare facilities, 5571 geographical zones and 31,441,506 hospital stays were identified in the database. In the first step, 132 GHTs were included corresponding to 14,992,531 stays. The rest of the stays were performed in private hospitals. There were 72 zones (1. 3%) allocated to a different GHT according to the two allocation methods. In the second step, 200 zones were manually reviewed by the group of experts including 72 zones that were previously identified. Among the 200 zones, 33 zones were allocated to another GHT than the one defined in the first step. The example of the GHT in the French department Deux-Sèvres is shown in Fig. 1  and it is worth noting that the zone for the facility in Mauleon, which legally belongs to the Deux-Sèvres GHT was attributed to the neighbouring GHT since the overwhelming majority of healthcare utilization of the residents of that area took place in the second GHT.
Discussion In this study, the attribution of a population under the responsibility of 132 GHTs in France was achieved using a relatively easy to use methodology and was validated by a national group of experts. The main strength of our study relied on the use of the French national hospital database including all hospitals and all stays in France. Since we chose to rely on stays and days and homogenized the results across all types of hospitalization and not on diagnostic and technical interventions, we minimized the risk of bias associated with incomplete or wrong coding and potential errors could not have affected the results obtained  [15] [16] [17]. The exploratory stepwise statistical method used allowed us to limit errors when allocating the zones to a GHT. Remaining discrepancies and unexpected results were manually checked by a group of experts in medical coding and public health.
Our study allowed us to have a fairly precise view of how many people would have specific healthcare needs and plan services in each territory including healthy but at-risk individuals. The findings in this study are the first to allow healthcare professionals including ambulatory providers in France to have a more precise view of the population for which they are accountable. Being able to draw relevant boundaries around Supra GHTs, and using GEO PMSI codes to do so allows healthcare professionals and healthcare authorities to know precisely which counties belong to their area of accountability. In conclusion, the geographical areas defined were used to generate relevant data for healthcare professionals in the five GHTs. These areas where well accepted by the stakeholders from those GHTs, recognized to be meaningful in their clinical work and constitute a first step in creating a shared awareness of a shared accountability.
Acknowledgments We would like to thank  Nikolay Bobev ,  Gianguido Dall'Agata ,  Antón Faedo ,  Gianluca Inverso ,  Carlos Nuñez Chris Rosen  and  Alberto Zaffaroni  for useful discussions and comments. DW is supported in part by the  STFC  Consolidated Grants  ST/P000762/1  and  ST/T000791/1. We acknowledge the  Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+  (Project  ID   39083149 ) for hospitality and support during part of this work.
The authors acknowledge the valuable contribution of all partners involved in the  H2020   BE-SMART  project. This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement  818009. Contribution in this work was also supported in the context of  INES. 2S , funded from the  French State  under the  programme "Investissements d'Avenir ", with reference  ANR-10-IEED-0014-01.
New insights 3. 1 Insight 1: Can global warming still be kept to 1. 5 °C, and if yes, how? The Paris Agreement aims to hold global warming to well below 2 °C and to pursue limiting it to 1. 5 °C. As of 2020, human-caused global temperature increase had reached 1. 2 °C above  1850-1900 levels (www. globalwarmingindex. org). Due to natural variability, an individual year's temperature statistically may exceed 1. 5 °C within the next five years  (World Meteorological Organization, 2021). But warming in a single year is not how to assess whether limits set by the Paris Agreement are met as they refer to longterm, global averages  (Rogelj et al. , 2017). Updates in historical temperature datasets now estimate about 0. 1 °C higher historical warming as a result of improved interpretation of temperature observations from the early-industrial period  (Kadow et al.
, 2020; Morice et al. , 2021; Rohde & Hausfather, 2020; Vose et al. , 2021). Targeting 1. 5 °C of warming above 1850-1900 levels using these updated temperature datasets therefore results in a shorter temperature distance between today and 1. 5 °C, and thus a lower remaining carbon budget than implied at the time of the Paris Agreement. A new uncertainty analysis (using this updated estimate of historical warming) concluded that in order to have even odds of not exceeding 1. 5 °C, the atmospheric carbon uptake would have to be capped at 440 GtCO 2 from 2020 onwards  (Matthews et al. , 2021). The associated remaining carbon budget estimate applies to total future emissions until net-zero CO 2 emissions are achieved, given the current understanding of climate sensitivity and carbon cycle responses to a typical 1.
Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice.
We may also wish to measure and compare accuracy and bias not only for alternative forecasts, but also for different subsets of the whole dataset. For example, we may wish to compare bias of forecasts obtained as a result of positive and negative judgmental adjustments to statistical forecasts, or to compare bias of forecasts obtained in different seasons or years. So, ideally, it should be possible to slice-and-dice forecast data and to obtain corresponding bias indicators for data subsets (see, e. g. ,  Davydenko et al. , 2021 , for examples of constructing queries to subset forecast data). A procedure for conducting a formal statistical test for the presence of bias is also desirable.
'Dataset1' The first dataset was generated using a normal distribution. It contains 1000 series, each series includes 36 actuals. All series were generated using the same equation:  , = 5 +  , , where  , ∼ (0,1), i. i. d. ,  = 1,. ,1000,  = 1,. ,36. Fig. 1  shows an example of a series generated using the above equation. The data generated resembles series (with relatively low observations) that can be met in practice. To generate forecasts ( ,, ) for any period  and any series  in 'Dataset1', we used the equations shown in Method 1  ,,1 = 5 Gives optimal estimates under both linear and quadratic loss. ,,1 is a mean-and median-unbiased forecast since the distribution of  , is symmetric and 𝐹 𝑖,𝑡,1 = 𝔼[𝑌 𝑖,𝑡 ]. 0 0 Method 2 𝐹 𝑖,𝑡,2 = 6 Both mean-and median-biased:  ,,2 = [ , ] + 1. -1 -1 Method 3  ,,3 = 4 Both mean-and median-biased: 𝐹 𝑖,𝑡,3 = 𝔼[𝑌 𝑖,𝑡 ] -1.
'Dataset2' The second dataset was generated using a non-symmetric distribution in order to better replicate real-world data. More specifically, we assume each actual to follow a log-normal distribution (i. i. d. ) with the following parameters:  , ∼ ( = 5,  2 = 0. 5 2 ). Given the above equation, for any series, and for any period, the expected outcome remains the same and can be found using the well-known formula for the mean of the log-normal distribution: 𝔼[𝑌 𝑖,𝑡 ] = exp(𝜇 + 𝜎 2 2 ) = 168. 1741. At the same time, for the log-normal distribution we expect the median to be 𝑀𝑒𝑑𝑖𝑎𝑛[𝑌 𝑖,𝑡 ] = exp(𝜇) = 148. 4132. When trying to predict  , , the optimal forecast under linear loss is therefore 148. 4132, whereas the optimal forecast under quadratic loss is 168. 1741. Fig. 2  shows a series from 'Dataset2' and the difference between optimal predictions depending on the loss function used to optimise the predictions.
2  below) give optimal predictions under quadratic and linear loss, respectively. To generate forecasts ( ,, ) for any period  and any series  in 'Dataset2', we used the equations shown in Table  2. Values for [ , ] and [ , ] give indication of mean and median bias, respectively. These values were found analytically. As shown in Table  2 , forecasts from Method 1 correspond to the mean of forecast density and are mean-unbiased ([ ,1 ] = 0), whereas forecasts from Method 2 correspond to the median of forecast density and are median-unbiased ([ ,2 ] = 0). We next applied a range of bias measures to the two data sets and evaluated them against the criteria we outlined earlier.
, weather forecasts). For example, an actual of 2 units and a forecast of 4 units has the same percentage error (-100%) as an actual of -2 and a forecast of -4, despite the biases being in opposite directions. As we show below, the use of PEs generally distorts the original properties of errors. Fig. 3  shows side-by-side boxplots of MPEs for the artificial datasets and Table  3  shows corresponding MPE values. As expected, the upper bound for MPE is 100%, whereas there is no lower bound, which makes the distribution skewed. For 'Dataset1' for Method 1 we expect to have zero mean and median bias, but the MPEs show a significant bias towards overestimation. Moreover, we expect Methods 2 and 3 ('Dataset1') to have equal absolute bias, but the absolute MPE of Method 2 is much higher compared to that of Method 3, demonstrating that the MPE tends to place a heavier weight on overestimation compared to underestimation.
For 'Dataset2', where the distributions of actuals is non-symmetric, the results are even worse. We should expect different signs of bias for Method 3 and Method 4 and no bias for Method 1, but, according to the MPE, all methods overestimate actuals. Table  3  shows that MPEs do not reflect the ME/MEAN ratio for 'Dataset2' and do not even reflect the true direction of bias. The interpretation of MPE results is therefore counterintuitive and can lead to erroneous conclusions. Our simulations show that the use of MPE as an indicator of mean bias and a proxy for ME is not advisable. Similar experiments we conducted showed that the median percentage error (MdPE) is not advisable as an indicator of median bias and a proxy for MdE (for brevity we have not presented these results here). Interestingly,  (Nikolopoulos et al.
Fig. 4  shows boxplots for AMScE for 'Dataset1' and  ] (where  denotes any series) reliably. Additional problems may arise when some MAEs appearing in the denominator are small so that the underlying distribution of the metric is highly skewed. Instead of scaling by in-sample MAE of the naïve forecast, errors can be scaled by series means (see  Davydenko and Fildes, 2016, p. 245 , for the disadvantages of this approach) or series standard deviations, but these alternatives will not eliminate the above problems. Some problems can be mitigated by just using the MScE instead of the AMScE. But, generally, the AMScE is not a good proxy for ME (see Table  4 ). The AMScE or MScE will exaggerate bias in the same way as the MASE (mean absolute scaled error) will exaggerate the performance of the benchmark forecasting method (see  Davydenko and Fildes, 2013).
Davydenko, A. , & Goodwin, P. (2021). Assessing point forecast bias across multiple time series: Measures and visual tools. International Journal of Statistics and Probability, 10(5), 46-69. https://doi. org/10. 5539/ijsp. v10n5p46 Fig. 5  demonstrates the application of AvgRelMAE to 'Dataset2' where the distribution of actuals is skewed. Under this condition, we would expect forecasts optimal under quadratic loss to have no mean bias and forecasts optimal under linear loss to have no median bias. Method 2 that is optimised for linear loss has no median bias and, as expected, shows the best performance when measured by AvgRelMAE as the AvgRelMAE is a proxy for MAE. Note that where AvgRel-metrics are being applied, we recommend that boxplots have a double scale, as in Fig. 5 , with one scale showing original values of the metric to aid interpretation.
We also recommend that the mean of distributions should be plotted to demonstrate their degree of skewness. Fig. 6  shows the application of AvgRelMSE to 'Dataset 2'. In this case, Method 1, optimised under quadratic loss, and therefore having zero mean bias, is the best performer rather than Method 2. This demonstrates both that the AvgRel-metrics are reflecting the true underlying performance conditions and that it is important to match the metric for accuracy and the metric for bias. However, this raises the question of how the AvgRel-metrics can be adapted to measure forecast bias. Figure  5. AvgRelMAE-boxplots (benchmark: Method 1). 'X' denotes AvgRelMAEs for each method Note: AvgRelMAE is a proxy for MAE and Method 2, having zero median bias, is the best in terms of MAE, as expected.
Fig. 7  shows side-by-side boxplots for RelAMEs (benchmark: Method 1) for 'Dataset1'. The problem is that since Method 1 is unbiased, the relative performances of alternative (biased) methods appear to be very poor (see Table  5 ). The interpretation of the AvgRelAME becomes problematic in this case. Nonetheless, the AvgRelAME identified the ranks correctly. Figure  7. AvgRelAME-boxplot with double-scale (benchmark: Method 1) Note: Method 1 is unbiased, the relative performance of alternative (biased) methods is therefore extremely high. Note: Bold font shows the best methods in terms of mean bias depending on the indicator. Index  denotes any series. To avoid dividing by near-zero AMEs, one quick solution is to use another (biased) method as the benchmark or to use the MSE of the benchmark method as the benchmark.
Nonetheless, if some methods in a dataset are unbiased, it is difficult to use the AvgRelAME or AvgRelAMdE as proxies for ME and MdE. Additionally, these AvgRel-metrics do not show the direction of bias, only the magnitude. Moreover, if   approaches 1, AvgRelAME and AvgRelAMdE will converge to the GMRAE and will no longer be good proxies for ME and MdE. Table  6  shows the results of applying the AvgRel-metrics described above to 'Dataset2'. Here we used Method 3 as the benchmark to avoid the extreme AvgRelAMEs resulting from the unbiasedness of the benchmark. The results correspond exactly to what should be expected. Method 2 (median-unbiased) delivers the best MAE and MdE, whereas Method 1 (mean-unbiased) delivers the best MSE and ME. In the subsections that follow we continue our search for improved metrics that provide an indication of both the direction and the magnitude of bias and avoid the problem of extreme values when benchmark forecasts are unbiased.
4 ). However, a value of Q=1 does not directly correspond to the case when ME=0. In other words, the geometric mean of Q is not always a good indicator of (1-RelME). For example for 'Dataset2' we know that Method 1 is mean-unbiased (see Table  2 ), but the mean of its LnQ is 0. 12 (the geometric mean of Q is 1. 13), which indicates the presence of bias. Another limitation of the LnQ is that it assumes only positive values.
The Overestimation Percentage Corrected (OPc) Calculated Across Multiple Series and Horizons One potential problem with the AvgRelMdE is that it can be found only when series contain non-negative values. Also, the calculation of the AvgRelMdE is relatively complex. In order to obtain a simpler metric for median bias, we propose to apply the Overestimation Percentage corrected (OPc), which we introduced earlier, to multiple series. The OPc for a given method  calculated across all series is: 𝑂𝑃𝑐 𝑗 = 𝑂𝑃 𝑗 + 𝑍𝑃 𝑗 /2, where   -the number of overestimates for method  over the whole dataset divided by total number of cases and expressed in percentages,   -the same for zero errors. If evaluation is made across multiple horizons, forecasts relating to all horizons are used. We can also construct the following formula using the sign function: 𝑂𝑃𝑐 𝑗 = 100% × 1 ∑ 𝑛 𝑖 𝑁 𝑖=1 ∑ ∑ 0.
If this assumption does not hold (we can, for example, use the runs test to check this), alternative approaches may be possible. For example, if errors within series are not independent, but those in different series are, tests could be carried out on the hypothesis that mean the OPc is 50%, with the series, rather than individual cases, treated as the sampling units. We propose the following visual tools to indicate the OPc where multiple series are involved. Firstly, we can use boxplots to explore the distribution of OPc across series, as shown on Fig. 10. The graph on Fig. 10  features the line representing median-unbiasedness. For both datasets we can see that OPc worked as expected showing values very close to 50% for median-unbiased methods. The corresponding results are presented in Table  9.