dataesr/scientific-paragraphs-categorization huggingface dataset:
Strength and limitations We used a systematic approach to search different databases, covering the period of VOC circulation that includes the first Omicron variants (BA. 1 and BA. 2) in 2022. Unlike preceding VOCs, Omicron comprises an increasingly large groups of multiple variants and subvariants. Information on the specific subvariants was not provided in the included studies, which limits the interpretation of the associated data in our review. We included a broad selection of study designs in various languages and screened reference lists of included studies. Our search strategy might have missed relevant studies, although we only excluded three records for language reasons. A limitation of the review is that misclassification of the variant could have occurred as only a minority of study samples from all cases was sequenced in several studies and we relied on dates during which a variant was dominant.
Acknowledgements We would like to thank all members of  WHO's Maternal, Newborn, Child and Adolescent Health and Ageing department , who contributed to the development of this review:  Kathleen Strong ,  Theresa Diaz ,  Anshu Banerjee ,  Maria van Kerkhove ,  Abdi Mahamud ,  Valentina Baltag ,  Judith Ann Mandelbaum-Schmid. Contributors MW, NL and MG conceived and designed the review. MW, LH and MG performed the literature search. MW, AMI, LA-C, NP, YTL, MIA, AGL, IZ, LH and MG screened the articles for relevance and extracted the data. MW, MG and NL adjudicated as third reviewers in case of disagreements during the screening and extraction. MW, AMI, LA-C and MG synthesised the data. MW, AMI, LA-C, LH, NP, YTL, MIA, AGL, NL and MG all discussed the interpretation of the findings. MW and MG wrote the first draft of the manuscript.
For the moment, within the ORCHIDEE-MICT model, there are three major modules: carbon, water, and energy. The carbon cycle module operates for each PFT sub-grid and the water cycle operates for each soil tile (divided into bare soil, tree PFTs, grass and crop PFTs, and peatland PFT categories), while the energy module is solved only at the total grid-cell level  (Best et al. , 2004). Figure  1  shows the schematic representation of energy budgets from the surface to snow and soil layers in the original and new versions of ORCHIDEE-MICT, namely MICT and MICT-teb. The details of the energy budget in the model are described as follows.
Snow energy budgets An explicit snow model of intermediate complexity has been introduced in MICT as described in  Wang et al. (2013). The snowpack includes three snow layers (Fig. 1 ), with snow settling, water percolation, and refreezing and thawing of snow taken into account. When evaluated against observation data, the new snow module has improved the heat interaction between snow and soil or ground surface  (Wang et al. , 2013). The heat conduction in snow layers uses the same onedimension heat diffusion function as that in soil layers (Eq. (  5 )), while with the snow's heat capacity (csnow) and thermal conductivity (𝜆snow): c snow = ρ snow × c p_ice (8) λ snow = 1a λ + b λ × *ρ snow - 2 5 + Ba λv + b λv T snow 7c λv D × P 0 P a (9) where 𝜌snow is snow density (kg m -3 ), varying with the snow settling; cp_ice is the heat capacity of ice (2.
Implementation of multi-tiling energy budget in ORCHIDEE-MICT-teb To represent the sub-grid energy budget in MICT, we calculate PFT-specific surface properties including the roughness height and the albedo of different PFTs to start the separation of surface energy budgets for each PFT, and then add the PFTspecific calculation for energy budget at the surface as well as in snow and soil layers (Figs. 1  and 2 ). Owing to using distinct input variables from the energy budget module, some processes in the hydrology cycle and carbon cycle are also modified correspondingly. The details of all of the modifications are described as follows.
The distinct surface properties among different PFTs propagate to differences in surface energy fluxes and then differentiate the Tsurf across different PFTs. In MICT-teb, all processes related to the changes in surface properties and Tsurf in the surface energy budget are separated and operate independently for each PFT (Fig. 2 ). For LE (or ET), it comprises four components: Esubli, Esoil, Etrans, and Einter in the model. As described in Sect. 2. 1, only Etrans and Einter are PFT-specific in the original MICT. However, due to the modifications made to surface energy budgets and surface properties resulting in varying snow cover fractions across different PFTs, Esubli is now separated for each PFT in MICT-teb. Regarding Esoil, the water limitation in the hydrology module differs among different soil tiles, whereas in MICT, it is considered at grid scale only.
Soil energy budgets Following Eq. (  5 ), modifications of energy budgets at surface and in snow layers could result in variations in the starting point of heat conduction in soil for different PFTs. While within soil, the heat conduction is more regulated by the heat capacity (c) and thermal conductivity (𝜆). Liquid SM, frozen SM, and SOC are three key factors influencing the two thermal parameters in the model (Eqs. (  6 ) and (  7 )). In the original MICT, the average values of these three factors across all PFTs are used due to the limitation of having a grid-scale mean energy budget. In the new version, we simulate PFT-specific liquid SM and frozen SM in energy modules to represent the heterogeneity of different PFTs, following the separation of soil heat conduction (Fig. 2 ). Regarding SOC, MICT uses the grid-cell SOC obtained from an observation-based SOC map (FAO, 2012;  Zhu et al.
Associated modifications of hydrological and carbon processes Soil temperature (Tsoil) is a key factor to influence hydrologic and biogeochemical processes in soil. Therefore, the PFTspecific variations in Tsoil result in a series of associated modifications of hydrological and carbon-related processes in relation to the original MICT (Fig. 2 ). For soil hydrology, there are three main modifications in MICT-teb compared to MICT: 1) the calculation of PFT-specific Tsoil for each PFT to calculate liquid-frozen ratio of SM; 2) the use of PFT-specific bare soil evaporation from the energy module; and 3) the separation of snow-related processes for each PFT. For the soil carbon cycle, there are four main modifications in MICT-teb: 1) the use of PFT-specific Tsoil and SM for litter decomposition; 2) the use of PFT-specific Tsoil and SM to calculate carbon flow from litter to soil; 3) the use of PFT-specific Tsoil and SM for root maintenance respiration; and 4) the use of PFT-specific Tsoil and SM for soil carbon decomposition.
Simulation protocol and forcing datasets To compare the differences in energy, hydrology, and carbon processes between MICT-teb and MICT, we design three groups of simulations (S0, S1, and S2) as shown in Table  1. 2018 ) for the peat grass PFT  (Xu et al. , 2018; Qiu et al. , 2019). In S0, the original MICT is used for all three periods. In S1, MICT-teb is used with the flags controlling the multitiling energy budget (MTEB) turned off for periods A and B (i. e. , identical to group S0), but turned on for period C. In this way, the differences in energy, hydrology, and carbon between S0 and S1 solely due to the MTEB can be compared based on the same starting point (end of period B). In S2, the flags controlling the MTEB are turned on from the beginning of period A. Thus, comparing S0 and S2 could infer differences in long-term equilibrium of energy and hydrology, as well as nearequilibrium soil carbon storage between MICT-teb and MICT.
Improvements for permafrost simulations Given the crucial role of Tsoil in permafrost simulations, we compare the simulated permafrost extent from MICT and MICTteb with two independent permafrost datasets from  Brown et al. (2002)  and  Obu et al. (2019) , hereafter named Brown2002 and Obu2019, respectively (Fig. 16 ). Brown's map is compiled based on national / regional maps and empirical knowledge, categorizing permafrost into four classes: continuous permafrost (permafrost fraction > 0. 9), discontinuous permafrost (0. 5 ~ 0. 9), sporadic permafrost (0. 1 ~ 0. 5), and isolated patches (0 ~ 0. 1)  (Brown, 2002 ). Obu's map is generated by using a temperature model to simulate soil thermal regimes in 3D at 300 m × 300 m spatial resolution  (Obu et al. , 2019). The Obu2019 data provides the absolute fraction of the landscape affected by permafrost when aggregated to a coarser grid-cell  (Obu et al.
, 2019). The simulated permafrost areas are identified following  Guimberteau et al. (2018)  with two definitions: 1) active layer thickness (ALT) less than 3 m; or 2) Tsoil of any soil layer remains below 0 °C for at least two years. Since the simulated permafrost areas are very similar between the two definitions, we only show the results using the ALT definition in the manuscript while the results using the Tsoil definition in supplementary (Fig. S21 ). Overall, our models can capture the spatial pattern of continuous permafrost from the two independent datasets. However, the simulated total area of continuous permafrost from MICT, after excluding Greenland (18. 5 Mkm 2 ) is 7. 6 and 6. 9 Mkm 2 larger than that from Brown2002 and Obu2019, primarily due to the overestimation of continuous permafrost in mid-high latitudes of Asia and the Tibetan Plateau.
Acknowledgements. This research was supported by the  European Union 's  Horizon 2020 research and innovation programmes  under grant agreement No  101003687  (PROVIDE). PC acknowledges support from the  CALIPSO ( Carbon Loss in Plant Soils and Oceans)  project, funded through the generosity of  Eric  and  Wendy Schmidt  by recommendation of the  Schmidt Futures program. DZ acknowledges support from  National Natural Science Foundation of China  (No. 42101090 ). https://doi. org/10. 5194/gmd-2023-207 Preprint. Discussion started: 22 November 2023 c Author(s) 2023. CC  BY 4. 0 License.
Code availability. The ORCHIDEE-MICT-teb model (r8205) code used in this study is open-source and distributed under the CeCILL (CEA CNRS INRIA Logiciel Libre) license. It is deposited at https://forge. ipsl. jussieu. fr/orchidee/wiki/GroupActivities/CodeAvalaibilityPublication/ORCHIDEE-MICT-teb and archived at https://doi. org/10. 14768/0954a0e9-6a7a-4006-803e-4db36ef2db88, with guidance to install and run the model at https://forge. ipsl. jussieu. fr/orchidee/wiki/Documentation/UserGuide. Codes to process data, generate all results, and produce all figures are archived at https://doi. org/10. 5281/zenodo. 10014533 (Xi, 2023).
15and Fig. S19, the simulated mean annual Tsoil at 20 cm from MICT and MICT-teb can well reproduce the spatial gradient of observed values, with a strong and positive correlation (R = 0. 94; p < 0. 001). However, when it comes to the mean seasonal cycle of Tsoil, a warmer Tsoil during winter but a cooler Tsoil during summer are simulated in comparison with observations, especially for sites located in continuous permafrost regions (Fig. 15(c)). Apart from climate forcing data uncertainties as suggested byGuimberteau et al. (2018), SM, SOC, and snow cover are three factors most likely to regulate the seasonal amplitude of Tsoil. Guimberteau et al. (2018)  has demonstrated that the snow insulation is underestimated by MICT when using both GSWP3 or CRUNCEP datasets to force the model. This implies that, from a snow perspective, our simulation should exhibit an amplified seasonal cycle.
Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for numerical nulls, on the other, theoretical research largely concentrates on the standard notions of certain and possible answers. In the presence of numerical attributes and aggregates, however, these answers are often meaningless, returning either too little or too much. Our goal is to define a principled framework for databases with numerical nulls and answering queries with arithmetic and aggregations over them. Towards this goal, we assume that missing values in numerical attributes are given by probability distributions associated with marked nulls.
This yields a model of probabilistic bag databases in which tuples are not necessarily independent since nulls can repeat. We provide a general compositional framework for query answering and then concentrate on queries that resemble standard SQL with arithmetic and aggregation. We show that these queries are measurable, and their outputs have a finite representation. Moreover, since the classical forms of answers provide little information in the numerical setting, we look at the probability that numerical values in output tuples belong to specific intervals. Even though their exact computation is intractable, we show efficient approximation algorithms to compute such probabilities.
INTRODUCTION Handling incomplete data is a subject of key importance in databases, but the practical side of it has many well-known deficiencies  [13] [14] [15] , and the state-of-the-art in theoretical research has a rather narrow focus in terms of its applicability (see, e. g. ,  [9]  for a recent survey). In particular, systems based on SQL follow a rather specific approach to handling incomplete data where all types of incompleteness are replaced with a single null value, and specific rules are applied to those nulls depending on their usage (e. g. ,  3 -valued logic in selection conditions with true tuples retained; 3-valued logic in constraint conditions with non-false constraints satisfied, syntactic equality of nulls for grouping and set operations). With these rules frequently leading to undesired behaviors, many practical applications attempt to impute incomplete data in a statistically meaningful way, i.
e. , resembling the distribution of other data values in a database  [18]. While standard query evaluation can be used on the now complete data, the knowledge that the original data was incomplete is lost for the users, and they may take the answers as correct without the healthy dose of scepticism they deserve. There is little that database research can offer to mitigate this problem, especially for numerical attribute values where imputation is most commonly used. For them, typical queries use arithmetic operations, aggregate functions, and numerical constraints. In fact, queries of this kind are very common in practice and form the absolute majority of standard benchmarks for database systems (e. g. , TPC-H or TPC-DS). For these queries, though, we have little theoretical knowledge to rely on.
As for possible answers, then every tuple (1, 𝑐) for 2 ≤ 𝑐 ∈ N is a possible answer, in cases where Null is interpreted as 𝑐 (since the tuple (1, 1) is excluded due to the WHERE clause). Hence, the usefulness of such answers is limited. A recent attempt to provide proper substitutes for these notions was made in  [41]  but the shape of answers presented is quite complex for the user to comprehend. Another approach, specifically focused on numerical attributes, was presented in  [10] , but it does not take into account aggregation and prior knowledge on the missing data. As for imputation, it would choose some value for Null, say 2 based on the other data in the database, and then simply return the tuple (1, 2) as the definitive truth -without any hint to the user as to the doubts of the veracity of the answer.
As a first theoretical model of this kind, our approach will not cover the entire SQL Standard and all the numerical attributes in it. However, we shall cover a significant portion of the query language (essentially, the usual SELECT-FROM-WHERE-GROUP BY-HAVING queries) and use the real numbers R as an abstraction for numerical attributes, for the ease of reasoning about probability distributions. Our first task will be to define the data model. The example above hints that we want to treat nulls as random variables, according to some distribution. In our model, for generality, we allow a real-valued random variable for each null, though, in a more down-to-earth approach, we could associate them with individual attributes (say, the height of a person that is usually assumed to follow a normal distribution  [39] ).
Thus, unlike the usual probabilistic databases  [38] , our model deals with uncountably infinite probability spaces. Such databases were the focus of recent studies  [8, 21, 22] , which mainly focused on the crucial issue of measurability of query mappings. Those papers, however, left open a crucial issue: how to construct suitable probabilistic databases from real-world incomplete numerical data. As our first task, we fill this gap and provide such a model. Our construction is general enough so that queries could be viewed as measurable maps between probability spaces given by infinite probabilistic databases. Then, we instantiate our framework to the case of databases with marked (or repeating) nulls  [2, 27]. The fact that nulls can repeat in different tuples will take us out of the realm of tuple-independent probabilistic databases that have dominated the field of probabilistic data so far.
In fact, the need for a model of "tuple-dependent" databases even transcends our immediate goal. Consider, for example, the query SELECT * FROM R JOIN S ON R. A = S. A with 𝑅(𝐴, 𝐵) having one fact (1, Null) and 𝑆(𝐴, 𝐶) containing  (1, 2)  and  (1, 3). The end result has tuples (1, Null, 2) and (1, Null, 3). Since Null is defined by the same random variable in both tuples, the probability that a tuple, say (1, 1, 2), is in the answer depends on the prior knowledge that another tuple, say  (1, 1, 3) , is in the answer. Thus, if we want to have a compositional query language, i. e. , the ability to query the results of other queries (taken for granted in languages like SQL), then we cannot rely on the tuple-independent model, as query results will be not be tuple-independent. We next instantiate a query language.
For the computation problem, we show that it is NP-hard. This means that one needs to resort to approximations. We first show that the standard FPRAS (Fully Polynomial Randomized Approximation Scheme  [3] ) approximation does not exist modulo some complexity-theoretic assumptions. We do show however that, if we allow additive error guarantees, approximations exist and are computable in polynomial time. This is a reasonable relaxation since numbers we compute are probabilities, hence in the interval [0, 1]. This development leaves two loose ends with respect to the feasibility of our approach. First, when a user asks a query, that user expects an output, not necessarily going tuple by tuple and asking for probabilities. Can there be a compact representation of the infinite answer space? We give the positive answer and explain how to construct finite encodings of infinite probabilistic databases that capture information in them up to a difference that has probability zero.
Second, our approximation algorithm creates several samples of the missing data by instantiating nulls in the input database. Even creating one such sample would be infeasible in real life, as it amounts to, essentially, creating a copy of the entire input data just to ask a query over it. To mitigate this issue, we show that sampling can be done smartly, i. e. , encoded in a query that is expressible in our relational algebra. Thus, the sampling approximation algorithm can be expressed by a single query ran over the input database. The remainder of the paper is organized as follows. We start by recalling relevant notions in databases and probability theory in Section 2. In Section 3, we present our framework of probabilistic databases and its instantiation by means of marked nulls with attached probability distributions.
In Section 4, we introduce the query language RA * for databases with numerical entries. Answers for RA * in our framework are then introduced in Section 5 where we also study their measurability and complexity of exact and approximate computation. We expand on approximation in Section 6, where we present an efficient approximation algorithm for RA * queries over probabilistic databases and show how it can be encoded within RA * queries. Finally, Section 7 shows that answers for RA * queries can be represented finitely. In Section 8 we conclude. Related Work. The majority of probabilistic databases found in the literature are based on Possible World Semantics  [38]. In these models, a probabilistic database (pdb) defines a probability space whose outcomes are complete database instances. Such pdbs are often based on tuple-level events, i.
To ensure tame behavior of the probability spaces thus defined, query languages considered are often limited to fragments of first-order logic. The model of this paper is based on Possible World Semantics and attribute-level events. It differs from existing work in that attributes of our pdbs have continuous domains, and their events are defined by continuous probability distributions. Moreover, we study query answering in a rich language that is close to actual SQL. Ours is the first formal framework of this kind, to the best of our knowledge. Probabilistic databases with continuous attribute domains have been studied in database systems literature  [26, 28, 29, 31, 36]. In this line of work, systems either consider only specific classes of queries or resort to ad-hoc semantics of incompleteness to achieve desired computational behavior.
BACKGROUND 2. 1 Incomplete Databases Schemas and instances. We assume a countable set R of relation schemas. Each relation schema 𝑅 ∈ R has an associated arity denoted by arity(𝑅). A schema S is a set of relation schemas. We work with the model of marked nulls, i. e. , we assume a countable set Null := {⊥ 1 , ⊥ 2 ,. } of nulls. The entries in databases come from the set R∪Null. That is, we assume that numerical values come from R; since non-numerical values can be enumerated in an arbitrary way, e. g. , as 1, 2,. , we assume without loss of generality that all non-null entries come from R. A tuple of arity 𝑘 is an element in (R ∪ Null) 𝑘. We follow SQL's bag semantics, that is, a relation R over a relation schema R is a finite multi-set (bag) of tuples with arity arity(𝑅). An incomplete database D, or just database for short, over a schema S consists of relations R D over each relation schema R in S.
We define adom(D) as the set of all entries of D, and Null(D) as all entries of D that are also in Null. A database D is complete if all its relations instances are complete, that is, do not include nulls; Or, alternatively, if Null(D) = ∅. A database query 𝑞 over database schema S is a function from databases over S into databases over S ′ , for some schema S ′ that consists of a single relation symbol. We write 𝑞 : S → S ′ when schemas need to be specified explicitly. Valuations. Valuations assign values to nulls. Formally, a valuation 𝑣 : Null → R is a partial mapping, whose domain, i. e. , the subset of Null on which it is defined, is denoted by dom(𝑣). We lift valuations to databases by defining 𝑣(D) as the database that is obtained from D by replacing every null entry ⊥ with 𝑣(⊥).
QUERYING AND INSTANTIATING PROBABILISTIC DATABASES Our model of probabilistic databases describes all possible data configurations together with a probability measure defining how likely they are to occur. This intuition is captured by the following notion. Definition 1. A probabilistic database (PDB) D over a database schema S is a probability space whose domain is a set of complete databases over S. Notice that, similarly to  [22] , the domain of a PDB D may be uncountable due to the fact that D uses reals as entries. However, in most models of probabilistic databases known in the literature, one assumes tuple independence, i. e. , the presence of each tuple is an independent event. This is not the case for the PDBs presented in Definition 1 where no restriction is imposed on the probability distribution.