dataesr/scientific-paragraphs-categorization huggingface dataset:
For transitive relations, one way to regain decidability for GF satisfiability was shown by  Szwast and Tendera [2004] : allow transitive relations only in guards. We now turn to the QA problem. Gottlob et al. [2013]  showed that query answering for GF with transitive relations only in guards is undecidable, even on arity-two signatures. Baget et al. [2015]  studied QA with respect to a collection of linear TGDs (those with only a single atom in the body and the head). They showed that the query answering problem is decidable with such TGDs and transitive relations, if the signature is binary or if other additional restrictions are obeyed. The case of TGDs mentioning relations with a restricted interpretation has been studied in the database community mainly in the setting of acyclic schemas, such as those that map source data to target data.
This latter condition holds in the translations of many classical description logics. Our results also imply that QAlin is decidable for BaseCovGNF, which allows constraints that arise from data integration and data exchange over attributes with linear orders -e. g. views defined by selecting rows of a table where some inequality involving the attributes is satisfied. We first consider QAtc, where σ B includes binary relations R 1 ,. , R n , and σ D consists of binary relations R + 1 ,. , R + n such that R + i is the transitive closure of R i. Theorem 1. We can decide QAtc(F 0 , Σ, Q) in 2EXPTIME, where F 0 ranges over finite sets of facts, Σ over BaseGNF constraints, and Q over UCQs. In particular, this holds when Σ consists of BaseFGTGDs. In order to prove Theorem 1, we give a decision procedure to determine whether F 0 ∧ Σ ∧ ¬Q is satisfiable, when R + i is interpreted as the transitive closure of R i.
In particular, this result holds for frontier-one TGDs (those with a single frontier variable), as a single variable is always base-guarded. This answers a question of  [Baget et al. , 2015]. Data complexity. Our results in Theorem 1 and Corollary 1 show upper bounds on the combined complexity of the QAtr and QAtc problems. We now turn to the complexity when the query and constraints are fixed but the initial set of facts varies -the data complexity. We first show a CoNP data complexity upper bound for QAtc for BaseGNF constraints. The algorithm uses the fact that a counterexample to QAtc can be taken to have a Frooted tree decomposition, for some F that does not add new elements to F 0 , only new facts. While such a decomposition could be large, it suffices to guess F and annotations describing, for each |ϕ|-tuple c in F , sufficiently many formulas holding in the subtree that interfaces with c.
This is similar to the way data complexity bounds were shown for QAtr (in Theorem 4). However, unlike for the QAtr problem, the constraint rewriting in this section introduces disjunction, so rewriting a QAlin problem for BaseCovFGTGDs does not produce a classical query answering problem for FGTGDs. Thus the rewriting does not imply a PTIME data complexity upper bound for BaseCovFGTGD. Indeed, we will see in Proposition 4 that this is CoNP-hard. Hardness. QAlin for BaseCovGNF constraints is again immediately CoNP-hard in data complexity, and 2EXPTIMEhard in combined complexity, from the corresponding bounds on GNF  [Bárány et al. , 2012]. However, we can show that hardness holds for the much weaker constraint language BaseID, by a reduction from DID reasoning, as in Section 3. Theorem 7. For any finite set of facts F 0 , DIDs Σ, and UCQ Q on a signature σ, we can compute in PTIME a set of facts F 0 , BaseIDs Σ , and CQ Q on a signature σ (with a single distinguished relation), such that QA(F 0 , Σ, Q) iff QAlin(F 0 , Σ , Q ).
Conclusion We have given a detailed picture of the impact of transitivity, transitive closure, and linear order restrictions on query answering problems for a broad class of guarded constraints. We have shown that transitive relations and transitive closure restrictions can be handled in guarded constraints as long as they are not used in guards. For linear orders, the same is true if order atoms are covered by base atoms. This implies the analogous results for frontier-guarded TGDs, in particular frontier-one. But in the linear order case we show that PTIME data complexity cannot always be preserved. We leave open the question of entailment over finite sets of facts. There are few techniques for deciding entailment over finite sets of facts for logics where it does not coincide with general entailment (and for the constraints considered here it does not coincide).
F. 2 Proof of Theorem 4: PTIME data complexity bound for QAtr We now turn to the case where our constraints are restricted to BaseCovFGTGDs and deal with QAtr, not QAtc. Recall that Theorem 4 states a PTIME data complexity bound for this case: Theorem 4. For any fixed BaseCovFGTGD constraints Σ and base-covered UCQ Q, given a finite set of facts F 0 , we can decide QAtr(F 0 , Σ, Q) in PTIME data complexity. The proof will follow from a reduction to traditional QA, similar to the proof of Proposition 3: Proposition 15. For any finite set of facts F 0 , constraints Σ ∈ BaseCovGNF, and base-covered UCQ Q, we can compute F 0 and Σ ∈ GNF in PTIME such that QAtr(F 0 , Σ, Q) iff QA(F 0 , Σ , Q). Furthermore, if Σ is in BaseCovFGTGD then Σ is in FGTGD. Proof. We define F 0 and Σ as follows: • F 0 is F 0 together with facts G(a, b) for every pair a, b ∈ elems(F 0 ) for some fresh binary base relation G, and • Σ is Σ together with the k-guardedly-transitive axioms for each distinguished relation, where k is |Σ ∧ ¬Q|.
G Hardness results Chase. In the proofs of this section and of subsequent sections, we will need the standard database construction of the chase  [Abiteboul et al. , 1995]  by TGDs: Definition 1. The chase applies to a set of facts F and to a set Σ of TGDs, and constructs a set of facts F ⊇ F, possibly infinite, which satisfies Σ, in the following manner. We first define a chase round as follows: for each TGD τ : ∀ x ϕ( x) → ∃ y ψ( x, y), for each homomorphism h from x to the elements of F such that the facts of ϕ(h( x)) are in F, if h does not extend to a homomorphism from x ∪ y such that the facts of ψ(h( x), h( y)) hold in F, then we call ϕ(h( x)) a violation of τ in F: we repair it by creating fresh elements (called existential witnesses) b for each variable of y, and add to F the facts ψ(h( x), b).
Acknowledgments Amarilli was partly funded by the  Télécom ParisTech Research Chair on Big Data and Market Insights. Bourhis was supported by  CPER Nord-Pas de Calais/FEDER DATA  Advanced Data Science and Technologies 2015-2020 and the  ANR Aggreg  Project  ANR-14-CE25-0017 ,  INRIA  Northern European Associate Team Integrated Linked Data. Benedikt's work was sponsored by the  Engineering and Physical Sciences Research Council of the United Kingdom (EPSRC) , grants  EP/M005852/1  and  EP/L012138/1. Vanden Boom  was partially supported by  EPSRC  grant  EP/L012138/1.
The delimitation of bioregions helps to understand historical and ecological drivers of species distribution. In this work, we performed a network analysis of the spatial distribution patterns of plants in south of France (Languedoc-Roussillon and Provence-Alpes-Côte d'Azur) to analyze the biogeographical structure of the French Mediterranean flora at different scales. We used a network approach to identify and characterize biogeographical regions, based on a large database containing 2. 5 million of geolocalized plant records corresponding to more than 3,500 plant species. This methodology is performed following five steps, from the biogeographical bipartite network construction, to the identification of biogeographical regions under the form of spatial network communities, the analysis of their interactions and the identification of clusters of plant species based on the species contribution to the biogeographical regions.
This area represents the northern limit of the Mediterranean climate in the western basin, and thus constitutes a climatic transition from a Mediterranean zone that has a summer drought to a temperate zone less prone to summer drought  (Walter & Breckle, 1991 1994). On a finer scale, the climate is more complex with several subtypes and intricated boundaries  (Joly et al. , 2010; Tassin, 2017). Several works have tried to map the distribution of biogeographical entities. To date, no statistical analysis had been ran to tackle those expert-based maps with up-to-date plant records, in order to test their reliability. In order to depict spatial structure in such a complex regional flora, a large dataset is required. While the level of diversity and complexity of such dataset may appear overwhelming at first glance, the emergence of network-based approaches has opened new paths for identifying and delimiting bioregions where the presence-absence matrix is represented by a bipartite network.
For example,  Kougioumoutzis et al. (2014)  applied the NetCarto algorithm  (Guimerà & Nunes Amaral, 2005)  in order to identify biogeographical modules within the phytogeographical area of the Cyclades. Similarly,  Vilhena & Antonelli (2015)  proposed a network approach for delimiting biogeographical region based on the InfoMap algorithm  (Rosvall & Bergstrom, 2008). By embedding species distributional data into complex networks, these methods have the great advantage to be generic, flexible and to incorporate several scales in the analysis. Most importantly, these methods integrate species community and spatial units within a single framework, which allow to test the relative contribution of each taxa to bioregions depicted, and to represent the relationship between those bioregions based on those contributions.
In this study, we present a biogeographical network analysis of plant species distribution in the French Mediterranean area at different scales. The French Mediterranean territory represents an interesting study area to test new approaches, given the excellent knowledge of the spatial distribution of the plant species revealed by botanical inventories  (Tison & Foucault, 2014; Tison et al. , 2014)  and the detailed databases compiled by the French National Botanic Conservatory of Porquerolles and the Alpine National Botanic Conservatory. The objective of this work is to delineate bioregions, identify groups of species and analyse the relationships between the two entities.
Dataset and study area The study area, situated in southern France, encompasses the former Languedoc-Roussillon region (five departments of the current Occitanie region: Pyrénées-Orientales, Aude, Hérault, Gard and Lozère) and the whole Provence-Alpes-Côte d'Azur region. It extends around the entire Mediterranean coastline of mainland France and inland, comprising almost all the Mediterranean hinterland, totalling 558, 776 km 2 (Figure  1 ). The topography is structured by three major mountain ranges, the Pyrenees in the southwest, the Massif central in the northwest and the Maritime Alps in the north-east. Inbetween, the landscape is mostly hilly with some lowlands around rivers that flow into lagoons or marshy deltas such as the Camargue. The Rhône is the main structuring river and delimitates western and eastern subregions.
Acidic substrates and silicate soils are mainly found in the aforementioned mountain ranges and in the smaller Maures-Estérel range in southern Provence. The remaining part of the territory is dominated by calcareous or marly substrates (principally Cretaceous and Jurassic), with some significant alluvial zones and small volcanic areas. The SILENE database 1  , has been created in 2006, and is the reference botanical database in the study area. It contains historical data gathered from the scientific literature and herbaria along with more recent data coming from public studies, partnerships, local amateur botanist networks and professional botanists of the Botanical Conservatory. Our analysis is based on a 5 × 5 km 2 grid cells. We decided to only retain data whose georeferencement precision is below 10 meters.
While the SILENE database contained nearly five million observations at the date of the export (June 2016), we deleted several taxa whose distribution is still insufficiently known and could distort the results (e. g. apomictic taxa such as Rubus or Hieracium). For the same reason, we also aggregated all sub-taxa at the species level. The final dataset results in 4, 263, 734 vegetation plant samples corresponding to 3, 697 plant species. We divided the study area using a UTM grid composed of 2, 607 squares of lateral size l = 5 km. In order to assess the impact of the spatial resolution on the results  (Divíšek et al. , 2016; Lennon et al. , 2001) , we also applied the aforementioned biogeographical network analysis with a grid composed of squares of lateral size l = 10 km (see  Figure S2 and Table   S1  in Appendix for more details).
Biogeographical bipartite network The bipartite network extracted from the database is composed of 2, 607 5 × 5 km 2 grid cells and 3, 697 plant species, where the links represent the occurrence of plant species in the grid cells. Two network degree distributions can be associated to this network: the number of species per grid cell and the number of cells covered by each species. The probability density functions of these two distributions are displayed in Figure  3. The spatial component of the network is very dense. Most of the grid cells host between 200 and 500 plant species, with an average of 360 species per cell (i. e. ∼ 15 species/km 2 ). For species side, the situation is different; the majority of plant species cover less than 10% of the study area, which highlight the importance of range restricted taxa.
DISCUSSION In this study we delineate spatial bioregions in southern France, a transition area between a mediterranean and temperate climate. The present analysis represents to our knowledge one of the largest network-based studies published to date, relying on a database containing more than four million data points across a territory of about 558, 776 km 2. While this territory has been divided into bioregions on expert knowledge, we confront those approaches to datadriven classification, and discuss the coherence of the   S3  in Appendix. different perspectives. We delineated eight statistically significant bioregions, which we will first present in relation to previously published work, and emphasize their specificity regarding associated groups of species. We discuss the observed spatial patterns in terms of ecological and historical drivers, to provide insights into mechanisms driving the assemblage of vegetation communities.
In this study, the network 2 http://www. eea. europa. eu/data-and-maps/ F50D9CF8-FFEE-475F-8A65-4E095512CBB7 (accessed the approach allowed to discriminate two "sub-networks" with little exchange regarding species composition and different relative contribution to each area, which globally relate to a temperate and a Mediterranean sub-groups. Several earlier bioregionalizations in the mediterranean basin have failed to separate mediterranean from eurosiberian ensembles, suggesting this boundary would be highly permeable  (García-Barros et al. , 2002; Saiz et al. , 1998)  and easily crossed by species. Here, the use of a precise dataset coupled with a network analyse has proven to be relevant to depict such spatial transition, which reinforce the need to gather coherent dataset to characterize complex and intricate spatial structures.
CONCLUSION The quality of a bioregionalization is dependent on the data and the method used. To our knowledge, the present analysis constitutes the densest speciescells network analysed in a bioregionalization study, at such a high spatial resolution. Therefore, results of this study demonstrate that new statistical methods based on network analysis can bring solutions to manage and analyse large databases, and provide efficient bioregionalization at different scales. New perspectives for bioregionalization will integrate community structure across different scales, in order to understand how deterministic (i. e. niche based) processes and stochastic events (dispersal, random extinction, ecological drift) interact to shape plant communities, from regional species pool to local assemblages  (Chase & Myers, 2011).
ACKNOWLEDGEMENTS This work was supported by a grant from the  French National Research Agency  (project  NetCost ,  ANR-17-CE03-0003  grant). Partial financial support has been received from the  French Ministère de la Transition Ecologique et Solidaire (MTES). We thank the  Alpine National Botanic Conservatory  for providing some of the  Provence-Alpes-Côte d'Azur data. We wish to thank  Christelle Hély-Alleaume ,  Virgile Noble  and  James Molina  for useful discussions. A special thank goes to  John D. Thompson  for correcting English and interesting remarks.
Y. Yang: board membership; Alimera Sciences, Novartis, Allergan, Bayer; consultancy: Alimera Sciences; grants and payment for lectures: Alimera Sciences, Novartis, Allergan and Bayer. F. Holz: grants; Alimera Sciences, Bayer and Novarti; consultancy: Bayer, Novartis, Roche and Heidelberg Engineering. U. Chakravarthy: grant; Alimera Sciences; lectures and speaking events: Allergan. The remaining authors have no conflicting interests to disclose. The sponsor participated in data collection, data management, data analysis, interpretation of the data, preparation of the manuscript, and review of the manuscript. Employees of Alimera Sciences, Inc (Kathleen Billman, Barry Kapik, and Francis Kane), participated in conducting the study, data acquisition analysis, and reporting. This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.
On the other hand, the OCDMA multiplexing technique is a very promising technique used to share all-fiber bandwidth and to reduce the effective cost and system complexity. In addition, with the help of OCDMA codes signature, network security becomes more effective and confident. Recently multiple-access systems based on OCDMA have been used and implemented in many optical networks  [11] [12] [13] , in which the proposed technique can offer higher data rates, better bandwidth efficiency, and a large number of simultaneous users. In order to achieve privacy and security in transmission, we use optical code-division multiple-access (OCDMA), which provides several attractive features like asynchronous access, ability to support variable bit rates, bursty traffic, and scalability of the network  [14].
An OOFDM-OCDMA PON architecture is considered by employing 2D-OCDMA codes for the first time. Analytical calculations are performed using different modulation formats to evaluate the behavior of the proposed PON extension from 2D-OCDMA-WDM architecture  [15]. Finally, transmission of 100 Gb/s OFDM-OCDMA PON over 80 km optical link is investigated as a function of the bit error rate (BER). Results show that five users can be covered with a 100 Gb/s peak data rate.
System model In this section, the Optical OFDM-OCDMA system is presented with the encoder, the channel and the decoder model, as depicted in Fig. 1. Fig. 1  shows the proposed Optical OFDM-OCDMA PON architecture. We study the downlink direction which is comprised by the Optical Line Terminal (OLT) which generates unique encoded OFDM data streams with orthogonal codes for different users and these are simultaneously transmitted to the Optical Network Unit (ONUs). Each user has a corresponding unique CDMA receiver which decodes its own data, while the interference between multiple users can be eliminated through a code auto-and cross-correlation process in decoding. The decoded data is then demodulated using an OFDM demodulator. The proposed architecture provides many benefits, including simple implementation, improved spectral efficiency, and security.
Acknowledgements The work of  Dr. Elias Giacoumidis  was emanated from  EU   Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreement No  713567  and in part by a research grant from  Science Foundation Ireland (SFI)  and is co-funded under the  European Regional Development Fund  under Grant Number  13/RC/2077.
e. , the departure from the standard composition. This resulted in an unprecedented global scale perspective of the tropospheric isotopic depletion of water vapor. In recent years, three satellite missions collected data retrieving stratospheric SWIs: the MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument on Envisat (Environmental Satellite) allowed for H 2 O and HDO retrievals from July 2002 to March 2004, roughly at the altitude range between 10 and 50 km  [16]. The 19-month observation record from the MIPAS revealed a clear seasonal cycle signal and transport of SWIs into the stratosphere  [17, 18]. The measurements of normal and deuterated water from the ACE-FTS (Atmospheric Chemistry Experiment Fourier Transform Spectrometer) were used to map global climatological behavior of HDO along with the HDO/H 2 O ratio in the upper troposphere-lower stratosphere, but for this dataset measurements were made in the tropics only during February, April, August and October  [19].
Data and Method The Odin satellite is part of a Swedish-led mission aimed at obtaining observations of trace gas profiles in the stratosphere and mesosphere  [28]. The satellite was launched on 20 February 2001 with a two-year mission plan but remains operational until today. Odin follows a quasi-polar sun-synchronous orbit at around 600 km altitude. Measurements are typically performed along the orbital track, resulting in a latitudinal coverage between 82 • S and 82 • N. Odin carries two instruments, one of them is the Sub-Millimetre Radiometer (SMR), which consists of five radiometers that cover several frequency bands between 486 GHz and 581 GHz and around 119 GHz, observes several thermal emission lines at the atmospheric limb using a 1. 1 m telescope. Stratospheric H 2 O, H 2 18 O and HDO information are obtained from emission lines centered at 488.
The atmosphere is typically sampled in the altitude range between 7 km and 110 km with an effective vertical sampling of 3 km. Such scan takes about 140 s, which corresponds to a horizontal sampling of one scan per 1000 km. SWIs retrieved from Odin/SMR measurements can be used for the study of the water cycle in the stratosphere at minimum height above 20 km from the Earth surface, where data with sufficient quality can be retrieved. Here we focus on observations made during the period 2002-2009. Later observations suffer from calibration and retrieval issues, in particular for HDO. These issues are currently under investigation to make the later observations available for future studies. Figure  1  shows an example of the sampling coverage by Odin in January 2003. The data are measured over limited regions due to the scanning interval.
Global Mean Vertical Profiles Figure  2  shows the climatology of global mean vertical profiles of the water isotopic composition along with their standard deviations. The vertical profile of H2O exhibits an irregular decrease with altitude in the lower stratosphere up to approximately 25 km, an increase from 25 km to 50 km, and then a decrease above 50 km. Similar profiles are obtained for HDO and H2 18 O (not shown). Lossow et al. [35]  compared HDO data from MIPAS with that of Odin/SMR and ACE-FTS and demonstrated a high consistency in the structures above 20 km between all three instruments. Even where the MIPAS HDO retrieval reaches its limits (above 40 km), there is still good agreement between HDO from MIPAS and Odin/SMR, pointing to the fact that data from different satellites can complement each other to some extent.