dataesr/scientific-paragraphs-categorization huggingface dataset:
The paper is divided in two main parts. Section 2 introduces the interface to recycling and block Krylov methods (KSPHPDDM) and discusses the readiness of the PETSc library with respect to block Krylov methods. Different applications from eigenanalysis are also provided. Section 3 introduces the suite of robust multilevel overlapping Schwarz methods (PCHPDDM) with examples from linear and nonlinear partial differential equations. Eventually, concluding remarks are provided in section 4. All PETSc keywords and options are typeset in typewriter font, these are public and documented at https://www. mcs. anl. gov/petsc/petsc-master/docs. Codes not already available in other public repositories are available at https://github. com/prj-/jolivet2020petsc. In Appendix A, a short guide to build the required set of libraries for running these codes is provided.
Applications and numerical results 2. 3. 1. Reproducibility of the results from Parks et al. [21]  Alongside the paper introducing GCRODR  [21] , a MATLAB implementation was provided and is since then available  3. It comes with a sequence of ten "linear systems from a finite element fracture mechanics problem constructed by Philippe H. Geubelle and Spandan Maiti. " The goal of this paragraph is to explain how the results can be reproduced with PETSc and KSPHPDDM: the matrix files used are available at https://gitlab. com/petsc/datafiles/-/tree/master/ matrices/hpddm/GCRODR while the driver code is part of the PETSc test suite and available at https://www. mcs. anl. gov/petsc/petsc-master/src/ksp/ksp/tutorials/ex75. c. html. In order to check the correctness of the KSPHPDDM interface, the following tests are performed: in MATLAB, unpreconditioned GCRODR  (40, 20) , ICC(0) left-preconditioned GCRODR  (40, 20) , and Jacobi right-preconditioned GCRODR  (40, 20) ; in PETSc with no preconditioning and no restart GMRES(∞) KSPGMRES; in PETSc with KSPHPDDM, all of the above.
The performance of the MatProductNumeric operation is evaluated for tall-and-skinny dense matrices with a varying number of columns N ∈ {2, 8, 16, 32, 64}. For the single column case N = 1, the MatMult operation is used. All results have been obtained using double-precision arithmetic and 32-bit integers. The scaled efficiency measured in GFLOP per second is reported with respect to the baseline MATAIJ implementation with N = 1 in figure  2 , where performances have been averaged over five consecutive product operations. They can be reproduced by using the mini-app MatProduct. c from https://github. com/prj-/jolivet2020petsc and any input MATAIJ stored in binary format, here using the default name binaryoutput, available at http://jolivet. perso. enseeiht. fr/binaryoutput. The mini-app is then used to benchmark intranode performance of matrix-matrix multiplications, either with multiple OpenMP threads, or by offloading the operation to a NVIDIA GPU and using cuSPARSE  [41]  as interfaced in PETSc.
Linear stability analysis In this section, we apply recycling Krylov methods in the context of linear stability analysis and consider the solution of the following generalized eigenvalue problem: J(q b )x = λ M 0 0 0 x, (1) where J is the Jacobian of the incompressible steady-state Navier-Stokes equation evaluated using a given base flow q b = u b p b and M is the discretization of the mass matrix on the space of velocities. The mini-app employed for the numerical results is built on top of FreeFEM  [50]  and it is available at https://github. com/prj-/moulin2019al. Interested readers are referred to  [51]  for more details and for larger runs. There are different methods to compute the eigenvalues of equation (  1 ) near a complex-valued shift σ. In this paragraph we consider a Krylov-Schur method  [52] , which, for interior eigenvalues, relies on spectral transformations and on the solution of successive linear systems such as: J(q b ) -σ M 0 0 0 x i = b i , (2) which, in SLEPc, are parameterized using the -st prefix.
More details on these solvers are given in the next section where focus is put on preconditioning rather than Krylov methods. We note here that only PCASM and PCHPDDM currently handle blocking, see the list section 2. 2, and that PCHPDDM and PCGAMG have lower contraction factors than the cheaper alternative PCASM. As a testbed, we consider the following generalized eigenvalue problem on a three-dimensional cube: -∇ • (κ∇u) = λu. This continuous equation is discretized with third-order Lagrange finite elements using FreeFEM. The script blocking-slepc. edp available at https://github. com/prj-/jolivet2020petsc can be used for reproducibility. The following timings and convergence histories have been obtained on 2,304 processes of Irène, for solving a problem of dimension 7. 46 • 10 7. By default, SLEPc applies at most 5 iterations of GMRES on each column of a so-called set of active columns.
Clearly, having both a KSP and a PC which can efficiently deal with multiple vectors is mandatory to achieve reasonable performance with such an outer solver that heavily relies on blocking. The script available at https://github. com/prj-/jolivet2020petsc may be used to solve the same eigenproblem using EPSCISS by providing the additional command line argument -eps type ciss. However, this eigensolver is mostly suited for finding interior eigenpairs, whereas the leftmost part of the spectrum, closest to 0 for a symmetric positive definite problem, is here sought. In this scenario, EPSCISS is not a suitable solver and for fairness, its algorithmic performance is not reported, but the options from the script can be readily used for problems where it is an appropriate choice. We finally note that blocking support is also available and tested in SLEPc for EPSSUBSPACE since version 3.
The current code for Arnoldi iterations would then handle block Arnoldi iterations, and shift-and-invert solves would operate on the whole block instead of column by column. Concerning HPDDM, its integration inside PETSc offers a much-needed flexibility compared to the standard implementation. Indeed, it is now possible to decide at runtime many solvers parameters that are instead determined at compile-time in a stand-alone HPDDM implementation. The interface between PETSc and HPDDM has room for future improvements. First, HPDDM handles mixed-precision, e. g. , using single-precision scalars for assembling coarse operators while using double-precision scalars at the fine level. The topic of mixed-precision is under scrutiny for the next major overhaul of PETSc. Second, HPDDM does not handle GPU efficiently currently, but the interface with PETSc provides a very thorough testbed with Mat and PC implementations that do exploit GPU.
unknowns with approximately 45 nonzero coefficients per row in the discrete coefficient matrix. The physical domain Ω is decomposed in 13,824 subdomains using the automatic graph partitioner ParMETIS [88]. There are heterogeneities due to jumps in E and ν. The following discontinuous piecewise constant values are considered: (E 1 , ν 1 ) = (2 × 10 11 , 0. 25) in blue regions, while (E 2 , ν 2 ) = (10 7 , 0. 45) in red regions, see figure8. The code used to produce these results was borrowed from the original paper about the multilevel extension of GenEO [86]  and it is available at https://github. com/prj-/aldaas2019multi.
[89]e the system is not too stiff here, both strategies lead to the same convergence history, which is displayed in figure11a. The complete set of options is given in figure11b. In case the preconditioner is being rebuilt at each of the four linearization steps, 81. 1 s are spent in PCSetUp and 27. 7 s in KSPSolve. Setting up the preconditioner only once is in this scenario a compelling way of amortizing this cost. Results can be reproduced using the FreeFEM script bratu. edpavailableat PCHPDDM for solving the coarse problem. The problem is generated using the MFEM[89]definite Maxwell example available at https://github. com/mfem/mfem/blob/ master/examples/petsc/ex3p. cpp. The strong formulation of the continuous problem is given.
Acknowledgments The authors would like to thank  S. Balay ,  J. Brown ,  V. Hapla ,  M. Knepley , and  B. Smith  for reviewing the successive merge requests in PETSc repository and for their feedback on this manuscript. This work was granted access to the  GENCI -sponsored HPC resources of: TGCC@CEA under allocation A0070607519; IDRIS@CNRS under allocation  AP010611780. Jose E. Roman  was supported by the  Spanish Agencia Estatal de Investigación (AEI)  under project  SLEPc-DA  ( PID2019-107379RB-I00 ).
resulting in 593 × 10 6 6 unknowns with approximately 45 nonzero coefficients per row in the discrete coefficient matrix. The physical domain Ω is decomposed in 13,824 subdomains using the automatic graph partitioner ParMETIS [88]. There are heterogeneities due to jumps in E and ν. The following discontinuous piecewise constant values are considered: (E 1 , ν 1 ) = (2 × 10 11 , 0. 25) in blue regions, while (E 2 , ν 2 ) = (10 7 , 0. 45) in red regions, see figure8. The code used to produce these results was borrowed from the original paper about the multilevel extension of GenEO [86]  and it is available at https://github. com/prj-/aldaas2019multi.
[89]e the system is not too stiff here, both strategies lead to the same convergence history, which is displayed in figure11a. The complete set of options is given in figure11b. In case the preconditioner is being rebuilt at each of the four linearization steps, 81. 1 s are spent in PCSetUp and 27. 7 s in KSPSolve. Setting up the preconditioner only once is in this scenario a compelling way of amortizing this cost. Results can be reproduced using the FreeFEM script bratu. edpavailableat PCHPDDM for solving the coarse problem. The problem is generated using the MFEM[89]definite Maxwell example available at https://github. com/mfem/mfem/blob/ master/examples/petsc/ex3p. cpp. The strong formulation of the continuous problem is given https://github. com/prj-/jolivet2020petsc. 3. 3. 3. Using PCHPDDM as a coarse grid solver for PCBDDC A last problem shows how one may switch between a multilevel BDDC solver to a two-level BDDC solver using This equation may model the temperature distribution in combustion models.
This paper presents a full procedure for the development of a Part-of-Speech (POS) tagged corpus of Old Catalan. As an extremely low-resource language with rich inflection and frequent homographs, Old Catalan poses non-trivial problems in the development of a searchable constituency-based treebank. We demonstrate, however, that a semi-supervised method of incrementally building training data using both neural and memory-based taggers, together with the Pyrrha annotation tool is highly efficient and yields accurate results. We propose that this simple and effective method could easily be extended to other low-resource historical languages for which no NLP tools exist yet.
ESTABLISHING THE MORPHOSYNTACTIC TAG SET The investigation of the evolution of syntactic constructions and the distribution of different forms diachronically benefits heavily from the analysis of large corpora that are consistently annotated. Manual annotation of thousands (and ideally, millions) of words is an extremely time-consuming task that is very prone to error. The use of Natural Language Processing (NLP) tools to automatise the annotation process and consistently treat large amounts of data in a minimal period of time have been successfully applied to various languages for the production of historical corpora, including Welsh, English and French. Like most Medieval languages, Old Catalan had not undergone standardisation, and therefore, it displayed a great degree of variation at orthographic level.
5 The Llibre dels Fets's composition probably began during the conquest of Mallorca, in 1224, and it ended with King James I's death, in 1276. The preface and the ending of the book were probably added after the King's death by another author, which explains the differences in tone (more erudite) and use of Latin  (Soldevila, 1971; Vinas & Vinas, 2008). Meelen and Pujol i Campeny Journal of Open Humanities Data DOI: 10. 5334/johd. 54 is based on the standard UPenn annotation scheme, 6 in order to render it readily comparable with similar resources in the UPenn historical corpora collections. At the same time, it has been simplified where possible and enriched where needed in order to adapt it to Old Catalan grammar and to provide as much information as possible for the study of word order variation at clausal level.
For a more nuanced analysis of the distribution of quantified phrases and word order in Old Catalan see Pujol i Campeny (2018). Meelen and Pujol i Campeny Journal of Open Humanities Data DOI: 10. 5334/johd. 54 One of the challenges that we encountered regarding the tagging of nominal categories is the abundance of non-finite verbal forms that underwent nominalisation and thus, have a homophonous nominal counterpart. These mainly include past participles  (i. e. , vinguda, presa, feyt, anada, estada, partida, meaning 'arrival, taking, event/fact, coming, stay, leaving, example 12)  and infinitives (i. e. , poder, saber, 'to be able to, to know', example 13). (12) (a) e nós que faríem gran nostre pro e gran nostra honor ab la and we that do-3pl. cond great our profit and great our honour with the lur venguda.
POS TAGGING HISTORICAL LOW-RESOURCE LANGUAGES FROM SCRATCH For extremely low-resource languages with complex morphology and a large amount of short, homophonous forms like Old Catalan, even basic NLP tasks like part-of-speech tagging can prove challenging at first. Apart from the digitised edition of the text, no further resources were available to us for Old Catalan at this point. In order to train the tagger, we therefore first manually annotated a text sample containing 4,500 words. Manual annotation was carried out through with the Pyrrha annotation tool  (Clérice et al. , 2021). Pyrrha allows for manual annotation of lemmas, morphological features and POS tags. Legitimate POS tags can be entered as so-called 'control lists' ahead of tagging. These options are then made available by means of a dropdown list while annotating, thus avoiding mistakes that could easily occur when typing every POS label separately.
MEMORY-BASED VS NEURAL TAGGING We initially chose the TiMBL's memory-based tagger (MBT,) because it has yielded very good results for historical, low-resource languages in the past (see, for example, the results for the Middle Welsh corpus in  Meelen (2016)  or the Tibetan historical corpora in  Meelen et al. (2021) ). In recent years, however, POS taggers based on neural networks have yielded very good results. One particularly good off-the-shelf model is TARGER, a BiLSTM-CNN-CRF tagger by  Chernodub et al. (2019). 12 Neural taggers generally work well on large data sets. As our initial set of training data was extremely small, we skipped the first round and only started testing once we had a gold standard of 10,000 tokens. Word embeddings, which are essential for TARGER to perform well, were created with FastText (www.
fasttext. cc). The total number of tokens of Old Catalan material available to us at present was with just over 156k tokens much too small to create very good embeddings, but at least it could facilitate neural tagging. We evaluated the results of both 10k and 60k gold standards, each divided into 80/10/10 splits for training, development and test sets with the following key parameter settings: batch_size=10 char_cnn_filter_num=30 char_embeddings_dim=25 11 The MBT is freely available here: http://languagemachines. github. io/mbt/. 12 TARGER is freely available here: https://github. com/achernodub/targer. A global accuracy of 91. 4% is not bad considering the large tag set consisting of 114 distinct POS labels. However, results could most certainly be improved once more Old Catalan data becomes available so that better word embeddings can be created.
In addition, higher accuracies could be achieved through feature engineering and by switching from a recurrent to a convolutional neural network or by adding further (Bi)LSTM and Conditional Random Field layers. We leave this for future research. Unlike TARGER, the memory-based tagger (MBT) does not need large data sets or word embeddings to get decent results on challenging historical data like our Old Catalan corpus. The MBT allows for different parameter settings according to features of the words themselves or the context in which they appear. We started testing the default settings, but then adjusted the parameters for known and unknown words so that morphological suffixes in particular could feed better into the morphosyntactic classifier. We specifically focused on context, selecting the maximal windows for tags preceding (d) and following (a) the focus word (f).
Building on previous work on other historical, low-resource languages like Middle Welsh and Classical Tibetan, we presented the results of our semi-supervised method consisting of five iterations of manual tagging and correction, incrementally building up our training set to >60k tokens. After each iteration, the memory-based tagger (MBT) was trained and the entire corpus was retagged based on the newly trained version, thus speeding up manual correction of subsequent batches. In addition to generating a memory-based tagger for Old Catalan, we also word embeddings with FastText in order to test TARGER, a BiLSTM-CNN-CRF tagger. Because of the small dataset, global accuracies were still lower for TARGER. Once more digitised Old Catalan data will be made available this tagger will most likely yield much higher accuracies as well.
For small and highly complex data sets like our Old Catalan corpus, semi-supervised, incremental annotation methods like these can thus yield highly accurate morphosyntactic taggers with minimum effort. Depending on the complexity of the tag set, multiple iterations of manual correction might be necessary to get started, but with each iteration, results clearly improve and the time invested on subsequent correction sessions is significantly reduced. This semi-supervised method of memory-based tagging, combined with manual correction in Pyrrha, is thus highly efficient to create reliable training data for historical, low-resource and morphologically rich languages. The data and code for this paper can be found on our GitHub repository: https://github. com/ lothelanor/catalancorpora.
ACKNOWLEDGEMENTS Research that partially facilitated the work presented in this article was funded by the  British Academy  ( PDF grant   pf170063 ), and the  Cambridge Humanities Research Grant  (tier 1 grant,  GANT011262 ). Additionally, this work has been supported by the  French government , through the  UCAJEDI Investments  in the  Future  project managed by the  National Research Agency (ANR)  with the reference number  C870A06228 -EOTP : SYVACA -D112. Meelen and Pujol i Campeny Journal of Open Humanities Data DOI: 10. 5334/johd. 54.
B. Determination of the Event Rates The power consumption of each pixel architecture, was estimated using post layout simulation data of the TFS and DVS pixels, as well as the event rate estimation of there highlevel pixel matrices simulations for different kinds of stimuli. In matlab, we designed behavioral models of the two pixels to serve as building blocks of the higher level model of the pixel matrices. The models of the pixel matrices were fed by stimuli extracted from two scenarios: the first one is a car driving on the road (High activity scene 11a) and the second is a parked car with almost no activity, only a person walking in front of the car for a few seconds (Low activity scene 11b). The duration of stimuli is 10 seconds in each scenario. The matlab simulations output the following: kernel (NAv), generated 168k events (road) and 4,4K events (parking), while kernel (Av) generated 78K events (road) and 2,1K events (parking) (see figure  12 ).
The data collected from the simulations were used to calculate the total power consumption of the pixel matrices (table  II ). The collected data from the matlab simulation also yields an approximation of the Signal to Noise Ratio (SNR) of our pixel architectures: for the nonaveraging (NAv), the SNR is approximately 11 dB, while the for the averaging pixel architecture the SNR is 20 dB. This can be mostly attributed to the area difference of the photosensitive part and to the averaging.
To extract scientific information out of these spectral data, a radiative transfer and retrieval pipeline is required. The aim of the radiative transfer model is to simulate gaseous absorption along the line of sight, while the retrieval stage then uses this model to convert input values of transmission into realistic vertical gas profiles and, where applicable, to extract information on vertical temperature and pressure variations. In this work, we present the code for Retrievals in the Infrared of Solar Occul-TaTiOns (RISOTTO), a new retrieval algorithm based on Bayesian inference with an implemented forward model that can retrieve atmospheric profiles using a rapid and optimised matrix inversion scheme. This code is also capable of simultaneously correcting for minor instrumental artefacts in the data, together with any distortions of the spectral baseline (for instance due to aerosol absorption), and can provide a first-order quantification of the signal-to-noise ratio (SNR) of each spectrum in the occultation without needing any prior information on sources of noise.
Molecular cross-sections For a given molecule, a Humlíček algorithm  [7]  is used to calculate molecular absorption cross-sections σ(p i , t j , λ k ) as a function of wavenumber λ k from a set of source line data (e. g. the HITRAN 2016 database  [8] ), assuming a Voigt lineshape. These are calculated independently for a set of n i pressure grid values (p i , in units of Pascals) and n j temperature grid values (t j , in units of Kelvin), chosen to efficiently sample the variation in molecular absorption for a temperature and pressure parameter space suitable for the planetary atmosphere in question. The cross-sections could then be linearly interpolated to intermediate temperature and pressure values during the forward modelling process, but this is both slow and increases the probability of inducing errors in the optical path integration due to aliasing or undersampling.
The cross-section values for these gases were calculated according to the HITRAN 2016 database  [8]. We assumed a fixed isothermal profile at a temperature of 180 K and a reference pressure at the planetary surface, estimated by the Mars Climate Database  [19]  given an arbitrary set of spatio-temporal variables, to be 5. 46 mbar. The pressure values were then extrapolated to higher altitudes according to equation 5. The atmosphere was assumed to have a constant molar mass of 43. 34 g mol -1. Since the gaseous abundances are degenerate with respect to both temperature and pressure, we chose to completely fix the temperature-pressure profile in the RISOTTO model to the aforementioned values, and only allow the instrumental variables and the molecular abundance profiles to vary in the model, starting from a prior of 1‰ H 2 O and 100 ppbv of H 2 CO at all altitudes.
We can define a region as a set of close nodes where there are users attached to them (i. e. , |   | > 0). Moreover, we apply the K-medoids clustering technique  [37]  to detect those regions. The K-medoids algorithm is a variation of the classical K-means algorithm. Despite the similarity between these two algorithms, K-medoids chooses points in the dataset as centers, or medoids, of the clusters and can be used with an arbitrary distance function, while in K-means, a cluster center is not necessary a point in the dataset. Moreover, Park and Jun  [37]  propose a simple and fast K-metoid algorithm with time complexity of  (), where  is the dataset size, and  is the number of clusters. These characteristics allow us to partition the subset of nodes where |   | > 0 in any connected graph using the network delay  ,,  as the distance function.