dataesr/scientific-paragraphs-categorization huggingface dataset:
In order to compensate for these differences, we define a "dressed" level to make the electron and muon channels compatible to within 1%. This is achieved by defining in simulation a particle momentum vector by adding the momentum of the stable lepton and the momenta of all photons with a radius of ∆R = 0. 1 around the stable lepton. All jets are required to be separated from each lepton by ∆R > 0. 5. The background-subtracted detector-level distributions from data are unfolded to the particle level. The unfolding response matrix includes detector resolution effects and efficiencies. We use MADGRAPH to build a response matrix which allows us to map detector-level distributions to particle level. To quantify the bias introduced by the choice of the MC model, we use SHERPA as an alternative.
The off-diagonal elements of the response matrices are small for both channels. For the dielectron channel, 85-95% of all events in a given bin of the reconstructed p ee T distribution are mapped onto the same bin at the particle level. For the dimuon channel, at low p µµ T around 85% fall in this category, whereas at very high p µµ T , only 67% stay in the same bin at the particle level. The remaining events typically fluctuate to directly neighboring bins. The iterative method used by d'Agostini  [44] , as implemented in the ROOUNFOLD package  [45] , is used to regularize the inversion of the matrix. Subsequently, the unfolded distributions from Z → e + e -and Z → µ + µ -are found to be compatible. They are combined using the best linear unbiased estimator  [46]  to obtain the final distributions.
Differential cross sections In Figs. 2  and 3 , we present the measured differential cross sections as functions of the p Z T and the p γ T for two selections of Z + jets and γ + jets events (n jets ≥ 1 and n jets ≥ 2) and compare them with estimates from BLACKHAT and MADGRAPH+PYTHIA6. In Fig. 4 , we present the ratio of the inclusive 2-jet events to the inclusive 1-jet events. For Z + jets, we also compare the data to SHERPA results. The NLO BLACKHAT estimate is corrected for nonperturbative effects (hadronization and underlying event) using MADGRAPH+PYTHIA6. These corrections are typically around 2%. We use the n-jets BLACKHAT sample for comparison with data and other MC generators in the corresponding inclusive n-jets selection. The Z + jets simulations from SHERPA and MADGRAPH+PYTHIA6 are rescaled by a constant NNLO K-factor of K = 1.
2  and 3 ), we observe the same qualitative behavior of the ratio of the MADGRAPH+PYTHIA6 simulation to data, which is flat about unity up to around 150-200 GeV and then increases to about 1. 3 at higher p T. Estimates from SHERPA are lower than the data for p Z T < 50 GeV, while for higher p Z T they increase to around 20% higher. In the n jets ≥ 1 case, BLACKHAT shows a flat ratio with respect to data starting around p Z T ≈ 100 GeV, but underestimates the yield seen in data by 8-10%, whereas in the n jets ≥ 2 case, BLACKHAT agrees with the data within the uncertainties for the whole range. For all multiplicity phase space selections, the systematic uncertainty in the MSTW2008 PDF set is 2-3% in the BLACKHAT estimate. The central points of CT10 show a difference compared to MSTW2008 of at most 4%, whereas NNPDF shows a variation of 2%.
The scale uncertainty for MSTW2008 in the BLACKHAT estimate, as determined through independent variations of the renormalization and factorization scales by factors of 2 and 0. 5, leads to an envelope with values of typically 5-10%. In the n jets ≥ 2 and n jets ≥ 1 γ + jets case, BLACKHAT reproduces the shape of the data distribution, but underestimates the rate by approximately 10-15% throughout most of the range. In Fig. 4 , we see that the inclusive 1-jet over inclusive 2-jet p Z T cross section ratio increases until a plateau is reached at around 350 GeV. The systematic uncertainties are treated as fully correlated in the ratio. The distributions are well predicted by MADGRAPH+PYTHIA6 in both channels. SHERPA underestimates the relative rate of inclusive 2-jets events. For BLACKHAT, the inclusive 2-jet generated sample is used to predict the 2-jet rate and to compute the ratio with the predicted rates from the inclusive 1-jet sample; BLACKHAT overestimates the ratio by 10% for p Z T > 100 GeV in both the γ + jets and Z + jets cases.
We see from the agreement in both the 2-and 3-jet cases that there is no evidence of any such contributions. The distribution of the second variable, log 10 (p Z T /p j1 T ), shown in Fig. 6 , shows similar behavior. For events with exactly one jet, the Z boson and the jet are back-to-back, with p Z T ≈ p j1 T , and the distribution peaks around zero. Events where the Z boson is the dominating object will have positive values. If the Z boson carries less p T than most of the jets, the variable has negative values. With increasing jet multiplicity the distribution still peaks around zero, but broadens. Figure  6  shows a comparison of MC estimates to data, which is unfolded to particle level. The MADGRAPH+PYTHIA6 calculation performs well in estimating the behavior of the data for all inclusive multiplicty selections, but there is a slope within uncertainties in the MC/data plot.
Summary Differential cross sections have been measured for Z + jets (with Z → + -) and isolated γ + jets as a function of the boson transverse momentum, using data collected by CMS at √ s = 8 TeV corresponding to an integrated luminosity of 19. 7 fb -1. The estimations from the MC multiparton LO+PS generators MADGRAPH+PYTHIA6 and SHERPA have been compared to the data. We find that the p T spectra for Z + jets and γ + jets are not well reproduced by these MC models. We observe a monotonic increase of the MC simulation/data ratio with increasing vector boson p T. Using the NLO generator BLACKHAT simulation, we find a smaller MadGraph stat. unc. [GeV] MadGraph stat. unc. [GeV]  discrepancy in shape between data and simulation, indicating that it is likely related to missing higher-order effects.
We present Clones, a Matlab toolbox for exact sampling from the stationary distribution of a closed queueing network with finite capacities. This toolbox is based on recent results using a compact representation of sets of states that enables exact sampling from the stationary distribution without considering all initial conditions in the coupling from the past (CFTP) scheme. This representation reduces the complexity of the one-step transition in the CFTP algorithm to O(KM 2 ), where K is the number of queues and M the total number of customers; while the cardinality of the state space is exponential in the number of queues. In this paper, we focus on the algorithmic and implementation issues. We propose a new representation, that leads to onestep transition complexity of the CFTP algorithm that is in O(KM ).
Note that this is the same as the complexity of the computation of the normalizing constant in the product-form case using Buzen's algorithm  [4]. The overall complexity of our algorithm depends however also on the coupling time of the chain, so it becomes of a practical interest when the network does not have a product form. The main focus of this paper is on algorithmic and implementation issues. We give a detailed description of the matrixbased representations used in our Matlab toolbox Clones. The paper is organized as follows. In Section 2 we describe the model and give a short overview of results in  [3]. We then introduce a new gap-free diagram representation and a new CFTP algorithm with one-step transition complexity of O(KM ). In Section 3 we present our Matlab toolbox Clones and discuss its functionalities and implementation issues.
TOOLBOX IMPLEMENTATION This section is devoted to the implementation of the transition function of diagrams. As we will see, it is convenient to represent diagrams with matrices. Then a natural choice for implementation is Matlab, as it handles matrix computations (specially when they are sparse) very well. The toolbox Clones is a Matlab toolbox that implements perfect sampling algorithms using different state space representations: state space, diagrams and gap-free diagrams. It is available at http://www. di. ens. fr/∼rovetta/Clones. At the same address there is also a detailed documentation on how to use the Toolbox. In this section, we first introduce the matrix representation of diagrams, then present the transition algorithms and finally describe some additional functionalities of the toolbox.
, 200}. We can see that for values from M = 5 to 60, the algorithm with diagrams is slightly faster than the one in gap-free diagrams, whereas for higher values of M , using gap-free diagrams is much more efficient than using diagrams. The latter result was expected, as the algorithmic complexity of one step transition is in O(KM ) for gap-free diagrams instead of O(KM 2 ) for diagrams. The running time when M ≤ 60 is more surprising. We believe that the main reason is that Matlab is optimized for matrix operations. Specially, when it comes to sparse matrices. On the other hand, our implementation of gap-free diagrams cannot benefit from this optimization, and there is room for improvement.
Data simulations suffer from the inherent difficulty of having to assume some genetic architecture as well as patterns of inheritance (such as, additive patterns) that could unduly bias the prediction models. The goal of this analysis was first, to identify a diverse set of publicly available plant and animal real data sets that can serve as a benchmark for the evaluation of such prediction algorithms. Secondly, assess the effectiveness of a diverse set of (state-of-the-art) methods, including parametric and non-parametric models. In particular, we also included variable selection methods in an attempt to assuage the implications of p > > n. We identified four publicly available data sets: Rice, Pig, Maize, and QTLMAS 2010 data. The data sets contain both real plant and animal data as well as simulated data (for completeness), with a range of population structure.
The Rice dataset  [25]  contains 31,633 Single-Nucleotide Polymorphism (SNP) variants from 413 accessions of O. sativa, taken from 82 countries and containing 34 phenotypes. From these we selected pericarp color and protein content as there were indications each was oligogenic and polygenic respectively  [25]. We evaluated the original phenotypes as well as phenotypes corrected for population structure. The Pig data  [26]  contains 52,842 SNPs on 3,534 animals and two of the five available traits were selected. The QTLMAS data, taken from the QTLMAS 2010 Workshop  [27] , consists of 2,326 sequenced individuals over five generations (F0-F4) with 20 founders, five male and 15 females, with 10,031 biallelic SNPs. Two phenotype traits were available, the first a quantitative trait and the second a binary trait.
Lastly, the Maize data  [28] , used for the European CornFed program, consists of two maize diversity panels with 261 flint and dent lines, and 29,094 and 30,027 SNPs respectively. The three traits recorded were male flowering time (Tass_GDD6), plant dry matter yield (DM_Yield), and dry matter content (DMC). See Methods section for more details on the data sets. The marker effects GS methods were chosen to reflect traditional as well as recent promising methods, some taken directly from the machine learning community. The methods applied were Bayes A, Bayes B, Bayes Cπ, rrBLUP, Epistasis-rrBLUP, Elastic Net, Bayesian LASSO, FOBA, ISIS, SVR, mRMR, and PCA FOBA and are very briefly described here. See Methods section for more details on each method. Ridge Regression Best Linear Unbiased Predictor (rrBLUP), Bayes A, Bayes B, and Bayes Cπ are all marker effects models  [2] , i.
Data Sets Three empirical data sets and one simulated data set from recent publications were identified as benchmark datasets for this problem. Rice. The asian rice-Oryza sativa (O. sativa)-dataset was taken from the supplementary material in  [25]. This dataset contains 44,100 SNP variants from 413 accessions of O. sativa, taken from 82 countries and containing 34 phenotypes. The 31,663 tagging SNPs derived from the OryzaSNP project as described in the Method section of  [25]  were used for the genomic selection study here. Among the 34 phenotypes evaluated, only two phenotypes-pericarp color and protein content-were chosen for testing. The protein content phenotype was selected because the associated GWAS p-value plots (supplementary material  [25] ) indicated a large number of influential SNPS.
In contrast, the pericarp color phenotype was selected as its GWAS p-value plots indicated only a few influential SNPs. Moreover, each trait seemed to have separate genetic mechanisms as there was a correlation of only -0. 11 between the two phenotypes. Additionally, monomorphic markers and markers with call rate < 10% were removed for the genomic selection study here, the phenotypes were corrected for populations structure by regressing on a PCA model of the population structure. GS methods in the study were performed on the original phenotypes as well as those corrected for population structure. Missing genotype data was imputed using fastPHASE  [40]. Pig. The Pig dataset-taken from  [26] -is a collection data on male and female pigs born since 2000 consists of 3,534 animals from a single PIC nucleus pig line yielding 52,842 SNPs with five measured traits (phenotypes).
Only traits 2 and 4 were randomly selected for study here, each a representative of the two types of traits available. In  [26] , the genotypes were sequenced from the Illumina PorcineSNP60 chip and full pedigree information was available, which we did not use in this study. In the original study, trait 2 was rescaled by a weighted mean of corrected progeny phenotypes, whereas trait 4 was corrected for environmental factors such as year of birth and location. Additionally, genotypes were filtered for minor allele frequency less than 0. 001 and with missing genotypes less than 10%. The original study used AlphaImpute to impute any missing data  [41]. For our study we used the data as described above which was given in the supplemental data of the original study  [26]. QTLMAS. QTLMAS dataset was taken from the QTL-MAS Workshop, which was held on May 17-18, 2010 in Poznań Poland  [27].
This dataset consists of 3,226 individuals over five generations (F0-F4) with 20 founders, five male and 15 females. There were two phenotype traits, the first a quantitative trait and the second a binary trait. Note, however, that epistasis was simulated only for Trait 1 but not for Trait 2 in this dataset. Only the first four generations (2,326 individuals) had phenotype records. The genome is approximately 500 million bp with five chromosomes, each 100 million bp. In total, each individual was genotyped for 10,031 biallelic SNPs. Maize. Maize dataset was taken from  [28] , which consists of two maize diversity panels with 300 flint and 300 dent lines used for the European CornFed program. This set of lines was aggregated from at least seven sources with the intent of covering "European and American diversity of interest for temperate climate conditions.
Evaluation of Genomic Selection Each genomic selection method was evaluated on all four datasets (Rice, Pig, QTLMAS, and Maize) using 10-fold cross-validation and global predictive ability. The 10-fold cross-validation (10CV) method is the technique of splitting, as close as possible, the samples (individuals) of the dataset into ten evenly sized sets called folds. Then, nine of the folds are used to train the genomic selection model and the remaining fold is used to test the predictive ability of the trained model. This procedure is repeated for all ten possible ways of choosing nine training folds and one testing fold. For each of the ten cross validations, the ten predicted phenotype vectors are concatenated and Pearson's coefficient of correlation, denoted by r, is evaluated between the vector of all predictions and the vector of the ground truth phenotypes.
We then computed the signed r 2 , i. e. r 2 times -1 if the correlation is negative, so that the sign of the correlation is preserved; we will slightly abuse the terminology, and call this score simply r 2 , or the coefficient of determination, assuming by default that it is always signed. For each dataset, and each phenotype, the folds were pre-computed and every GS method used the same folds. This ensures that the predictability results are comparable across different GS methods. Note that we treated the binary trait in QTLMAS similarly to the rest of the traits which were quantitative, i. e. we computed the r 2 metric directly between the actual binary trait and the real-valued predictions made by our methods. Applying binary thresholding to the latter can be used to obtain the prediction for a binary trait.
In general, using binary classifiers instead of thresholded regression techniques for binary trait prediction can sometimes (though not always) yield better classification accuracy; however, the focus of current study was rather on quantitative traits and r 2 metric. For global predictability, the GS model was trained on all available data and the coefficient of correlation was taken between the predicted phenotype data and the actual ground truth phenotype data, also denoted r 2. Some of the GS methods presented in this paper rely on feature selection; that is, these methods utilize a reduced set of markers to build/train the model. For these methods, we compute feature selection stability during 10CV. Feature selection stability is computed as follows. For each of the ten folds, the selected features were recorded.
Genomic Selection Methods We give a brief overview of the GS selection methods used in the analysis of the four empirical datasets. We label the fifteen methods BayesA, BayesB, BayesCpi, rrBLUP, Epistasis rrBLUP, Elastic net, Bayesian LASSO, FOBA, ISIS, SVR Linear, SVR Polynomial, SVR Radial, SVR Sigmoid, mRMR, and PCA-FOBA. The order of the methods was chosen to roughly match their similarity to one another if possible. Bayes A, Bayes B, Bayes Cπ (Parametric). Consider the typical situation for genomic selection, where we have the phenotype y 2 R l , and the genotype data x 2 R lÂn. The foundational model for Bayes A, Bayes B, and Bayes Cπ can be described by y j ¼ m j þ X n k¼1 x jk b k d k þ e j ; ð1Þ where x jk is the kth marker for individual j. Each method differs on the underlying assumptions of β, δ, and the error e.
rrBLUP (Parametric) Ridge regression BLUP can be described by interpreting Eq (1) as a mixed model equation. Assume δ k = 1 for all k, μ is the fixed effect, and β and e are the random effects. Moreover assume b k $ Nð0; s 2 a Þ for all k and e i $ Nð0; s 2 e Þ. Given data y and x one can use maximum likelihood or restricted maximum likelihood to estimate s 2 a and s 2 e and solve for μ, β k , and e using Henderson's mixed model equations. This approach to genomic selection was originally given in  [2]. rrBLUP is equivalent to ridge regression (see below), if one takes l ¼ s 2 a =s 2 e , and was used in genomic selection in  [45]. More interestingly, rrBLUP is theoretically equivalent to GBLUP  [3] [4] [5]. The R package rrBLUP  [46]  was used to perform rrBLUP analysis labeled 'rrBLUP' below.
Epistasis rrBLUP (Parametric) Epistasis is the interaction of two or more SNP's which effect the phenotype of interest. It is the departure of the sum of the marginal effects of each SNP alone. We explored the prediction accuracy of modeling all possible pairwise epistasis using the rrBLUP model. That is, the original set of k SNP features were augmented with an addition k(k -1)/2 features where each addition feature was given by the multiplication of all possible pairs of SNP feature. The set of original features and the pairwise epistais features were then modeled exactly as in Eq (1) and rrBLUP method was used to solve. However, the rrBLUP R package was unable to handle such a large input. Therefore, custom software was written to perform rrBLUP, specifically, a specialized parallel linear algebra algorithm to perform the underlying operations of rrBLUP.
Namely, l 1 penalty on the regression coefficients enforces sparsity by "shrinking" some coefficients to zero, while the l 2 penalty removes the limitations on the number of nonzeros and enforces grouping effect, i. e. highly correlated predictors are assigned similar coefficients  [29]. This can improve the interpretability of the model, for example, by discovering a group of relevant SNPs instead of just single representative from the group. For Elastic Net, we use publicly available Matlab code  [54]  that implements the LARS-EN algorithm of  [29]. It takes as an input the grouping parameter λ 2 and the sparsity parameter that specifies the desired number of selected predictors. Since this number corresponds to a unique value of λ 1 , as shown in  [53] , we will slightly abuse the notation, and denote the sparsity parameter as λ 1 , while always interpreting it as the number of selected predictors.
The procedure is then repeated. As reflected in its name, SIS enjoys the theoretical guarantee of sure screening, namely with asymptotic probability one, SIS will not discard any relevant predictors. When comparing the overall quality of different methods across all datasets, measured by their normalized average r 2 , as shown in  Fig 3,  we see that mRMR is a clear winner among all the methods we tried, with the highest normalized average r 2 of 0. 90. Moreover, as we can see in Fig  1 , mRMR also has the highest median (0. 92), and even its worst performance (minimum of 0. 45) is among the best worst-case performances across all methods. When looking at the individual datasets, corresponding to columns in Figs  1  and 2 , mRMR is the top performer, or among several top-performers, on 8 out of 14 datasets (see the columns 3,4,5,6,8,9, 13,14), and appears well above average, and quite close to the top, on almost all the remaining datasets.
These results suggest that, contrary to popular belief, univariate variable selection methods such as mRMR can be well-suited for genomic selection problems. We also note that the Elastic Net, which is a form of embedded variable selection, also performs quite well, even on complex traits, as we show below. Moreover, on the Rice Pericarp color (normal and corrected), the Elastic Net outperforms all other methods. This can be possibly explained by the fact that a relatively few input variables are believed to be responsible for this trait, and thus sparse regression models are well-suited for modeling such data (for more detail, see the Discussion section below).
Also, as discussed above, SVR Linear does not seem to be a natural modeling space for the data, as compared to SVR Radial or SVR Sigmoid. We note that Epistasis rrBLUP performance varies greatly. For example on QTLMAS Trait 2, it performs very well relative to the other methods; however, on Rice Protein content corrected it performs poorly. Both are polygenic traits, i. e. many influential markers. Thus, Epistasis rrBLUP may be overly sensitive to population structure. Additionally, given the addition of nearly a square factor of the number of parameters with respect to the number of SNPs, one would suspect Epistasis rrBLUP to overfit. Surprisingly, this seems to not be the case considering Figs  4  and 5  showing the coefficient of determination (r 2 ) of methods trained on all data (global) and the difference between 10CV and global r 2.