dataesr/scientific-paragraphs-categorization huggingface dataset:
Let us review the current formats of presentation of likelihood data. The presentation of first-order data is standardised while currently no third-order data are usually given. Regarding second-order data there is unfortunately no standard representation currently established. A review of the second-order data in HepData and on the experiments' analysis websites reveals a mixture of presentation styles: • Table format: 2D histograms of either covariance or correlation matrices. This has the difficulty that the convention used is not made clear (other than by inspection of the matrix diagonal), and without a structural association with a first order dataset it is impossible for computer codes to unambiguously construct the relevant likelihood. In the case of the presentation of a correlation (as opposed to covariance) matrix, the diagonal variances must be provided with the first-order dataset.
• Error source format: a vector of labeled ± terms associated to each element of the first-order dataset. The correlations between the error sources is indicated via the labels, (e. g. , a "stat" label to be a purely diagonal contribution, a "lumi" label to be 100% correlated across all bins, and all other labeled uncertainties treated as orthogonal). The correlation or covariance matrices can be constructed using 6 Using the elementary uncertainties maybe more convenient when one wishes to include the systematic uncertainties on the signal, i. e. α-dependent b, c, ρ. Since these systematics are not crucial for new physics searches we do not take them into account here.
JHEP04(2019)064 eq. (4. 5). This format presents the second-order data in the form of "effective" elementary uncertainties. • Auxiliary files in arbitrary format: the ad hoc nature of these makes them impossible to be handled by unsupervised algorithms. This includes 2D histograms in ROOT data files, since variations in path structure and the ambiguity between covariance or correlation matrices are an impediment to automated use. This presentation style will be disregarded below. The table and error source formats may be readily extended for automated data handling and are thus appropriate to release SL data. In the case of the table format, in addition to the observed central values and statistical uncertainties usually released, extra HepData tables can encode the m 1,I , m 2,IJ , m 3,I moments describing the combined nuisance parameters.
However the HepData table headers will have to be augmented in a standardised fashion to express the relationships between tables, i. e. unambiguously identifying the moment data tables associated with a first-order dataset. While the format is conceptually straightforward, introducing the semantic description of the tables is at present highly impractical. We hence recommend the error source format for which identifying the associations between datasets is trivial. In the error source format, the m 1,I , m 2,IJ , m 3,I moments are all encoded in the form of labeled vectors. The m 2,IJ matrix is reconstructed via a sum of the form m 2,IJ = a I,i a J,i (4. 5) where the a I,i are the released error sources. The vector of third order data can be indicated via a special label. There is not limit in the number of labels associated to an element hence this format is very flexible.
For instance the a I,i error sources corresponding to the decomposed covariance can just get bland names such as "sys,NP1", but can also be extended with, e. g. , a "th" prefix to allow separation of experimental and theory systematics (since the theory can in principle be improved on in future reinterpretations). This format requires some keyword standardisation. The final scheme should be capable of equally applying to any kind of experimental data and systematic uncertainties. In particular it should be valid for event counts, differential cross-sections with bins correlated by the systematic uncertainties, correlations between the bins of different distributions/datasets, and so on. Summarising, our recommendation is to release the moments of the combined uncertainty distributions via the HepData error source format, which has built-in semantics of arbitrary complexity and can thus make the most of the SL framework.
Simplified likelihood in a realistic LHC-like analysis In this section we introduce a realistic pseudo-analysis that is representative of a search for new physics at the LHC. This analysis will be used to validate the SL method and to JHEP04(2019)064 test its accuracy in realistic conditions. It is also used to validate the SL reference code presented in appendix B. Finally, this pseudo-analysis provides a concrete example of SL data release via the HepData table format (see above). The SL and subsequent results of the pseudo-search can be reproduced using these data. As already mentioned in section 2, the dominant systematic uncertainties relevant in searches for new physics are those related to the background processes. Imperfect knowledge of detector effects or approximations used in the underlying theoretical models will lead to uncertainties in the predictions of these processes.
A LHC-like pseudo-search for new physics In order to illustrate the construction of the SL, a model has been constructed which is representative of a search for new physics at the LHC. Typically, in these searches the observed events are binned into histograms in which the ratio of signal to background contribution varies with the bin number. A search performed in this way is typically referred to as a "shape" analysis as the difference in the distribution (or shape) of the signal events, compared to that of the background, provides crucial information to identify a potential signal. Our pseudo-search requires to make assumptions for an "observed" dataset, for the corresponding background, and for the new physics signal. These ingredients are summarised in figure  2 , which shows the distribution of events, in each of three categories along with the expected contribution from the background and the uncertainties thereon, and from some new physics signal.
Validation of the simplified likelihood Here we compare the true and simplified likelihoods arising from the pseudo-search. It is also instructive to consider the simplified likelihood obtained when neglecting the third moments, i. e. when setting the coefficients of the quadratic terms c I to zero in eq. (2. 3). This less accurate version of the SL will be referred to as "symmetric SL", as opposed to the more precise "asymmetric SL" developed in this work. We constructed 100,000 pseudo-datasets by taking random values δ, generated according to π(δ), and evaluating n b,I ( δ) for each dataset according to the eq. (5. 6). Figure  3  shows the distribution of ni , for an example bin, i = 62, from the SL. The values of m 1 , m 2 and m 3 are calculated using the pseudo-datasets and subsequently used to calculate the coefficients for the SL.
In Figure  4 , 2D projections of the background distributions are shown between four pairs of signal-region bins: bin pair (4, 7) shows a projection for high-statistics bins where both the asymmetric and symmetric SL agree closely with the true distribution (that obtained in the pseudo-datasets); the true distribution in (4, 62) starts to display deviations from the multivariate normal approximation which are well captured by the asymmetric SL. This is expected when the skew, defined as m 3,I /(m 2,II ) An advantage of the asymmetric SL is that a strictly positive approximate distribution can be guaranteed, while the symmetric SL can have a significant negative yield fraction as seen in the figures for bin 86. Sampling from the symmetric SL, e. g. for likelihood marginalisation, requires that the background rates be positive since they are propagated through the Poisson distribution.
The signal hypothesis is "excluded" at 95% CL if µ up < 1. When determining the SL coefficients, we have relied on pseudo-datasets, as we expect this will often be the case for anyone providing SL inputs for real analyses. The accuracy of the SL coefficients will necessarily depend on the number of pseudo-datasets used to calculate them. To investigate this, we have performed a study of the rate of convergence of the SL coefficients by calculating them using several different numbers of pseudo-datasets, the largest being 100,000 pseudo-datasets. The coefficients for the three bins calculated using 100,000 pseudo-datasets are; a = 84. 9, b = 8. 27, c = 0. 32 for bin 4, a = 2. 61, b = 0. 90, c = 0. 11 for bin 62, and a = 0. 90, b = 0. 47, c = 0. 13 for bin 86. The calculation of the coefficients is repeated using many independent sets of a fixed number of pseudo-datasets, resulting in a distribution of calculations for each coefficient.
The root mean square (RMS) of the resulting distributions provides an estimate for how much variation can be expected in the calculation of the SL coefficients given a limited pseudo-data sample size. The RMS values are normalised to the RMS of the distributions resulting from a sample size of 100,000 pseudo-datasets to give a relative RMS. The relative RMS of the distribution of the coefficients calculated using increasing numbers of pseudo-datasets is shown figure  6. The coefficients a and b can be calculated with relatively high precision using only 1000 pseudo-datasets in each case. This is true whether the value of b is large compared to a, as in the case of bin 86, or not, as in the case of bin 4. The determination of the c JHEP04(2019)064 coefficient for bin 4 however is slower to converge, requiring 5000-10,000 pseudo-datasets to calculate accurately.
However, since the value of c for this bin is relatively small compared to b, the coefficient c is less relevant so that a poor accuracy will have little effect on the accuracy of the SL. In bin 86, the value of c is relatively large, compared to b, meaning it will significantly contribute to the SL. In this case, the convergence is quite fast, with only 2,500 pseudo-datasets required to achieve a 10% accuracy in the value of c. We find the property that bins with large c values, compared to b values, require fewer pseudo-datasets to achieve a good accuracy than bins for which the c value is less relevant generally holds in this study.
The SL formalism discussed in this paper focusses on datasets with more systematic uncertainties than observables (i. e. N ≥ P ), and a few extra simplifying approximations have been made. The conditions of its validity are summarised as follows: • Convergence of the central limit theorem: there should be enough independent sources of uncertainties for the combined distribution to tend towards a Gaussian. This is the fundamental condition underlying the SL approach. The leading, asymmetric corrections to the Gaussian can be treated as described in this work. • Sufficiently symmetric combined uncertainties: alltough we have consistently included skewness in our formalism, it cannot be arbitrarily large, as discussed in where n b,I (θ) = a I + b I θ I + c I θ 2 I. The reference code has been written with reverse engineering and comprehensibility of the calculations explicitly in mind.
While it computes likelihood statistics on a reasonable timescale, further (but less readable) optimisations can be added for production code. A demo of the construction of the simplified likelihood, and profiling as a function of a signal strength parameter, is given in simplikedemo. py. Finally, the SL pseudo-data are available on the HepData repository at https://www. hepdata. net/record/sandbox/ 1535641814. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4. 0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Acknowledgments This work has been initiated at the LHC Chapter II: The Run for New Physics workshop held at IIP Natal, Brazil, 6-17 Nov. 2017. We thank the  IIP Natal  for hosting the workshop and creating a most inspiring working atmosphere. AB is supported by a  Royal Society University   Research Fellowship grant. MC is supported by the  US Department of Energy  under award number  DE-SC0011702. SF is supported by the  São Paulo Research Foundation (FAPESP)  under grants # 2011/11973 , # 2014/21477-2  and # 2018/11721-4. SK is supported by the  IN2P3  project " Théorie LHC-iTools " and the  CNRS-FAPESP  collaboration grant  PRC275431. NW is funded through a  Science and Techologies Facility Council (STFC)  Fellowship grant # ST/N003985/1.
ACKNOWLEDGEMENTS We are grateful to the authors of Ref. [40], and in particular to  Henry Fu , providing the Mathematica notebook including the resistive force theory calculations for a helix subjected to shear flow. We thank  Angela Dawson  and  Vincent Martinez  for providing the AB1157 E. coli strain. AM acknowledges funding from the  Human Frontier Science Program  ( Fellowship LT001670/2017 ). EC, NFM, AL, GM acknowledge funding from the  ANR-15-CE30-0013  BacFlow. AL and NFM acknowledge funding from the  ERC   Consolidator Grant PaDyFlow  (Agreement 682367). AZ acknowledges funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Sk lodowska-Curie grant  ( Agreement 653284 ).
This is identical to other commonly used hyporheic models such as OTIS and is a necessary simplification in the up-scaling process  [Runkel, 1998]. The original version of FINIFLUX  [Frei and Gilfedder, 2015]  only supported an exponential distribution model for pdfRT. As part of this study we additionally implemented power law and gamma-type pdfRT models (Equations 8 and 9) to account for 222 Rn emanation in the HZ (modified version of FIIFLUX can be obtained from http://www. hydro. unibayreuth. de/hydro/en/software/software/software_dl. php?id_obj=129191). By using the standard exponential pdfRT Equations 11 and 12 can be solved analytically giving 1 1   m Rn hw     and 1 2    m Rn Rn hw      [Cook, 2013]. In the case of power law or a gamma distribution models the integrals in Equation 12 and 13 are solved numerically by using the adaptive quadrature techniques implemented in MATLAB.
FINIFLUX is coupled to the automated parameter estimation software PEST  [Doherty et al. , 1994]  for model optimization. PEST is used to derive an objective function between the in-stream 222 Rn observations and numerical predictions, and depends on a set of pre-defined model parameters. Optimal parameter settings are systematically estimated within PEST targeting the best parameter set that minimizes the objective function. PEST estimates this optimal parameter set by applying the Gauss-Marquardt-Levenberg algorithm  [Doherty et al. , 1994]. PEST coupling within FINIFLUX is set up to search for optimal groundwater inflow rates I and optimal hyporheic exchange parameters τm and h simultaneously.
Acknowledgments This research was supported in part by the  Loire Brittany Water agency (AELB) , the  Franco-Bavarian University cooperation center BayFrance  (www. bayern-france. org/en/)and the  German Research Foundation (DFG)  project number  FR 2858/2-1-3013594. It was also supported by the internal funds of the  Limnological Research Station, Bayreuth. The authors thank  Christian Camerlynck  for the seismic cross section and the anonymous reviewers for their helpful comments. Data to this manuscript can be downloaded from http://www. hydro. unibayreuth. de/hydro/de/software/software/software_dl. php?id_obj=151411 ©2019  American Geophysical Union. All rights reserved.
Compared with other metaheuristic algorithms such as GA, PSO has the advantages of simplicity, few parameter configurations, global exploration, adapted ability to some complex and continuous variable problems, and fast convergence. With the study of the MOPSO algorithms for problems of data clustering in general, several works have been proposed  [34, 35]. However, applying these algorithms to MOO clustering of image segmentation, particularly segmentation of MR brain images, needs to be further explored  [25]. To achieve more accurate results, we propose in this paper a new method for brain MRI image segmentation, which takes advantages of both fuzzy clustering and region-based active contour methods, and simultaneously solves their main problems: (i) sensitivity to noise and INU artifact; (ii) trapping into lo-cal minima and dependency on initialization.
The output is a set of non-dominated Pareto optimal solutions, from which the L 2 -metric method is used to select the final one  [39]. To validate the effectiveness of the proposed algorithm, we evaluate it on both simulated and real MR images from BrainWeb  [40]  and IBSR database 1  , respectively. The results are reported and compared with other recent segmentation methods in the literature. The rest of the paper is organized as follows. The problem formulation is described in Section 2. The MOPSO fundamental and advanced concepts to improve the search ability and the quality of solutions are presented in Section 3. The description of the proposed method, using MOPSO approach and decisionmaking process for MR brain image segmentation is given in Section 4. The performance of our method is evaluated and compared with a set of algorithms from the literature in Section 5.
Goal and proposed solution The objective is to segment the MR image in an unsupervised way with accurate results. To achieve this, the problem of MR image segmentation is formulated within a MOPSO framework and a decision-making process to simultaneously estimate the true image with several segments and the bias field. The MOO approach to the problem is motivated by seeking two important properties in segmented images: compactness and separation, from two complementary approaches named fuzzy clustering and region-based active contours. Particularly, the first fitness function, which is taken from our previous work  [15] , called kernelized fuzzy entropy clustering with local spatial information and bias correction, will have the purpose of minimizing the variation or scattering of the data within a particular tissue (compactness).
Additionally, the well-known region-based level set method, called LIC  [18] , and the metaheuristic multilevel threshold with Markov random field (PSO-MRF)  [59] , the PSO based on global and local region-based active contour (PSO-AWGLAC) and our previous work, called PSO-KFECSB algorithm  [15] , are used. These references can be consulted to seeThe algorithms' parameters setting is specified in Appendix A. All of the algorithms are implemented in MATLAB 2014b and executed with a computer with Intel Core i7 1. 8 GHz CPU, 8G RAM using Microsoft Windows 10. Furthermore, from recommendations in similar context in the literature  [15, 18]  and the "trial-and-error" method with experiments around those parameter values, we sorted out parameter values for the proposed algorithm as follows: swarm size N p = 30, external archive of non-dominated solutions size N r = 30, number of grids per dimension N g = 10, maximum number of iterations K max = 200 (180 for real MR images), and selection probabilities for the leftmost, rightmost, and middle solutions: 15%, 15%, and 70%, respectively.
Datasets The MR images used in this study include both T1-weighted simulated and real 2D MRI brain images. For simulated MR images, they are downloaded from a well-known database: the BrainWeb from a McConnell Brain Imaging Center  [40]. The size of the synthetic images is 181 x 217 and that of the voxels is 1 x 1 mm 2. On the other hand, real images are taken in the 20 normal MR brain data sets provided by the Center for Morphometric Analysis at Massachusetts General Hospital, which are available at 2. The size of the images is 135 x 142 and that of the voxels is 1. 171751 x 1. 171751 mm 2. Note that several image modalities used in medical imaging, such as Roentgen rays (X-Rays), Magnetic Resonance Imaging (MRI), Ultrasound (US), Computed Tomography (CT) and Positron Emission Tomography (PET), each with its own advantages and disadvantages, have appeared over the years.
However, as pointed out in the section 4. 3. 2, when the intensity inhomogeneity in the input image is severe, such as for real MR images in the IBSR database, the correctness of the proposed region-based active contour model relies on the LFE force. In such case, we should choose a higher value for (ζ); otherwise, the GFE force may cause the deformable curves falling into fake edges. For images with minor inhomogeneity and high level of noise, such as simulated MR images examined in section 5. 4, the influence of the GFE force in the model should be increased. In this situation, we can use a smaller value for (ζ) and a higher value for (ρ). In the experiment, we need to select appropriate values for (ρ, ζ) according to the degree of INU artifact and noise existing in input images.
Complexity analysis The proposed method benefits both advantages of fuzzy entropy clustering and region-based active contour approaches to satisfy multiple requirements of image segmentation problem. In addition, using multiobjective particle swarm optimization algorithm to avoid the dependence on initial labelling is also taken into account. To analyse the complexity of the proposed algorithm, we calculated the running time when segmenting brain MR images. Both simulated and real brain MR image datasets are involved in experiments. Since the eventual computational cost will be the multiplication of cost for each iteration and the number of iterations for convergence, the average time cost of each iteration is recorded. The mean and standard deviation of the time cost of our algorithm (Intel Core i7 1.
Figure3shows an example of segmentation results when applying the proposed method to segment brain MR image both with and without skull (slice 80 in BrainWeb dataset with 9% noise and 40% INU artifact). It is noticeable that the proposed method provides better qualitative segmentation results in case of the skull-stripped image. To clarify this issue, three different unsupervised criteria: Levine Nazif, Rosenberger Type I and Borsotti Q [49] [50] [51] , were used for a quantitative performance evaluation. Table 2 also illustrates that better segmentation results can be achieved with input image without skull.
Real MR brain imagesWe have also examined the ability of the proposed method when segmenting real MR images from Internet Brain Segmentation Repository (IBSR) database (the 20 normal T1-weighted MR brain images, which have a high level of intensity inhomogeneity, in the 4 th volume). Each image is segmented into three regions: cerebro spinal fluid (CSF), gray matter (GM) and white matter (WM). The background pixels are ignored in the computation. The rest of parameters is a set of the weighting coefficients (ν = 0. 003 * 255 2 , ρ = 0. 4, and ζ = 1. 65).
5. 5. 5 Real MR brain imagesWe have also examined the ability of the proposed method when segmenting real MR images from Internet Brain Segmentation Repository (IBSR) database (the 20 normal T1-weighted MR brain images, which have a high level of intensity inhomogeneity, in the 4 th volume). Each image is segmented into three regions: cerebro spinal fluid (CSF), gray matter (GM) and white matter (WM). The background pixels are ignored in the computation. The rest of parameters is a set of the weighting coefficients (ν = 0. 003 * 255 2 , ρ = 0. 4, and ζ = 1. 65).