dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction Atom probe tomography (APT) is a materials characterisation technique that aims to form a 3D image at a near atomic resolution within a material subvolume. By combining analysis data from a two-dimensional position-sensitive detector * Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4. 0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. with a mass spectrometer, individual ion types and original positions can be estimated via an algorithmic process known as reconstruction. These algorithms assume a simple model for specimen evolution during APT analysis. The most common reconstruction protocols are mathematical projectionbased models  [1] [2] [3] [4] [5].
g. Γ t and Γ t+γ ), enabling a time-dependent trajectory mapping (T : S → D) to be constructed between the original material sample space (S = R 3 ), and the detector space (D = R 2 × N). Under this definition, for a particular ion with initial launch coordinates x l and final detector coordinates x d , the true trajectory mapping yields T (x l ) = x d. The process of data reconstruction then falls down to deriving an estimate for the inverse of this mapping R -1 ≈ T -1. For the implementation in this work, when constructing this inverse mapping (R -1 ), a bijective assumption has to be currently assumed. Ions are launched from the corner points of the triangular surface panels, their trajectories calculated up to the detector (under the transfer function in section 3. 2), and their final impact positions on the detector recorded.
In this work, the diffeomorphic density matching algorithm described in  [35, 36]  is applied between the predicted model detector space ion densities (sections 3. 4. 5 and 3. 4. 3), and the experimental detector space ion hit densities (calculated via Kernel Density Estimation  [37] ) through the ddmatch tool  [38]. This matching algorithm attempts to determine a smooth and well-behaved function-a diffeomorphism-that best transforms the model density image back onto the experiment density image. These diffeomorphic mapping algorithms are commonly applied in the field of computational anatomy in order to match a patient's imaged organ structure back to a model  [35, 39, 40]. In our case, this algorithm will instead match the evaporation model's ion density predictions back to the experimental APT image data by determining a local matching transformation.
This determined local transformation is then applied to the model's trajectory mapping prior to data reconstruction, with the magnitude of the required local matching transformation providing information about the local model error. The application of the diffeomorphic density matching algorithm implemented in ddmatch between a predicted model and experimental density detector hitmap for a fin fieldeffect transistor (finFET) semiconductor dataset is shown in figure  12  (further discussed in section 4. 2). It can be seen that this algorithm derives a transformation (figure  12(c )) that better aligns the original model predicted hitmap (figure  12(a) ) to the experimental hitmap (figure  12(b) ). This relaxation of the model transforms the predicted trajectory mapping such that model detector densities (figure  12(d) ) better match the experimental data densities (figure  12(b) ).
Results and discussion Through the workflow outlined in figure  1 , the reconstruction of experimental APT datasets using the defined evaporation model can be performed. In the following section, the modeldriven reconstruction of two semiconductor structures will be considered: a SiGe multilayer system (section 4. 1), and a fin field-effect transistor (finFET) device (section 4. 2). Both of these will be compared to their conventional point-projection reconstructions under the Bas protocol  [3]. For both these following reconstructions, a simulated flight path of L = 0. 102 m and detector radius of R d = 0. 038 m has been used. This configuration matches the LAWATAP instrument on which both these experimental datasets were obtained.
This required extrapolation of the internal layer phases up to the specimen surface. Possible causes for this loss of contrast include ET reconstruction artefacts or material amorphisation due to Ga implantation. Now that the specimen model geometry has been defined, model-driven reconstruction can be considered. Simulations were performed on a 48 × 38 × 133 level set grid, with cell widths of 1. 5 nm. Initially, depth calibration of the APT data against the model must be performed. From the approach outlined in section 3. 4. 5, values for the ionic volumes are determined to use between these landmarks that ensure this alignment through manual placement of specific landmarks in the experiment ion evaporation sequence (figure  14(b) ). For the model, these landmarks' corresponding positions are automatically extracted from when the Ge layers first appear within the model predicted detector space (figure  14(a) ), with the local phase on the detector determined via the method in section 3.
It was found that the normalised density spread was minimised when the microstructural similarity between the model and experiment was maximised (figure  15(a) ), even though the local density has not been considered by the MI microstructural optimisation. The calculated normalised density spread for the optimum model-driven reconstruction was 0. 24, lower than the value of 0. 28 obtained for the calibrated conventional Bas reconstruction. These results provide additional quantitative evidence that the new automated calibration approach is indeed improving reconstruction quality. By defining an emitter model from ET data of the initial specimen shape prior to evaporation, the proposed modeldriven reconstruction has successfully corrected for multiphase tilting distortions within an experimental dataset for this SiGe multilayer structure.
Reconstruction of a finFET device While the new reconstruction algorithm successfully corrected for the layer tilting distortions within the SiGe multilayer  dataset, the protocol's stability and performance for nonaxisymmetric systems and concave specimen apex shapes has yet to be tested. To investigate this, the protocol was applied to reconstructing an APT dataset for a finFET device. In the authors' previous work  [7] , this same dataset was 'naively' reconstructed by assuming specific evaporation field values. However, here model alignment, compression, and evaporation field parameters will be automatically selected under the new calibration procedure outlined in section 3. 6. Experimental details for the finFET dataset can be found within section III of the supplementary material. Applying the conventional Bas protocol to the finFET dataset reveals a narrowing distortion and increased density within the central fin region (see figures 16(c) and (d)).
This narrowing is not present within the correlative electron micrographs (see figures  16(a)  and (b)), implying that the narrowing is likely an APT imaging artefact, due to the differing evaporation mechanics of the SiGe and SiO 2 phases. This differing phase evaporation behaviour results in a specimen apex shape deviating significantly from the assumed hemisphere of the Bas protocol  [3, 7, 34]. In order to drive the reconstruction protocol, we must first define the specimen model. Unlike the multilayer system, correlative ET data was unavailable for the finFET dataset. Instead, the model's specimen structure was estimated using prior knowledge of the device geometry and correlative electron micrographs (figures 16(a) and (b)). Using this data, an initial specimen geometry for the evaporation model could be determined as shown in figure  16(h).
Limitations and improvements This study builds on our previous continuum modelling and APT image prediction from  [6, 7]. By applying the results from this continuum model, a new model-driven reconstruction protocol has been demonstrated on a SiGe multilayer and finFET device experimental APT dataset, successfully correcting for multiphase distortions. Unlike previous reconstruction attempts leveraging this continuum model  [7] , model parameters have been automatically calibrated by optimising the similarity between the final generated reconstruction, and our prior knowledge of the specimen structure. The numerical limitations of the current evaporation model formulation and implementation were previously outlined in  [6, 7]. These included the limited accuracy of the electrostatic BEM solution close to the boundary, as well as the model's poor computational scalability at higher simulation resolutions.
As mathematical projection laws are known to well approximate the charged optics of homogeneous material apex shapes  [4, 5] , these results provide some support for the study's use of a projection-based trajectory transfer function. It is also worth briefly commenting on the physical accuracy of the current evaporation model. Both the multilayer and finFET datasets were obtained under the APT laser-assisted evaporation mode. It is known from experiment that the presence of the laser can significantly effect the specimen apex shape, e. g. anisotropic blunting of the apex  [49]. Therefore, whilst the tilting distortions in the SiGe multilayer system have been successfully reduced by the assumed model through specimen-detector spatial realignment (figure  11 ), the true major cause of this tilting could be from laser apex blunting.
Further simulation results supporting this hypothesis can be found in section II of the supplementary material. Future work should explore validation of the model-driven approaches' compositional accuracy through correlative techniques, such as EDS. Additionally, specimen faceting has been omitted from the specimen models during data reconstruction due to a current lack in understanding of the relevant evaporation physics at a continuum-scale. Previously, a simple non-physical model reproducing faceting was proposed in  [7]. This faceting is clearly present as low density poles in the experimental datasets (see figure  12 ), and whilst the model relaxation step can partially correct for these pole distortions, future continuum models should aim to physically capture this demagnification occurring at surface facets.
For example, the adaptive surface remeshing currently required by the driving model is preventing the model from being fully parallelisable  [7]. A solution to this could be replacing the BEM with a meshfree solver  [51]. Whilst successfully correcting distortions in semiconductor datasets, the protocol remains technically challenging and additional progress is required before a widely applicable model-driven reconstruction protocol is achieved. The current workflow still requires significant user input, such as the initial geometry, and some preprocessing, such as landmark placement in the detector event sequence. The potential to further reduce user input and automate the analysis through datadriven approaches could prove critical for its wider adoption within the APT community. Finally, it should be noted that the continuum modelling framework is largely independent from the assumed law governing material evaporation (equation (  1 )).
Conclusions In this study, a new model-driven reconstruction protocol has been outlined, capable of correcting for multiphase distortions within experimental APT data. Unknown model parameters such as phase evaporation fields and specimen orientation have been automatically tuned by maximising the similarity between local composition in the generated reconstruction, and the prior knowledge of local phase in the original specimen structure. Through this new approach, distortions within a semiconductor multilayer system and a finFET device have been significantly reduced. An additional model relaxation step, that applies a diffeomorphic density matching algorithm developed for computational anatomy, was also applied to the finFET dataset, further reducing multiphase distortions. A new method was also outlined for efficiently predicting detector density hitmaps, as well as predicting detector regions where trajectory crossover is occurring.
Acknowledgments Charles Fletcher  acknowledges support from  CAMECA ®  for financially supporting this research. Charles Fletcher  and  Michael P Moody  acknowledge support from the  EPSRC Impact Acceleration Account Award   EP/R511742/1. Michael P Moody  and  Daniel Haley  acknowledge support from the  ESPRC Project Advanced Nuclear Materials   EP/P001645/1. The imec core program members, local authorities, and the imec pilot line are acknowledged for their support. The authors acknowledge the financial support by  FWO-Hercules  through Projects  ZW13_09  and  AKUL/15/22. The authors would like to thank  Hugo Bender ,  Paromita Kundu  and  Olivier Richard  ( imec Belgium ) for performing the electron microscopy in this work, and  Masoud Dialameh ,  Davit Melkonyan  and  Jeroen E Scheerder  ( imec Belgium ), for obtaining the experimental APT datasets.
The Validation Framework: DESCQA 12 https://sourceforge. net/projects/healpix/ The DESCQA validation framework  (Mao et al. 2018)  provides an efficient, flexible and convenient infrastructure that allows developers to produce and run a wide range of validation tests. 13 The streamlined workflow enables non-expert users to run the available tests very simply. The framework is composed of three principal parts: (1) a catalog reader interface, (2) a validation test interface and (3) a web interface. A main script 14 runs the selected catalogs and tests and outputs the test results. These results are viewed on a dedicated web page that is generated by the web-interface portion of the framework. Each test typically produces comparison plots of the catalog and validation data and delivers a status and an optional score that is the result of applying a test-specific metric comparing the catalog and validation data.
Color-Color Distributions We have expanded the test suite to include 2dimensional distributions as well. It is well known that, unlike the CvM statistic, there is not a well-defined metric to compare multivariate datasets in a unique way. In this case, we have instead used the so-called Wasserstein metric  (Dobrushin 1970, in Russian)  measured across several random directions in color-color space, where the distributions are projected. These different measurements are averaged and provided as additional outputs for our color-color plot comparisons, which include a heatmap versus contour plot visualization as well. We implemented a kernel two sample test from  Gretton et al. (2012)  as an additional cross-check. In Figure  4 , we show the two dimensional distribution of gr and ri cosmoDC2 colors compared with that of the DEEP2 data for the redshift range 0.
Galaxy-Galaxy Angular Correlation Function In this test we use the TreeCorr 19 package  (Jarvis 2015)  to compute the two-point angular correlation function, w(θ), the over-abundance of galaxy pairs at some angular separation θ relative to a random distribution. We apply selection cuts to the catalog sample to mimic measurements from  Wang et al. (2013)  of w(θ) in bins of SDSS r-band magnitudes in the range 17 < r < 21. The computation of w(θ) uses the estimator of  Landy & Szalay (1993). This test has been described previously in  Korytov et al. (2019) , so we do not reproduce it here. The results for the test showed that the amplitudes and slopes of the clustering signals for the catalog data were in reasonable agreement with the validation data, except at very small angular scales (θ 0.
We see that the first method, in general, gives similar richness to the second method and that the catalog data are scattered about the observed relation and have similar slopes. We note that the mass definitions for the halo masses, M FoF and M 200m , in cosmoDC2 and the observational data respectively, are not identical. In Appendix B we show that for the cosmoDC2 catalog, the expected ratio between these two definitions is M 200m /M FoF ≈ 1. 08 (see Figure  32 ). Hence we expect the red triangles and blue points from cosmoDC2 to be scattered about the observed mass-richness relationship but biased slightly low. We conclude that mass-richness relationship for redMaPPer selected clusters in cosmoDC2 are in qualitative agreement with the expectations from observations.
Emission-Line Ratios ies are selected to lie in the redshift range 0. 0 < z < 0. 7. Galaxies in the range 0. 0 < z < 0. 4 are further required to have r-band magnitudes < 19. 5, while those in the range 0. 4 < z < 0. 7 are required to have i-band magnitudes < 19. 9. These magnitude cuts correspond to the published SDSS spectroscopic detection limits  (Bolton et al. 2012). The distributions are compared using a two-dimensional KS test. We find that we need to limit the sample sizes for both the catalog and the validation data to random subsamples of 30000 in order to prevent the KS test from becoming too discriminatory. We report the log p-value for the KS test, the corresponding D value, and the shift in distribution medians in the upper left corner of the right panel. While the SDSS data set does not span the same range of redshifts that the LSST will probe, we can already see many artifacts in the cosmoDC2 emission-line ratio distribution.
Additionally, it is apparent that the mode of the two-dimensional emission-line ratio distribution for cos-moDC2 in the right panel is shifted to lower values of both line ratios in comparison to those of the SDSS sample on the left. This shift could be indicating an overrepresentation of [OIII] luminosity in cosmoDC2. In the future, this emission-line ratio test will require an observed comparison sample that more accurately represents the redshift range probed by LSST. In Figure  26  we show a comparison of the stellar mass function for cosmoDC2 galaxies with PRIMUS data  (Moustakas et al. 2013)  for selected redshift slices in the range 0 < z < 1. Overall, the agreement between the catalog and observational data is good, but not perfect, over a wide range in redshift. The most discrepant regions in stellar mass and redshift, where the catalog data falls below the PRIMUS data, are M * /M < 10 9 and 0 < z < 0.
1 and M * /M 10 11 and z > 0. 5. The level of agreement shown here is obtained without explicit tuning of the catalog data to the SMF. Instead, the underlying empirical model used for cosmoDC2 employed resampling of galaxies and their stellar masses from a simulation with somewhat different cosmology, resolution and size  (Korytov et al. 2019; Behroozi et al. 2019) , which has been tuned to match the observed SMF. The resampling is performed in narrow bins of halo mass. Hence, provided that the resampling procedure is unbiased, we expect that the distributions of stellar masses in cosmoDC2 will follow those of the observational data. This test thus validates that no significant distortions of the stellar-mass function have been introduced by the hybrid catalog-production algorithm.
SUMMARY AND DISCUSSION In this paper we have presented a test suite for validating synthetic catalogs that have been developed primarily for evaluating dark energy science targets based on data from optical surveys. Generating synthetic catalogs for these surveys requires a large amount of human effort and consumes significant computer resources. Crucially, these catalogs must be sufficiently realistic to ensure that they are useful for testing survey and data analysis pipelines. Therefore it is imperative to validate them against observational data and theoretical expectations. It is only by carrying out these validation steps that catalog users can in fact assess how useful the catalogs will be for studying their science case of interest. This in turn implies that prospective users have specified their science goals and have developed some validation criteria that the catalogs must meet in order to fulfill those goals.
We emphasized the importance of running the catalogvalidation program concurrently with the catalog production. Some of the intended uses of the synthetic catalog, such as image simulations, are extremely costly and cannot be easily rerun if problems with the catalog surface at a later date. Ideally, the catalog production process should be flexible enough to incorporate changes when problems are discovered. Similarly, the test suite and the framework in which it is run should also easily accommodate changes or additions to the tests. Both of these features of the catalog-production and DESCQA validation pipelines were heavily used during the production and validation of cosmoDC2. One example of this interplay is the validation test for the presence of a prominent red-sequence of galaxies, which in early iterations of the cosmoDC2 catalog, could not be identified by the redMaPPer algorithm.
Since cosmoDC2 is built partly on an empirically-tuned model, it was possible to change the model parameters to enhance the red sequence to solve this problem. Another example is the development of the readiness tests during catalog production when it was discovered that outlying values in some galaxy properties were causing the image simulation code to crash. Rapid development and deployment of the readiness tests were made possible by the flexibility of the DESCQA framework that we use to run our test suite. We anticipate that our validation test suite will be expanded in the future as users pursue more detailed analyses of the catalog data and begin prototyping new scientific analyses. Indeed, many of the tests of cluster member galaxies shown in this paper have been developed only recently as the specialized redMaPPerselected galaxy sample became available.
At the time of production of the cosmoDC2 catalog, only FoF masses were available, so SO masses are not included in the cosmoDC2 catalog. Since then, further post-processing of the saved particle data from the Outer Rim simulation has produced SO masses for halos containing > 1000 particles (or mass 10 12 h -1 M ). These SO masses are measured by centering the SO halos on the FoF halo centers, so we can make a direct comparison of the halo masses in each case. We estimate the relationship between M 200c and M FoF for cluster-sized halos in the cosmoDC2 catalog by selecting halos from the Outer Rim simulation with M FoF > 10 13 h -1 M and z < 1 and compare their FoF and SO masses. In Figure  31  we show the scatter in the values (upper panel) and ratios (lower panel) of M 200c and M FoF for this halo sample.
ACKNOWLEDGEMENTS This paper has undergone internal review in the  LSST Dark Energy Science Collaboration. We thank the internal reviewers  Ian Dell'Antonio ,  Alex Drlica-Wagner  and  Andrés Plazas Malagón. We also thank  Peter Brown  for reading the manuscript and providing comments and  Andrew Hearin  for many useful discussions on the results of the validation tests. In addition, we thank  Minghao Yue  for providing feedback that helped us to identify and correct a bug in the ellipticity distributions in cos-moDC2. We also wish to thank the paper referee for a thorough and thoughtful review and for suggesting a number of changes to improve the clarity and readability of the paper. The contributions from the authors are listed below. Eve Kovacs: Co-developed the validation framework, developed and worked on many validation tests, contributed text to the paper and led the writing of the paper.