dataesr/scientific-paragraphs-categorization huggingface dataset:
Conclusions The poor data-efficiency of generic machine learning models poses a major challenge to their application in chemical reactivity studies, since for most specialized predictive tasks in this domain, only limited training data is available. In this work, we have explored a strategy to make machine learning workflows for reactivity prediction significantly less data-hungry, by making use of an intermediate informative reaction representation. This informative representation was constructed based on a VB analysis for generic HAT reactions. A surrogate model, able to predict (most of) the identified quantum chemical informative descriptors was subsequently built based on a repurposed, publicly available dataset of descriptors and geometries of organic radicals. Combining the surrogate model with a secondary reactivity model, we achieved unequivocally superior performance on a medium-sized, in-house generated, dataset of DFT computed re- action profiles of diverse HAT reactions, compared to any other machine learning approach we tried.
Because of the extreme data efficiency of our descriptor-augmented models, we were able to demonstrate that they can be fine-tuned and applied to small datasets across various reaction conditions, settings and application domains, ranging from regular (liquid phase) synthesis, over metabolism and drug design, to atmospheric chemistry. The presented modular approach towards reactivity prediction has the potential to significantly expand the scope of machine learning workflows for focused reactivity predictions, as long as the reactivity type is qualitatively understood and can be modeled accurately, and high-quality descriptor datasets are available for surrogate model training. In this context, it is crucial to emphasize the necessity for careful curation of these property datasets, ensuring that the chosen descriptors are pertinent, i.
Acknowledgements JEAR and TS acknowledge the  French National Agency for Research (ANR)  for a  CPJ grant  ( ANR-22-CPJ1-0093-01 ). This work was granted access to the HPC resources of IDRIS under the allocation  2023-100732  granted by  GENCI. RMN thanks the  Zeno Karl Schindler Foundation  for their generous financial support, and  Connor Coley  and  Gisbert Schneider  for their guidance during her Master's thesis work.
The main code used to generate the presented results can be found at https://github. com/chimie-paristech-CTM/bde_ hat. The code associated with the final reactivity model, i. e. , the surrogate model in combination with an FFNN, can be found at https://github. com/chimie-paristech-CTM/energy_ predictor_HAT. The (generated/curated) datasets can be downloaded at https://figshare. com/projects/Hydrogen_atom_ transfer_reactions/188007 and https://figshare. com/ articles/dataset/dataset_surrogate_model_cs/24754341 respectively.
more, upon re-training on the 73 computed RMechDB reaction profiles, an outstanding accuracy is recovered; in 10-fold cross-validation, our ensembled FFNN with transfer learning now reaches R 2 = 0. 88 (MAE = 1. 29 kcal/mol, RMSE = 1. 51 kcal/mol); our multivariate linear model reaches R 2 = 0. 88 as well (MAE = 1. 20 kcal/mol, RMSE = 1. 57 kcal/mol). With both of these fine-tuned models, we made predictions for the remaining reactions extracted from the database (cf. https: //github. com/chimie-paristech-CTM/energy_predictor_ HAT/tree/master/reactivity_model/RMechDB_pred).
Numerical results In this section, we present numerical results to illustrate the theoretical statements established previously. All the simulations have been obtained with the finite element software FEniCS  [39, 40]  using a direct LU solver. First, we validate numerically the discrete energy balances for the two schemes under study, and show the influence of the fluid mass source term θ on the schemes stability. Then, the error results of Theorems 19 and 23 are discussed by means of convergence plots. Finally, we illustrate the importance of the choice of the finite element spaces employed when entering the incompressible regime.
VII. APPLICATION TO THE CARE PATHWAYS OF CANCER PATIENTS This section applies the best performing algorithm "Our" to study the care pathways of sarcoma patients. We first present the background and the relevant data in Section VII-A. Section VII-B is a sensitivity analysis of the process model with respect to model precision level parameters. Section VII-C compares our data representation with alternative ones. Section VII-D compares the care pathways of various strategies for managing sarcoma patients. Section VII-E compares our approach with the generic process mining software Disco. Note that only the proposed algorithm ("Our" algorithm) is considered.
NetSarc was a clinical network dedicated to patients of soft tissue and viscera sarcomas, while RRePS was created as its complementary network to guarantee the pathological review. ReSoS was funded for bone sarcomas patients by integrating both clinical and pathological functionalities. In 2019, the three networks were grouped into one network named NetSarc+, and share the same database  [35]. The data used in this case study were from NetSarc+. Interested readers are invited to have more information at https://netsarc. sarcomabcb. org. For each sarcoma patient, NetSarc+ records the following healthcare data: the sequence of care activities correspond to events with information on when-where-by whom for each. It also records the change of sarcoma state including metastatic progression and local progression.
ACKNOWLEDGMENT The authors would like to thank the  NetSarc Network and Community , in particular  Prof. Jean-Yves Blay  for his valuable comments,  Françoise Ducimetiere, Ph. D. , and  Claire Chemin ,  M. Sc. , for access to the clinical and biological national database dedicated to sarcoma (https://sarcomabcb. org/). The author  Zhihao Peng  is grateful to  Dr. Omar Rifki  for his help in experimentation and fruitful discussions.
Note to Practitioners-This paper is motivated by our collaboration with the French cancer by Associate Editor Hupon evaluation of the reviewers' comments. This work was supported in part by the  French Ministry of Health through Programme de Recherche Médico Economique  under Grant  PRME-18-0162  and in part by the  National Natural Science Foundation of China  under Grant  72192822. (Corresponding author:  Xiaolan Xie. )This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was granted by the  French National Committee on Informatics and Privacy (Commission Nationale de l'Informatique et des Libertés)  under Approval No. DR-2021-035.
Dataset description We validate our algorithm by applying it to data collected during the Individual-Based Investigation of Resistance Dissemination (i-Bird) study  [17, 31]. This study took place in a We used hospital staff schedules to determine the hourly presence of each staff and compared these schedules to the dates and times when staff had any contact recorded. We assumed that, in reality, staff would have at least one contact with any other individual during any given hour of their presence time, hence if no contact was recorded for a given hour of presence we considered this was missing data rather than true absence of contact. Through this, we estimated that the median percentage of a staff's total presence time when no contact data was recorded was 40. 0% (interquartile range (IQR): 0-75.
Description of HCS contact heterogeneity: the example of the i-Bird dataset In this section, we illustrate the typical complexity of contact structures in HCS using the i-Bird network. While the algorithm makes use of data at the hourly level, in this section the contact data are aggregated at the daily level, so that if two individuals have two separate contacts with each other at different times of the day, this is only counted once. The contact network is considered undirected, since contacts are assumed to be reciprocal. Daily-averaged contact matrices built from these data are described in a previous work  [31]. We first summarise the observed temporal network recorded in the LTCF during the i-Bird study, comparing the total daily network and subgraphs with only patient-patient, staff-staff, or patient-staff contacts (Figure  1a-d).
This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. AD, LT and LO received funding from the  French National Research Agency  ( SPHINX-17-CE36-0008-01 ). DG received funding from the  National Clinical Research Program  and the  Investissement d'Avenir program ,  Laboratoire d'Excellence "Integrative Biology of Emerging Infectious Diseases"  ( ANR-10-LABX-62-IBEID ). The authors would like to thank  Eric Fleury ,  Pierre-Yves Boëlle ,  Vittoria Colizza  and  Pascal Crépey  for helpful discussions on the analysis of the contact network.
We chose these two underlying algorithms since they are known to be embarrassingly parallelizable, and therefore expected to scale well. In Sec. 5  we demonstrate the benefit of using PLMSS for effective data analysis and visualization on four datasets. We compare PLMSS against the corresponding subprocedures of two state-of-the-art Morse-Smale complex software libraries, i. e. , the implementations available in the Topology ToolKit (TTK)  [8]  and MSCEER  [9]. Specifically, we performed two strong scaling studies (Sec. 6) that show that MSCEER outperforms TTK, but PLMSS is still up to an order of magnitude faster than MSCEER, while also providing superior parallel efficiency. However, the qualitative and quantitative comparison between the region separators computed by PLMSS and their counterpart of MS complex 2-cells is more challenging.
Although they both separate regions with different gradient flow behavior, they are defined and computed differently (Sec. 3 ). Yet, for many applications-including the scenarios presented in Sec. 5the computation of region separators is sufficient without the need for expensive discrete gradient field and dual mesh computations. In short, the contributions of our work are: • A scalable algorithm with high parallel efficiency for the computation of piecewise linear Morse-Smale segmentations (PLMSS); • A detailed performance benchmark that compares PLMSS with the corresponding subprocedures of two state-of-the-art Morse-Smale complex software libraries (TTK and MSCEER); and • The integration of PLMSS in TTK to facilitate future benchmarks and reproducibility. -e ). Each color represents the influence area of a specific extremum (the areas of minima 0 and 1 are shown in red and yellow, while the area of maxima 14 and 15 are shown in blue and green).
Gyulassy et al. [20]  implemented a region-growing algorithm that labels the vertices to extract 3-, 2-, and 1-cells, also extendable from 3D to higher dimensional scalar fields. Discrete Morse theory was developed by Forman  [21] , applying Morse theory to any type of simplicial cell complex. Many algorithms build upon the discrete gradient vector field to effectively compute the MS complex  [22, 23, 24]. To efficiently compute the MS complex for large datasets, several parallel and distributed memory implementations were introduced. Gyulassy et al. [25]  first proposed splitting a dataset into subsets called parcels, extracting the MS complex from each parcel to later merge them in a cancellationbased step. This allowed for the computation of datasets that do not fit into memory and gave rise to distributed memory approaches  [26, 27].
Cancellation-based simplification  [36, 37, 38]  is often used in applications, where pairs of critical points are removed to simplify the MS complex and eliminate noise in the dataset. It counteracts over-segmentation of the domain and enables the extraction of persistent features. The Watershed transform, originally defined by Beucher and Lantuéjoul  [39] , is another approach to Morse theory, segmenting the domain, usually gray-scale images, into catchment basins that represent the zone of influence of minima and watershed lines, separating catchment basins from each other. Beucher  [40]  described catchment basins as areas where each drop of water ends up at the same minimum when flowing down the surface. In contrast to Morse theory, minima don't have to be distinct but can rather consist of multiple vertices of the same function value.
If the link Lk(τ ) includes vertices which do not belong to M i , we say that τ is a boundary simplex for M i. Then the region boundary of M i is the simplicial complex formed by the union of all the boundary simplices of M i (and their faces). Each region boundary separates M i from the remaining dataset. The region separators separate all regions M i ∈ M from each other. To create them, every d-simplex of M that contains vertices belonging to at least two distinct MS regions spawns (d -1)-simplices inside its convex hull, as depicted in Fig. 4  and Fig. 5.
RESULTS In this section, three example datasets and their regionseparating geometry outputs for both algorithms are provided. The Noisy Terrain dataset in Sec. 5. 1 is used to highlight differences between both algorithms in the 2D case. Sec. 5. 2 shows that both algorithms produce a very similar output when no saddle-saddle 2-cells are present. The last two datasets indicate that the MS complex is providing more geometry than necessary to effectively extract useful information in many cases, while the PLMSS can extract the areas of influence without additional preprocessing.
Noisy Terrain The Noisy Terrain dataset is a triangulated surface with elevation scalars attached, chosen as an illustrative example. It has a 300x300 resolution and can be found in the TTK data repository  [67]. Generally, the dataset consists of hills and valleys on a regular grid, where the hills are getting smaller the closer they are to the border. Additionally, noise was added to the terrain to showcase topological simplification. Fig. 6  compares the PLMSS with the MS complex, using the same color coding for critical points, separating geometries, and segmentation in both versions. Slight differences can be detected regarding the separating geometries, where the MS complex separating geometries are defined on the dual graph and are connecting triangle centers in the 2D case. Concerning the PLMSS, triangles are split according to the labels at the triangle vertices.
AT Molecule The AT dataset from the TTK Tutorial Data  [68]  shows the simulation of the electron density of a molecule restricted to a plane but embedded in 3D space. This example, provided in Fig. 7 , shows that the PLMSS and MS complex extract. Noisy Terrain dataset  [67]  showing the PLMSS and MS complex next to each other. Both show critical points (blue = Minima, white = Saddles, red = Maxima), separating geometries in white, and the surface colored by MS complex ids. The border region of the MS complex is not fully segmented as a vanilla implementation of the expansion-based discrete gradient computation algorithm  [23]  may miss maxima on the boundary, whereas the boundary of the PLMSS is fully segmented. (c) visually compares the region-separating geometry of the PLMSS (blue) and the MS complex (red).
The MS complex produces geometries with a characteristic step-function shape (red), whereas the PLMSS produces separating geometries with a linear-slope shape (blue). the same underlying geometry at heart if no saddle-saddle 2-cells are present in the dataset. To allow an easier comparison of the separating geometries, all geometries were colored by the underlying segmentation (ascending in red and descending in blue) and smoothed. Most of the separating geometry coincides with at most 1 tetrahedron space in between both representations. The largest difference can be seen in the two narrow red geometries on the middle right of the images, as their distance is smaller when using the PLMSS. The difference between both representations themselves is a result of the dual graph definition of MS complex, compared to the per-vertex definition of the PLMSS.
Viscous Fingering The Viscous Fingering dataset  [67]  represents the result of finite pointset method simulations that simulate the mixing of salt solutions inside water. Regions of high salt concentration form structures called viscous fingers. The analysis of such structures usually involves Reeb graphs or iso-surfaces to identify single fingers in the dataset  [69]. The MS complex suffers from additional saddle-saddle 2-cells in such scenarios that stem from discrete Morse theory, complicating effective analysis. Filtering these saddle-saddle 2-cells out of the set of 2-cells is usually expensive as further postprocessing is required to identify and simplify the saddles responsible for such 2-cells. The PLMSS, on the other hand, segments the data into regions of influence of maximaminima pairs, providing a region for each partial viscous finger.
The granularity of these separating geometries can be controlled by topological simplification, allowing users to achieve the desired level of detail of the segmentation. Fig. 8  shows the Viscous Fingering dataset from the TTK data repository  [67]  with an applied persistence threshold of 0. 1. The colored isosurfaces provide the finger surfaces that correspond to regions of high salt concentration. To allow a deeper look into the dataset, it was clipped in the middle after all geometries were created. Figure  8a  shows that the PLMSS effectively separates fingers from each other, providing the area of influence of the maxima and hence, for the viscous fingers. The region separators are used to extract the area of influence of single fingers to analyze the area they are growing into with increasing salt concentration.
Fig. 9  compares the visual results of the PLMSS with the MS complex, using one timestep of a Rayleigh-Taylor instability simulation. Here, the PLMSS manages to extract the area of influence of minima and maxima in the dataset. The region-separating geometry is very structured and the boundary between regions of interest can be identified. In contrast, the MS complex introduces a lot of noise due to the remaining saddle-saddle 2-cells that clutter the resulting image. Additionally, the maxima on the boundary are missing, as a vanilla implementation of the expansion-based discrete gradient computation algorithm of Robins et al. [23]  (implemented in TTK) may miss PL maxima on the domain boundary.
PERFORMANCE In this section, the computational performance of our implementation is analyzed and compared to the MS complex implementation of TTK  [60]  and MSCEER  [9]. As hinted by the authors of MSCEER, we use the "steepest lstar" and "extractms" packages, as they supply the fastest implementation without accurate geometry. Both strong scaling studies show that the PLMSS is scaling well with core count due to the mentioned improvements. We utilize the Rayleigh-Taylor instability (Miranda) dataset  [70]  at a resolution of 512 3 and the Foot dataset  [67]  at a resolution of 256 3 for the computation speed comparisons of all three algorithms.
Algorithmic improvements In general, three main aspects of the PLMSS result in a strongly reduced computation time as compared to the MS complex. First, the segmentation of the domain is improved by path compression, which is much faster than computing   [70]  dataset. The image shows extrema as large orange spheres, additionally providing saddles as green small spheres in the MS complex, as saddle-saddle separatrices are the actual reason for the cluttered MS complex visualization. Even though filtering out saddle-saddle separatrices is possible, the computational overhead will favor the PLMSS in situations where saddle-saddle separatrices hide important features.
MSCEER PLMSS TTK Fig. 10. Rayleigh-Taylor instability dataset  [70]  performance of all three algorithms at a resolution of 512 3. The left graph shows the runtime sum of the DGF, ascending and descending segmentation, and indexing as a log-log plot regarding the number of cores used for the experiment. In the middle, the speedup factor, i. e. the runtime of 1 thread divided by the runtime of x threads, is also shown as a log-log plot regarding core counts. On the right, the parallel efficiency, i. e. the speedup factor divided by the number of cores, is represented in a semi-log plot.
MSCEER PLMSS TTK Fig. 11. Foot dataset  [67]  performance of all three algorithms at a resolution of 256 3. The left graph shows the runtime sum of the DGF, ascending and descending segmentation, and indexing as a log-log plot regarding the number of cores used for the experiment. In the middle, the speedup factor, i. e. the runtime of 1 thread divided by the runtime of x threads, is also shown as a log-log plot of core counts. On the right, the parallel efficiency, i. e. the speedup factor divided by the number of cores, is represented in a semi-log plot. putation, "Asc/Desc" refers to the ascending and descending segmentation, and "MS" refers to the MS segmentation. Please note that the MSCEER algorithm does not compute an MS segmentation in the provided implementation. Even in a single-threaded environment, the performance gains of retrieving the ascending and descending segmentations already show strong improvements in the computation time of the PLMSS compared to the MS complex implementations.
Tab. 2 shows the timings of those steps in the 4th and 5th row, where "Index" refers to the computation of simplex indices that will spawn triangles, and "Geometry" represents writing the triangles to memory. Please note that the MSCEER algorithm does not compute the geometry itself in the provided implementation, but only gathers the indices of relevant simplices. A comparison of the single thread timings with the Miranda dataset shows that the indexing is almost four times faster compared to TTK and three times faster than MSCEER. These speedups come from the excessive use of lookup tables and a per tetrahedra execution that does not require any tracing of paths. With the additional memory counting in the indexing step and the lower number of triangles created, the geometry-creating part strongly improved regarding computation times.
Strong Scaling Setup Both strong scaling studies were carried out on a dual Intel XEON SP 6126 node with 24 CPU cores and 384GB of RAM. For each algorithm, various timings were created, starting with the computation of the discrete gradient field, ascending and descending segmentation, MS segmentation, indexing of tetrahedra or cubes that generate region-separating geometries, and writing the region-separating geometries to memory. The results for both studies are shown in Tab. 2, where the last row shows the total time to get an ascending and descending segmentation and mark all top-level cells that generate region-separating geometries. To mimic the layout of the 2-cells of the MS complex, the region separators of the PLMSS were computed for those results. For each combination of the dataset, the number of threads, and the algorithm, the experiment was executed 10 times.
Strong Scaling: Rayleigh-Taylor Instability Utilizing the Rayleigh-Taylor instability dataset  [70] , a strong scaling analysis was carried out for a 512 3 subset of the data, simplified with a persistence threshold of 0. 1. Computation times, speedup factor (i. e. the time a single thread takes divided by the time the current number of threads take), and parallel efficiency (i. e. speedup factor divided by the number of threads) are plotted against the number of cores, shown in Fig. 10. The total execution time in the last row of Tab. 2 shows that the PLMSS is more than an order of magnitude faster than TTK and 5 to 7 times faster than MSCEER. As the PLMSS still has to be executed on roughly three times the cells, this is still an improvement of an order of magnitude regarding the time per cell.