dataesr/scientific-paragraphs-categorization huggingface dataset:
(3) Combining either the list of fragment ions or the list of covered amino acids from multiple spectra on a given peptide within one or across multiple Mascot results files, and determining the resulting peptide CSC. (4) Compiling protein-level CSC data from either single peptide spectra with highest score or CSC, or from multiple spectra combined at the covered amino acid or fragment ion level. Any amino acid covered in any of the peptides is considered covered at the protein level. Full transparency is provided into the specific fragments, spectra, and result files, thereby supporting the assignment of each single amino acid in the protein (sample outputs are provided in the SI). We employed this program to collect CSC vs collision energy shift curves from the measurement results. These curves were normalized in Microsoft Excel and then were subject to agglomerative cluster analysis,  35  using the XLSTAT add-on.
36 uclidean distance measure was employed between curves, and Ward's method  35  was used to choose pairs of clusters to merge. Zero CSC was assumed for all the collision energy shifts where a peptide was not identified. Our Serac program was also employed to compute protein level CSC from all information available in a single run, or in 2, 3, or all 21 runs at different energies, combining it either at the amino acid or at the fragment ion level. All possible combinations of 2 or 3 energies were tested. We report CSC values as percentages for each entire mAb, i. e. , as a weighted average over the two protein chains, throughout the paper.
■ RESULTS AND DISCUSSION Determination of Confirmed Sequence Coverage: Reference Values from a Basic Approach. The main objective of the present research was to establish a workflow for efficient validation of mAb sequences. The efficiency was characterized by the confirmed sequence coverage (CSC), using its rigorous definition, acceptable in the pharmaceutical industry, as discussed in the beginning of this paper. Recognizing that the most widely employed proteomics evaluation programs do not offer a functionality to report CSC, as a first step, we created a software tool to determine CSC in a transparent manner using result files of the Mascot search engine. We base our CSC analysis only on the fragment ions considered for scoring by Mascot, i. e. , on only those that can be clearly distinguished from experimental noise.
e. , still using a single nano-LC-MS/MS run. The gain so far only stems from selecting better experimental parameters. Maximum Achievable Confirmed Sequence Coverage from Multiple Nano-LC-MS/MS Runs. To take advantage of large measured datasets, we first set out to implement data processing enhancements into our Serac program. Following an intermediate step of picking the spectrum with maximum CSC (instead of maximum score) for each peptide ion, we focused on the combined use of multiple MS/MS spectra of the same peptide (see Figure  4 ). The combination can happen at the level of amino acids (Figure  4A ), or, more efficiently, even at the level of fragment ions (Figure  4B ). As illustrated in Figure  3 , these enhancements could increase the CSC of the investigated mAbs by 13. 1% and 11.
6% in the case of rituximab and trastuzumab, even using the data from only a single run at the optimized energy, exploiting that multiple MS/MS spectra of the same ions are usually taken. As a final step of the establishment of our sequence validation protocol, we investigated the potential CSC increase using multiple LC-MS/MS runs. Serac was used to determine the CSC values at both the amino acid and fragment ion level combination across all the spectra taken during the LC-MS/ MS runs. Throughout this section of the manuscript, we report results only from the fragment ion level combination, which are consistently a few percent higher than the amino acid level combination results; the latter are shown in detail in the SI. To establish a benchmark, we first determined the CSC values by combining all the recorded spectra from the 21 LC-MS/MS runs taken at different collision energies.
■ CONCLUSIONS Validation of the amino acid sequences of original and biosimilar protein drugs is a crucial, and from a regulatory perspective, mandatory step in their characterization, which requires extensive experimental and data evaluation efforts. Our aim in this work was to demonstrate on the example of mAbs how collision energy optimization and automatized data processing can yield streamlined bottom-up workflows for the sequence validation process. The key results of the work can be summarized as follows: (1) To reduce the manual annotation efforts and to allow all information in the measured spectra to be utilized in the validation while keeping full transparency, we created software called Serac that consumes results of the Mascot database search engine and identifies the covered amino acids in the sequence.
a b s t r a c t The game of chess is undoubtedly one of the most popular two-player strategy board games in history, enjoyed by casual players and competing celebrated professionals alike, and serves as prototype research subject in a vast variety of fields. Although a plethora of parsers on a large number of different platforms is readily available for processing records of chess games provided in online databases, Mathematica remains, somewhat surprisingly, exempt. ChessY attempts to fill this gap, by providing a simple set of tools for handling Portable Game Notation (PGN) chess records and their translation into positional chess graphs, thus opening the door for a systematic analysis of chess games within the powerful confines of graph theory using Mathematica.
Motivation and significance With its 64 squares, 32 pieces of 6 types, and discrete moves of pieces between squares governed by a strictly limited, arguably simple set of rules, chess can undoubtedly be viewed as a classical example of a network in graph theory  [1]. Although many chessrelated problems and their solutions, such as the Knight's Tour Puzzle or Queens Domination Problem, find representations within a graph-theoretical framework (e. g. , see  [2, 3] ), a systematic analysis of available datasets of chess games recorded over many decades within a graph-theoretical context remains, however, scarce and mostly restricted to visualizing various chess strategies and search algorithms (e. g. , see  [4]  and references therein). One reason hindering a thorough graph-theoretical analysis of chess games is certainly the inherent difficulty associated with parsing online PGN (Portable Game Notation) databases.
PGN E-mail address: rudolph@unic. cnrs-gif. fr. URL: http://mrudolphlilith. github. io. records utilize the Standard Algebraic Notation (SAN) standardized by FIDE (Fédération Internationale des Échecs; [5]) to encode positional changes during a chess game by specifying the type and target square of the piece being moved. However, such a compact representation is subject to potential ambiguities, for instance, multiple pieces can reach a given target square, which require sophisticated and often computationally demanding parsing algorithms in order to be fully resolved. Although a whole plethora of both open-source and proprietary parsers and chess game engines in a variety of programming languages is readily available (see  [6]  for a recent and comprehensive review), such engines focus exclusively on assessing game positions using evaluation functions not unlike that originally proposed by Shannon  [7] , and selecting advantageous moves through searches in vast databases of available chess games.
Indeed, most software packages available for the analysis of real-world networks are only equipped for handling simple graphs, with an inclusion of chess graphs typically requiring the manual alteration of core data and procedural structures. With data structures and functions tailored to handle positional chess graphs, ChessY provides a basic set of tools to parse, validate and visualize available PGN chess game records, and to construct, manipulate and analyze chess graphs. ChessY, thus, opens the door for a systematic and thorough study of chess games using the computer algebra environment Mathematica [9] as a powerful explorative engine. Unfortunately however, despite the historical role of chess as a most prominent board game, to the best of the Author's knowledge, no package or toolbox is yet available in Mathematica for both the parsing of available PGN records and the construction of chess graphs from such records, thus rendering ChessY the first thorough attempt in opening the door for a more systematic analysis of the game of chess using the graphtheoretical and algebraic tools made available on this powerful platform.
Software architecture ChessY is built around three principal types of data objects, the chess position P, nodes N , and edges E. While the position object contains a list of pieces, their location on the chessboard, and supplementary information characterizing a given position, nodes and edges are 1-dimensional and 2-dimensional lists, respectively, uniquely describing the positional chess graph associated with a given position: P = {info, {{i 1 , p 1 }, {i 2 , p 2 },. }}, N = {s 1 , s 2 ,. }, E = {{i source 1 , i target 1 , s i 1 }, {i source 2 , i target 2 , s i 2 },. }, were i denotes a unique square, or node, identifier ranging from 1 to 64, starting in the lower left-hand corner with the a1 square on the chessboard and ending in the upper right-hand corner (h8 square), p is a piece identifier containing color (w and b for white and black pieces, respectively) and type (K , Q , R, B, N, and P for king, queen, rook, bishop, knight and pawn, respectively), and s is the node state, e.
g. s = -1 or s = 1 for squares occupied by white or black pieces, respectively, or s = 0 for unoccupied squares. Finally, info denotes a simple association list with information about the target node of a possible en passant move, the possibility of castling moves, as well as an eventually issued check or checkmate. This information is used by ChessY to process records of complete chess games, and to construct valid chess graphs associated with each position during a game. The data objects presented above are returned by functions for the generation of chess positions and chess graphs, as well as ChessY 's parser for PGN chess game records, and are used as arguments in functions for the visualization of chess positions, graphs and complete games, as well as the analysis of positional chess graphs.
Software functionalities ChessY 's primary focus is on providing tools for the generation of positional chess graphs and their associated data objects for visualization and subsequent analysis from PGN chess game records. The construction of positional chess graphs from these records starts with the conversion of the file-rank square identification fr commonly utilized in chess records into a numerical node identi- fier i ∈ [1, 64] using the function i(f , r) = 8 * (r -1) + (f -1) + 1, were the board's files are successively mapped to numbers, i. e. a → 1,. , h → 8. Each node i can have one of three states s i , depending on whether the corresponding square is occupied by a white or black piece (s i = -1 and s i = 1, respectively), or empty (s i = 0). Each occupied node i serves then as source for the graph's edges to target nodes j, depending on the legal moves a piece occupying the source square can potentially perform, thus populating an adjacency matrix with elements a ij = s i.
The generated positional chess graphs are fully described by their nodes N and associated edges E, and, together with the positions P obtained manually or by parsing valid PGN game records, are available for visualization and analysis using tools provided in ChessY, or the explorative potential of the embedding platform Mathematica. Specifically, both the list of edges E as well as the adjacency matrix a ij returned by ChessY 's respective getEdgesFromPosition and getAdjacencyMatrix functions (see Section 2. 1) provide data objects which serve as arguments for the construction of graph objects utilizing Mathematica's native graph construction and representation library.
Performance evaluation In order to assess the performance of ChessY, a PGN database containing 2000 records of chess games was analyzed on a 2013 model Mac Pro (3. 5 GHz 6-Core Intel Xeon E5, 64 GB of 1866 MHz DDR3 ECC) running on OSX 10. 11 (El Capitan). The average CPU time for parsing a single PGN chess game record and generating the associated game positions (function getPositionFromGamePGN) was 1. 95 s with a standard deviation (SD) of 0. 77 s, the CPU time for constructing positional chess graphs for each position during an average game (functions getNodesFromPosition and get-EdgesFromPosition) was 6. 03 s (SD of 2. 34 s). The comparably large error is these evaluations is a direct consequence of the inherent variability of chess games, with an average number of positions of 74 (SD of 40) in the investigated sample dataset.
Impact Although the game of chess with its finite and discrete spatiotemporal makeup can be viewed as a prototypical example of a network in graph theory, systematic studies of the vast number of available chess game records within the powerful confines of graph theory remains, to date, scarce, mainly due to the inherent difficulties associated with the construction of chess graphs from PGN game records, and the peculiar nature of positional chess graphs. The ChessY toolbox attempts to bridge this gap, by providing a basic set of data objects and functions for both the efficient parsing of PGN records and the construction of positional chess graphs associated with these records using Mathematica. The computer algebra environment Mathematica was chosen as its explorative, sandbox-like nature allows for an easy extension of the tools provided in ChessY, as well as an almost limitless potential for further examination of chess graphs by employing its numerical and algebraic capabilities.
To our best of knowledge, ChessY is the first serious attempt to provide a coherent set of functions and data structures for the construction, visualization and analysis of chess graphs in Mathematica, and was already successfully utilized in the analysis of chess games between Grandmasters and computer players aimed at identifying and characterizing strategical approaches used by humans and computer players  [10]. The goal of ChessY is to provide an easy-to-use and expandable toolbox for researchers studying chess games in a graphtheoretical context, and, thus, to facilitate the understanding of the dynamical complexity inherently associated with this intriguing boardgame by making chess game records accessible to the mathematical field of network analysis. With the choice of Mathematica as embedding platform, ChessY will hopefully stimulate the consideration of new approaches for studying chess games beyond a mere numerical analysis, towards more formal algebraic and operator graph-theoretical avenues.
The response of the mutual impedance probe RPC-MIP on board Rosetta orbiter electrostatically modeled considering an unmagnetized and collisionless plasma with two Maxwellian electron populations. A vacuum sheath surrounding the probe was considered in our model in order to take the ion sheath into account that is located around the probe, which is immersed in the cometary plasma. For the first time, the simulated results are consistent with the data collected around comet 67P/Churyumov-Gerasimenko (67P), but strong discrepancies were identified with the previous simulations that neglected the plasma sheath around the probe. We studied the influence of the sheath thickness and of the electron populations. This work helps to better understand the initially unexpected responses of the mutual impedance probe that were acquired during the Rosetta mission.
The probe was modeled as a mesh immersed in a Maxwellian plasma, and the Debye length spanned from several millimeters up to a few centimeters. These conditions correspond to what was expected by way of a surrounding around comet 46P/Wirtanen, the original destination of the European Space Agency's Rosetta spacecraft. However, a large discrepancy was observed between simulations and experimental data after the first measurements had been acquired around comet 67P/Churuymov-Gerasimenko (hereafter 67P). In particular, the Debye length was observed to be much larger, from a few tens of centimeters to a few meters. Thus, the first modification of the simulation was to extend the Debye length toward higher values. Then, a second Maxwellian electron population was introduced in the plasma because suprathermal electrons have been commonly observed in space plasmas, superposed on a Maxwellian-like core  (Pilipp et al.
Discussion Considering a vacuum sheath around the mutual impedance probe RPC-MIP exposed to the cometary plasma enabled us to make the simulations consistent with the experimental data that were collected during the Rosetta mission. This highlights that the sheath surrounding the mutual impedance probe needs to be considered for electrostatic modeling. As observed during the Rosetta mission, the plasma signature on the simulated response of the probe is much more marked in phase mode than in the other operating modes (see Fig. 9 ). The singular behavior of the response in singleE1 mode compared to the behavior of the response in the other operating modes shown in Fig. 9  is also observed experimentally. This mode was suspected to operate incorrectly before this work because of this singularity.
Despite a strong increase in random access memory needs and computation time, such a modeling would require to know the spatial distribution of the evdf in the sheath. This is expected to be reachable with a future release of the modeling software SPIS. However, if the evdf in the sheath does not correspond to a Maxwellian or a to double-Maxwellian evdf, which is likely to append, the function φ/φ 0 will have to be determined as it is an input of the simulation. The evdf inside the sheath is expected to be a shifted and/or truncated (double-) Maxwellian because of the local electric field. If confirmed, the incomplete plasma dispersion function  (Baalrud 2013)  will arise when the function φ/φ 0 in the sheath is computed. In addition, it is possible that the double-Maxwellian evdf is sometimes a crude approximation of the real plasma evdf at the comet.
However, indexed convolution and pooling are very general solutions, easily applicable to other domains with irregular grids. At first, a reminder of how convolution and pooling work and are usually implemented is done. Then we present our custom indexed kernels for convolution and pooling. This solution is then applied to standard datasets, namely CIFAR-10 and AID to validate the approach and test performances. Finally, we discuss the results obtained as well as potential applications to real scientific use cases.
This section proposes a method to efficiently handle hexagonal data without any preprocessing as a demonstration of the use of indexed convolutions. We first describe how to build the index matrix for hexagonal lattice images needed by the indexed convolution. For easy comparison, we want to validate our methods on datasets with well-known use cases (e. g. a classification task) and performances. To our knowledge, there is no reference hexagonal image dataset for deep learning. So, following Hexa-Conv paper  (Hoogeboom et al. , 2018)  we constructed two datasets with hexagonal images based on wellestablished square pixel image datasets dedicated to classification tasks: CIFAR-10 and AID. This enables our method to be compared with classical square pixels processing in a standardized way.
Experiment on CIFAR-10 The indexed convolution method, in the special case of hexagonal grid images, has been validated on the CIFAR-10 dataset. For this experiment and the one on the AID dataset (see Sec. 5. 3), we compare our results with the two baseline networks of HexaConv paper  (Hoogeboom et al. , 2018). These networks do not include group convolutions and are trained respectively on square and hexagonal grid image versions of CIFAR-10. The network trained on the hexagonal grid CIFAR-10 consists of masked convolutions. To allow a fair comparison, we use the same experimental conditions, except for the Deep Learning framework and the square to hexagonal grid image transformation of the datasets. The CIFAR-10 dataset is composed of 60000 tiny color images of size 32x32 with square pixels.
Each image is associated with the class of its foreground object. This is one of the reference databases for image classification tasks in the machine learning community. By converting this square pixel database into its hexagonal pixel counterpart, this enables to compare hexagonal and square pixel processing in different case studies for image classification. This way, the same network with: • standard convolutions (square kernels), • indexed convolutions (square kernels), • indexed convolutions (hexagonal kernels), has been trained and tested, respectively on the dataset for the square kernels and its hexagonal version for the hexagonal kernels. For reproducibility, the experiment has been repeated 10 times with different weights initialization, but using the same random seeds (i. e. same weights initialization values) for all three implementations of the network.
Building a Hexagonal CIFAR-10 Dataset The first step is to transform the dataset in a hexagonal one. Compared to a rectangular grid, an hexagonal grid has one line out of two shifted of half a pixel (see figure  5 ). Square pixels (orange grid) cannot be rearranged directly in a hexagonal grid (blue grid). For these shifted lines, pixels have to be interpolated from the integer position pixels of the rectangular grid. The interpolation chosen here is the average of the two consecutive horizontal pixels. A fancier method could have been to take into account all the six square pixels contributing to the hexagonal one, in proportion to their involved surface. In that case, the both pixels retained for our interpolation method would cover 90. 4% of the surface of the interpolated hexagonal pixel.
Results As shown in table 2, all three networks with hexagonal indexed convolutions, square indexed convolutions and square standard convolutions exhibit similar performances on the CIFAR-10 dataset. The dif-ference between the hexagonal kernel and the square kernel with standard convolution on the one hand and between both square kernel is not significant, according to the Student T test. For the same number of parameters, the hexagonal kernel model gives slightly better accuracy than the square kernel one in the context of indexed convolution, even if the images have been roughly interpolated for hexagonal image processing. However, to satisfy this equivalence in the number of parameters, since hexagonal convolutions involve fewer neighbors than the squared counterpart, some more neurons are added all along the network architecture.
Experiment on AID Similar to the experiment on CIFAR-10, the indexed convolution has been validated on Aerial Images Dataset (AID)  (Xia et al. , 2016). The AID dataset consists of 10000 RGB images of size 600x600 within 30 classes of aerial scene type. Similar to section 5. 2, the same network with standard convolutions (square kernels) and then with indexed convolutions (square kernels and hexagonal kernels) have been trained and tested, respectively on the dataset for the square kernels and its hexagonal version for the hexagonal kernels. The experiment has also been repeated ten times, but with the same network initialization and different random split between training set and validating set, following  Hoogeboom et al. (2018).