dataesr/scientific-paragraphs-categorization huggingface dataset:
It is also interesting to note that, in both views, it is difficult to see all information for realistic datasets. In the 3D view we thus need to rely on techniques such as explosion and peeling, while in the 2D view we need the world-in-miniature thumbnail view. Complexity of cell lineage. According to one of our participants, it is already very difficult for biologists to establish the lineage for embryos starting at a few tens of cells, especially when they want to reconstruct the hierarchy for several generations (i. e. , from the observed generation to the very beginning of the division process). Our novel support of also top-down specification made this process easier for the experts, and all our participants took advantage of both ways of establishing the lineage. From their responses it seems that the top-down process makes it easier for them to control their interactions and have more confidence in the results, in particular since they deal with incomplete information most of the time.
Limitations and Future Work Both our specific realization of LineageD and our empirical evaluation have some limitations that we will discuss next. We only focus on major issues, while minor usability issues as highlighted by our study naturally also need to be addressed. First, the actual shape of the cells depicted in the 3D views is a result of an approximative surface reconstruction from the segmentation of the original volumetric data. We only relied on the shapes on the lowest level and merged them for higher stages in the hierarchy. It would be better to actually apply any new hierarchy data to the segmentation masks and then re-extract the cell shapes at the coarser levels, which we also plan to do in the future. Second, for our machine learning support we adopted a neural network model to provide predictions for biologists to interact with.
A deep learning approach, using a network of the U-net type to segment the pixels belonging to a single surface of interest, has also recently been reported  [17]. While promising as they can provide state of the art segmentations of epithelial surfaces in difficult imaging conditions, machine learning approaches require the prior manual annotation of a sufficiently large set of surfaces to generate suitable training sets. This process can be very time consuming, often necessitating several rounds of trials and errors to obtain satisfactory results, without guarantees to be generic, i. e. , to generalize to a wide range of datasets. So far, no solution to the multiple surface extraction problem has been proposed, which is satisfactory both in terms of genericity and ease of use. However, such a tool is highly desirable for modern biology studies.
Example 2: Extracting a thin cochlear epithelium surface from a multilayer dataset. As the first model in which planar cell polarity signalling was shown to be conserved in vertebrates  [35] , the mammalian auditory organ, the cochlea, is arguably our most valuable model to study epithelial patterning and morphogenesis beyond the fly and zebrafish  [36, 37]. Cochlear morphogenesis involves complex and tightly controlled patterning processes during which the cochlear sensory epithelium extends and develops its characteristic coiled snail shape, while adopting a striking cellular mosaic organization, with graded changes of morphogenetic parameters along the cochlea  [38, 39]. These morphogenetic processes are well recapitulated in organotypic cultures, on the condition that the mesenchyme that underlies the epithelium be preserved.
Regarding the control parameters of step 2 (the assembly step), for the four examples presented except for example 1, the quality of the reconstructed surfaces is stable and high over the main part of their respective intervals of variation, deteriorating occasionally only when extreme values (≃ 1) are used for these parameters (see Figures  S2-S6 , Figure  7B  and Supplemental note 4). Example 1 poses particularly stringent constraints on the control parameters of the reconstruction due to the requirement of reconstructing the 4 surfaces of different contrast and texture present in this sample using the same set of parameters. Finally, the computation times for running Zellige on a given dataset ranged between a few seconds and a minute on a standard PC computer (see Figure  S7  and Supplementary note 5), except in a few exceptional cases corresponding to extreme values of the control parameters.
In the Drosophila specimen (Figure  3 ), the software readily extracts the 4 surfaces of interest that could be identified. Since Zellige detects putative surface pixels in the first step by combining local and global thresholds, it can deal with images where the multiple surfaces display different features, such as in the mouse cochlear embryo (Figure  3 ). With this difficult dataset, we could also confirm Zellige's robustness against very low signal-tonoise levels. The constructive approach of surface region growing used by Zellige in its second step enables it to circumvent the surface smoothness requirement, that is classically assumed by other surface extraction tools. For instance, it could reconstruct the highly irregular surface of a bronchial tissue infected by SARS-CoV-2 (Figure  5 ).
Acknowledgements. We thank  Maia Brünstein  of the  Hearing Institute Bioimaging Core Facility  - C2RT/C2RA  and  Florian Rückerl  of the Photonic BioImaging - C2RT/C2RA , for sharing their expertise on light microscopy. We thank  Romain Levayer  for sharing flies and lab space with us. We thank  Gilles Trébeau  (https://fr. linkedin. com/in/gillestrebeau-427601212)for helpful discussions regarding the  Java frontend deployment of Zellige. We thank  Lisa Chakrabarti ,  Rémy Robinot  and  Vincent Michel  for sharing data. This work was supported by  Fondation pour l'Audition  ( FPA-IDA-STARTING-GRANT );  Institut Pasteur  ( PTR#272 );  DIM ELICIT 's grant from  Région Ilede-France  ( QP-IDF-DIM-ELICIT-2019 ) ; The  French Agence Nationale de la Recherche  ( ANR-21-CE13-0038-013-01  and  LabEx  LIFESENSES  ANR-10-LABX-65 ).
Identification of orthologous genes Using the genome of A. pompejana as a reference database, we analyzed 94,006 pairwise Blastn alignments between the Northern and Southern transcriptomes of A. pompejana and 68,963 pairwise Blastn alignments between the transcriptomes of A. pompejana and A. caudata. As these putative genes contain paralogs, tandemly repeated paralogs, allelic forms of a gene in either genes with or without introns, we filtered our datasets to only keep a subset of the most likely orthologous genes. This reduces the number of pairwise alignments to 22,558 and 48,134 respectively. Determination and translation of the CDS with a minimum threshold length of 300 bp and sequence-similarity search against the Uniprot database reduced the two final datasets to 6,916 and 6,687 pairwise alignments of orthologous coding sequences on which further analyses were performed.
Early stage of speciation (A. pompejana south/north comparison) Among the 41 genes under positive selection (d N /d S >1) for which d N /d S values remained significant after the resampling test of the d N /d S difference and the FDR procedure, only 12 of them were annotated in the UniProt database. These genes are encoding proteins involved in  (1)  transcription/translation/replication regulation and biosynthesis (ribosomal protein rpl19, GTPbinding protein 1, elongation factor 1alpha, zinc finger protein GLI1) some of which being involved in a wide variety of biological functions including spermatogenesis, (2) endocytosis and immunity regulation, which may play a crucial role in the worm's epibiosis (Rab5 protein, CD209 antigen protein A), (3) neuro-transmission regulation (complexin) and the development of sensory organs (protein mab-21), (4) development of nephridies, and possibly gonoducts in alvinellids (actin-binding Rho protein), (5) mRNA methylation (pre-miRNA 5'-monophosphate methyltransferase), and (6) setae/modified hook formation that should influence reproductive/thermoregulatory behavior (chitin synthase).
Late stage of speciation (the A. pompejana/A. caudata comparison) In the same way, among the 102 orthologous genes between A. caudata and A. pompejana for which d N /d S values were greater than one, only 37 remained significant after the resampling test of the d N /d S difference and the FDR procedure but, in this case, most them were annotated (31 genes) in the UniProt database. These genes encode for proteins involved in  (1)  carbohydrate catabolism (deoxyribose-phosphate aldolase) , (  2 ) immunity (innate and adaptive), viral responses, apoptosis (fibrinogen-like protein, lysosomal protective protein, acetylcholine receptor), (3) steroid/lipid metabolism and membrane composition (transmembrane protein, 3oxo-5-alpha-steroid 4-dehydrogenase, methylsterol monooxygenase, protein DD3-3-like), and tegument structure (actin, collagen, epidermal growth factor named fibropellin, GTP-binding protein, protein-methionine sulfoxide oxidase MICAL1), (4) sexual differentiation, spermatogenesis/oogenesis, sperm adhesion (zonadhesin, innexin), (  5 ) DNA damage repairs and methylation (ATP-dependent RNA helicase DDX51 and DDX58, poly-(ADP-ribose) polymerase, forkhead box G1 protein WD repeat-containing protein), oxidative stress response and protein glycosylation (beta-1.
3) Estimation of divergence and d N /d S for pairs of orthologous genes We designed a customized pipeline (described below) in order to calculate divergence and estimate the selective pressures along the coding regions of assembled transcriptomes of closely related species previously positioned on our reference genome, using a 24-columns MegaBLAST outputs. The code to perform analyses for this study is available as a git-based version control repository on GitHub (https://github. com/CamilleTB/dNdS_cartography_Alvinella_speciation).
e. exonic regions). Paired orthologous sequences obtained in the two last categories (exon and uniq) were then used to estimate divergence and associated d N /d S ratios in the pipeline. • Search for coding DNA sequences (CDS) in pairwise alignments Nucleic acid sequences were translated in the six reading frames to select for the longest CDS between two subsequent stop codons. Coding sequences containing gaps, undetermined nucleic acids (N) or alternative frames without stop were removed. To avoid false positives and reduce the risk of calculating erroneous d N /d S values from non-coding or incorrectly framed sequences, we performed a sequence-similarity search against the UniProt database using BlastP from NCBI BLAST+ 2. 2. 30 (set expectation value cutoff = 10 -10 , maximum hits to show = 1).
Availability of data and materials The AP genome: Two replicate runs of Illumina were performed onto the same individual (2 sets of R1 and R2 compressed files of 33 Go: cf. SRA project under experiment accession numbers ERX5990023-25; ERX5990051 and, run accession number: ERR6358489-91; ERR6358517) and, used in combination to generate the first genome draft (V1). The reads of transcriptomes are available from the Sequence Read Archive (SRA) database under accession numbers SRP076529 (Bioproject number: PRJNA325100) and SPX055399-402 (Bioproject number: PRJNA80027)), and from the EST database under accession numbers FP489021 to FP539727 and FP539730 to FP565142.
Convolutional neural networks (CNN) have shown great potentials and have been proven to be an effective tool for some image-based deep learning tasks in the field of computational electromagnetism (CEM). In this work, an energy-based physics-informed neural network (EPINN) is proposed for low-frequency electromagnetic computation. Two different physics-informed loss functions are designed. To help the network focus on the region of interest instead of computing the whole domain on average, the magnetic energy norm error loss function is proposed. Besides, the methodology of energy minimization is integrated into the CNN by introducing the magnetic energy error loss function. It is observed that the introduction of the physics-informed loss functions improved the accuracy of the network with the same architecture and database.
Although DL has achieved many satisfactory results, the requirement for big data has greatly limited its further application in electrical engineering, where the data generally comes from complex experiments or expensive computations. It does not make too much sense for the DL application if its performance heavily relies on a large number of training samples because it costs lots of experiments or computation just to prepare these datasets, let alone the training and tuning of the DL network itself. To solve this problem, in our previous research, we have investigated the feasibility and efficiency of CNN U-net to the magnetothermal coupling problem  [15]. It is observed that due to its excellent feature extraction capability, the CNN U-net can be effectively trained with a small dataset.
Another work employs the domain decomposition in the PINN framework and puts forward a conservative PINN to provide more flexibility in the multiscale problem  [32, 33]. Besides, PINN is employed to solve the radiative transfer equations and the rigorous upper bounds on the generalization error of PINN approximating solutions for PDE have been presented in  [34, 35]. Furthermore, PINNs have achieved some satisficing performance when facing heat transfer equations, Navier-Stokes equations in fluid mechanics, high speed fluid flow and solid mechanics  [36, 37]. Although PINN has shown good potential in various fields, it still has certain limitations. One of the main limitations of PINN is the dependence on a large amount of database, especially for some over-parameterized PINN models  [38, 39] , a significant amount of data is often necessary to reinforce such physical knowledge and generate predictions that satisfy certain physical laws such as symmetries and conservation rules.
In this case, an immediate difficulty relates to the cost of data acquisition, which for many applications in the physical and engineering sciences could be prohibitively large, as observational data may be generated via expensive experiments or large-scale computational models. Therefore, it is crucial to enhance the convergence and accuracy of the network without increasing a large number of samples. On the other side, while many good application results have been obtained from PINN applications; however, a lot of work stops at interpolation, and only a few research studies have investigated the extrapolation capability of PINN  [31]. Based on a relatively small database, we applied an energybased physics-informed neural network (EPINN) to solve the CEM problem with a wide range of geometrical parameters.
Among them, the MENE can be seen as a specific MSE that is weighted according to the material permeability, which can help the EPINN to concentrate on the learning objective which has higher energy density, that is, the quantity of interest (QOI). As for the MEE, it is reinforced with the energy minimization principle in the DL loss function, considering that the principle of FEM computation is energy minimization, it is a reasonable strategy to evaluate the magnetic field distribution results via magnetic field energy instead of pure pixel error. 2. We discuss the implementation of various types of loss functions. To investigate the effect of introducing the two physics-informed loss functions, this paper compares the EPINN with the traditional CNN using MAE and MSE. While keeping the network architecture, configurations, and the database unchanged, these four loss functions are respectively adopted to train the network.
The numerical experiments demonstrate that when compared to other loss functions, the physics-informed loss function developed for a specific task can achieve better accuracy on that task. With the introduction of the physics-informed loss functions, the neural network is more sensitive to the structural changes in the windings because the magnetic energy is mainly concentrated in the windings and the nearby air. This can help the DL network to better concentrate on the QOI instead of taking the same weight over the whole image only from a pixel-wise point of view. 3. We conduct a sensitivity analysis of EPINN to explore the effect of hyperparameters on the model performance. The physics-informed loss function is a double-edged sword. While it improves the accuracy of the converged network under the same database, it is also observed that it increases the sensitivity of the DL network to the input information and some corresponding network hyperparameters, especially, those that control the generation of Gaussian distribution from the labelled geometric information.
| The EPINN With ground truth data obtained from FEM being represented as magnetic flux density distributions, EPINN, a CNN with physics embedded into the loss function is utilized to extract hidden features and is trained in a supervised manner. Adopting the aforementioned three geometric variables as labels, the relationship between the magnetic field distribution and corresponding geometric parameters is established via DL. Using part of the database to train the network, once the network converges, the effectively trained EPINN can be used to predict the magnetic field distribution with other geometric parameters without further FEM computations. The schematic diagram of the presented EPINN is shown in Figure  4. First and foremost, we establish the physical model according to the research objectives, as shown in Figure  4b , after setting the material parameters, boundary conditions and initial conditions, etc.
, we use the geometric parameters as variables and perform FEM computation to obtain the corresponding magnetic field distribution. These FEM computation results are displayed via 256 £ 256 £ 3 red-green-blue (RGB) images and employed as the database, as shown in Figure  4a. Samples are labelled according to the corresponding geometric parameters x 1 , x 2 , and y. Let us denote z1 , z2 , z3 the vector composed by the normalization data for different value issues from the labels x 1 , x 2 , and y, the Gaussian distributions are generated from these geometric variables and used as input for the DL network, as shown in Figure  4d. The input consists of three layers of mutually independent Gaussian distributions, and each layer is controlled by parts of the geometric variables, denoted by f i (1 ≤ i ≤ 3), where f i z j ; z k À � ¼ exp - z j -μ zj � � 2 þ z k -μ zk � � 2 2σ 2 0 B @ 1 C A ð4Þ with 1 ≤ j < k ≤ 3, where j ≠ i and k ≠ i, μ zi is the average value of all the components for zi ð1 ≤ i ≤ 3Þ.
| The training and post-test procedure The training and post-test procedure of the proposed approach are illustrated in Figure  5. One thousand database samples are generated and indexed as #1 to #1000 by incremental iteration of the three geometric parameters one by one in the order x 1 , x 2 , y. All samples are labelled according to their geometric parameters and divided into 10 groups according to the single digit of the index number. The 10 groups are indexed as #0 to #9, with 100 samples in each group. The 10 groups of samples are divided into three categories: training samples, validation samples and test samples to participate in the network training and post-test.
| The loss evaluator DL networks are trained to solve supervised learning tasks by minimizing the residual of the evaluation losses. In the process of training a feedforward neural network, the iteration is generally based on the gradient descent and backpropagation algorithm: the backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, iterating backward from the last layer and update the weights along with the inverse of the corresponding error gradient to minimize the loss. Therefore, choosing the proper loss function is crucial for DL networks to have a good performance on a certain task. MAE and MSE are two of the most common evaluators employed to measure accuracy for computer vision tasks. The MAE represents the average of the absolute difference between the actual and predicted values in the dataset.
For the magnetic flux distribution prediction, the target is the magnetic flux density: MAE ¼ 1 N X N i¼1 jjB dl ðiÞj -jB fem ðiÞjj ð5Þ where N represents the number of pixels in an image, which is 256 � 256 = 65,536 in our case, B dl stands for the DL prediction result of the magnetic flux density distribution, B fem is the magnetic flux density distribution obtained from FEM. It measures the average of the residuals in the dataset. As a contrast, the MSE represents the average of the squared difference between the original and predicted values in the dataset: F I G U R E MSE ¼ 1 N X N i¼1 jjB dl ðiÞj -jB fem ðiÞjj 2 ð6Þ It measures the variance of the residuals. These two loss functions have their own advantages and disadvantages: MSE penalizes the large prediction errors compare to MAE, but MAE is more robust to data with outliers.
Take the considered magnetostatic problem as an example, the ground truths we obtain from FEM are computed following the magnetic energy minimization principle. For a magnetostatic system, the magnetic field energy E stored in a magnetic field, the energy per unit in a region of permeability μ i containing the magnetic field B is: E ¼ X N i¼1 1 2 jBðiÞj 2 μ i ð7Þ where μ i denotes the magnetic permeability in the ith pixel. Therefore, naturally, when it comes to the magnetic problem, researchers can be more interested in magnetic energy than magnetic flux density distribution. In this situation, utilizing loss functions that are only considered from the perspective of pixels, we can only measure the difference in magnetic flux density distribution between the predicted results and the dataset, but ignore the meaning of the FEM based on the principle of minimum magnetic energy.
To enforce this point, inspired by our previous work about error estimates in the low-frequency problem  [40, 41] , we try to introduce the energy sense into the EPINN network for the prediction of the magnetic field distributions by modifying the loss function. In addition, when modelling a physical system, instead of the whole computation domain, researchers are tended to be more interested in a particular region based on some prior information or experience. For instance, when analysing the transformer magnetic leakage problem and the corresponding stray losses, we are most concerned with the leakage magnetic flux in the windings and nearby air as a QOI, which dominantly affects the eddy current losses, and less interested in the flux distribution inside the core. In this case, using MAE and MSE, we can only measure the difference in magnetic flux density distribution between the predicted results and the dataset on average, and cannot pay more attention to the area of interest.
The MENE can help the DL network to concentrate more on the region of interest by introducing some prior physical information. However, the evaluation of loss is still from the perspective of pixels. As we mentioned before, when it comes to magnetic field analysis, since the magnetic flux density computed by FEM is based on the minimization of magnetic energy, the value within a specific pixel alone does not make too much sense to evaluate the accuracy of the entire FEM magnetic field computation. Instead, the difference between the ground truth and the results obtained by DL should be interpreted in a global energy sense. In this situation, utilizing loss functions that are only considered from the perspective of pixels, we can only measure the difference in magnetic flux density distribution between the predicted results and the dataset, but ignore the meaning of the FEM based on the principle of minimum magnetic energy.