dataesr/scientific-paragraphs-categorization huggingface dataset:
Training and Evaluation Data augmentation. The postulates of analogical proportions described in Section 2 enable the generation multiple analogies from each quadruple in our analogy dataset. We refer to this process as data augmentation. It extends the amount of data available, but also makes the models learn how to fit the formal postulates of analogy. We follow a similar intuition for two losses based on the L 2 distance or Mean Squared Error (MSE): M SE(e D , e D ) = 1 n i∈[1,n] (e D,i -e D,i ) 2 (3) A second option is to normalize with regards to some random embedding e z : L norm. random = 1 + M SE(e D , e D ) 1 + M SE(e z , e D ) (5) As the model is trained with batches of randomly selected samples, we associate each prediction with an unrelated embedding e z by permuting e D along the batch dimension.
Data For our experiments, we used the analogies from 11 languages available in the Siganalogies dataset  [22] : Spanish, German, Finnish, Russian, Turkish, Georgian, Navajo, Arabic (Romanized), Hungarian, and Maltese extracted from Sigmor-phon2016  [6] , and Japanese from the Japanese Bigger Analogy Test Set  [12]. It is noteworthy that we use the data of the original Sigmorphon2016 dataset, which produces a different set of analogies than the one used by  [11, 25]. In particular, Siganalogies contains analogies that are hard to solve for a non-data-driven approach (e. g. , "be : was :: go : went"). For training and evaluation we use the original split of the Sigmorphon2016 [6] dataset, from which we extract the analogies independently. For the Japanese Bigger Analogy Test Set  [12]  however, no such split is available and so we split 7  the extracted analogies into 70% for the training, 5% for the development, and 25% for the test set.
For each quadruple A : B :: C : D, we generate ρ = 100 potential solutions for A : B :: C : x and select the most frequent one. Kolmo  [25]. The generation model proposed by Murena et al. considers some transformation f such that B = f (A) and f (C) is computable. The simplest transformation f is usually the one human use to solve analogies  [25] , and is found by minimizing the Kolmogorov complexity of f. This complexity is estimated by first expressing f using a language of operations (insertion, deletion, etc. ), and computing the length of the resulting program. Unlike Alea, Kolmo is able to handle mechanisms like reduplication (repeating part of a word). Arithmetic on embeddings. 3CosAdd  [24]  and 3CosMul  [19]  are standard methods to retrieve the fourth element of an analogy within an embedding space, Table  2 : Top-1 accuracy (in %) of ANNr using L norm.
random against the baselines. We report mean ± std. over 10 random seeds for our models, and when relevant the timeout rate for the baselines. Arithmetic on ANNc emb. Symbolic baselines Timeout (%) ANNr 3CosAdd  [24]  3CosMul  [19]  Alea  [14]  Kolmo  [25]   and are still used even if their limitations are known. In Table  2 , we report results of 3CosAdd and 3CosMul applied on the embeddings trained with ANNc to measure the improvement brought by ANNr. 3CosAdd (  7 ) can be seen as the parallelogram rule (D = B -A+C) with a cosine similarity to recover the closest existing solution. As 3CosMul (  8 ) is harder to describe intuitively, we refer the reader to  [19]  for a detailed description. To avoid a 0 denominator, a ε (small) is added in  (8). Timeout on Alea and Kolmo. On a small portion of the dataset, Alea and Kolmo can take a significantly longer time to compute the results (more than 10 seconds against usually less than a second).
Distance of the Expected Result While for some languages (mainly Navajo but also Russian and Arabic) ANNr struggles to reach a high overall accuracy, further analysis of the results indicates that the expected solution can be found in the close vicinity of the prediction. Notably, some analogical equations can have multiple viable solutions (e. g. , sing : sing :: am : x for which am and are are viable). For such cases, finding a particular solution as the top candidate is less likely as other viable solutions could be preferred, which can explain part of the increase of performance. Indeed, as can be seen in Table  3 , looking at the top 3 solutions increases the accuracy of the Navajo models from 52% to 78% in average, from 73% to 89% for Arabic and from 72% to 95% for Russian. Increasing the margin to the top 10 brings the accuracy of all models to at least 98%, except for Arabic and Navajo which are at 95% and 92% respectively.
Case Analysis: Navajo and Georgian To get further insight on the behavior of the model, we perform a more detailed analysis of where the model makes mistakes for Navajo and Georgian, the languages on which ANNr performs worst and best respectively. To be able to analyze more in-depth, we consider only one of the 10 models trained in the transfer setting with L norm. random. Overall, there is no significant predominance of a particular permutation nor of a particular postulate (symmetry, central permutation, nor any usual combination of both) in the mistakes on either Navajo or Georgian. Additionally, less than 0. 3% of mistakes on Navajo involve expected cases of reflexivity (i. e. , forms like A : B :: A : B or A : A :: B : B), and no such case was observed for Georgian, indicating that reflexivity is well handled by ANNr.
Verbs correspond to 73. 79% of all mistakes in Navajo (75. 35% if we exclude cases described in the previous paragraph). Navajo is originally an oral language of the Native-American languages, and according to Eddington and Lachler  [9]  "Verb stem inflectional patterns in Navajo are arguably one of the most intractable problems in modern Athabaskan linguist studies". They also refer to a work by  Leer [15]  which states that this complexity can be attributed to "analogical innovation, which is thus quite difficult to analyze synchronically". This could explain why symbolic baselines have a low performance on Navajo even if ANNr reaches above 92% of accuracy using the 10 most likely solutions. The remaining mistakes in Navajo are composed of 21. 11% of nouns in the first or second person of singular, both mixing prefixing and alternation but including variations which are hard to predict from the A, B, and C alone (e.
Conclusion and Perspectives In conclusion, we propose ANNr and a fitting training procedure for morphological analogies. Our approach outperforms state of the art symbolic baselines as well as more traditional methods on embedding spaces. We demonstrate the added value of ANNr compared to 3CosAdd and 3CosMul and provide in-depth analysis of results for two languages, displaying interesting properties of our framework on morphology. We provide ad hoc explanations of the behaviour of ANNr using mistakes made by the model, and explain why some unexpected predictions made by the model could be desirable, like the fact that our model prevents violations of strong reflexivity and strong inner reflexivity. We think that the ANNc/ANNr framework can generalize to analogies on a wide range of data types and applications.
6. In Subsection 4. 1, we briefly describe the dataset used and explain our choice of training procedure in Subsection 4. 2. The performance of our model is compared with state of the art baselines in Subsection 4. 3, and we explore how far the model prediction is from the expected output in Subsection 4. 4. Model mistakes on Navajo and Georgian are studied in Subsection 4. 5. Our experiments are implemented in PyTorch and PyTorch.
Results Based on the holograms collected on the high-contrast feature, the effective pixel size for each distance of the defocusing series was found to be 18. 30 nm, 19. 30 nm, 20. 30 nm and 21. 34 nm, respectively. This information was required to run the holographic reconstruction algorithms for each frame. First, contrast transfer function (CTF) retrieval  (Guigay, 1977)  was carried out. Then, the CTF results were used as the input of hybrid input-output (HIO) and error reduction (ER)  (Gerchberg & Saxton, 1972; Fienup, 1982)  iterative approaches within the PyPhase package  (Langer et al. , 2021). The resulting phase-shift images were converted into units of electron density  (Cloetens et al. , 1999)  by assuming a homogeneous composition through the 2 mm-thick sample. Such conversion was only carried out in order to translate the recovered electron density from units of A ˚À2 to the more familiar A ˚À3 and it should not be taken to imply that the sample actually is homogeneous throughout its thickness.
Exploiting the overlapping region of two adjacent frames, the achieved resolution was estimated to be 200 nm, based on Fourier ring correlation using the 1-bit threshold criterion (  Van Heel & Schatz, 2005). This exceeded the 70 nm spatial resolution limit for this experiment, possibly because of minor stitching artefacts. XRF data were analysed using the Python-based software PyMCA  (Soleet al. , 2007). A list of chemical elements expected to give rise to detectable fluorescence emission was produced taking into account the known chemical composition of the sample as well as the peaks observed within the raw fluorescence spectra. For each fluorescence scan, this listalong with other experimental parameters such as detector specifications, sample geometry, photon beam energy and scanning parameters -was fed into the PyMCA batch fitting algorithm.
3. In this case the elements of interest were Cl, Fe and Os. As expected, Os was present throughout the sample, but its area mass density was particularly high in the myelin surrounding the axons, as intended by the initial staining process for morphometry  (Sundkvist et al. , 2000; Mohseni et al. , 2017). The area mass density map of Fe clearly confirms the presence of a blood vessel and an Fe-rich blood cell therein. In the RGB representation, the electron density map from the holography scan is combined with area mass density maps from the fluorescence scan: red, green and blue channels are assigned to electron density, Fe and Os, respectively, in order to highlight co-localization. Principal component analysis (PCA) over the whole dataset for this ROI revealed that a single component accounted for 98% of the variance, with a dominant positive correlation between Os and P.
Though preliminary images of sufficient quality to identify ROIs suited for longer nXRF scans (cf Fig. 2 ) were available within minutes from the end of data acquisition, converged quantitative phase maps (cf Fig. 3 ) required a few hours of computation time. The continuous development of the PyPhase package  (Langer et al. , 2021)  will further increase user friendliness and enable novice users to generate converged holography reconstructions. However, it is expected that experiment design and setup will still require a solid understanding of holography and should hence be carried out by or in collaboration with experienced users or beamline staff. On the other hand, the high-resolution nXRF scan used to obtain Fig. 4  took 168 min, with an effective imaging speed of 0. 36 mm 2 s À1. The absorbed dose was estimated at 30 MGy, based on the (2.
Over one sequence (15 frames with a 5s timestep), the measured actin velocity is represented using 40 blue boxplots and the measured substrate displacement under the cell using 40 red boxplot. Each boxplot is computed considering all the data points in 1/40 of the cell. The blue line represents the linear regression of the measured actin velocity over the sequence. The red line is the predicted substrate displacement obtained using our model (  24 ), where the value of ξ is extracted by performing a least square minimization between the predicted (red line) and measured (red boxplots) substrate displacements. v x (x) v 1 x , where the coefficient v 1 can be physically interpreted as the slope of (  13 ) at the origin. In order to reduce the effect of fluctuations, a linear regression is performed at every time frame and then averaged over the total number of frames: v x (x) = 1 N N n=1 v n 1 x, where N is the total number of time frames in a sequence (N = 15) and v n 1 x is the linear regression of the actin velocity for frame n.
It is important to select the appropriate image frequency, since we need to capture fast actin polymerization but we should not expose the cells to too much light (phototoxicity). Our loop was a series of 15 pairs of images (FITC then DAPI) taken every 5 seconds, then a 15-minute pause was held before starting a new series of images. Thus actin fibers and beads could be followed over short periods of time during cell migration for about 30 minutes. At the end of the experiment, we added trypsin to the Petri dish to detach the cells from the substrate. After waiting for 15 min, the last beads image was captured to obtain the initial beads position when the gel is in a rest state. Finally, series of FITC and DAPI images could be treated using image processing in Matlab T M and Fiji T M software for tracking beads and PIV analyses of actin motion.
Image acquisition In this work, a code formerly written  (Mireux (2019) ; Jahangiri (2020)) was improved. The initial code is divided into four main parts. It reads 16-bit images taken from the microscope and converts them into a Due to the addition of trypsin to detach cells and also possible shifts of the camera (thermal changes), it was necessary to rewrite the code in order to process images. Here, the DAPI images (15 DAPI images taken every 5 seconds + DAPI image taken after adding trypsin to the Petri dish) as blue color and FITC images (15 FITC images taken every 5 seconds + blank image corresponding to the absence of cell on the substrate) as green color were merged. Then we used the StackReg plugin  Thévenaz (2009)  in the Fiji software to shift all images in order to correct for any camera shift.
Tracking Beads By using a previously written Matlab code  (Mireux (2019) ), we could find bead positions at each time (for example DAPI images at t 0 and t 1 in Fig. B. 19). The particle tracker is a routine adapted for Matlab of a previous program  Crocker and Weeks (2011). This function reads the first DAPI image and processes it interactively to figure out what settings are needed in order to identify all the beads. It then repeats this process on all the images. Finally, it links the beads coordinates to form trajectories. By replacing the last image (obtained after adding trypsin, Fig. B. 19a at time t 0 ) from the end of the treated DAPI stack to the first and running the tracking function in Matlab, we obtain a list of trajectories including the beads identities numbered from 1 to the total number of beads as well as their positions (x,y).
Actin and PIV We found Particle Image Velocimetry (PIV) to be a suitable technique to estimate the actin velocity. In general, PIV is an optical technique of flow visualization used to obtain instantaneous velocity measurements and related properties in fluids. Basically, a pair of images is divided into smaller areas named interrogation windows. The cross-correlation between these image sub-regions measures the optical flow (incremental displacement or velocity of the objects) between the two images. To improve resolution, higher PIV resolution can be achieved by progressively decreasing the interrogation window size  Tseng (2014). The PIV analysis was conducted using the MATLAB tool "PIVlab"  Thielicke and Stamhuis (2014).
Acknowledgements We thank  Alain Duperray  for providing the transfected cells, and for related discussions. We acknowledge support from a  CNRS MOMENTUM  grant and the  ANR  (grant No. 12-BS09-020-01 , TRANSMIG). C. V. , J. E. and P. R. are members of the  LabeX Tec 21 (Investissements d'Avenir : grant agreement No. ANR-11-LABX-0030 ).
Choice of the simulation software Several solving methods can be used to model eddy currents in power electronics systems. The PEEC (Partial Element Equivalent Circuits) method  (Ruehli, 1974; Schanen and Roudet, 2008)  is well suited for modeling thin wire-like conductive regions. However, the standard PEEC method is not adapted to the modeling of massive conductors (3D currents) and therefore to this work which uses massive heat sinks as power connectors. The finite element method (FEM) is known as an effective tool for the calculation of 3D electromagnetic fields and eddy currents. However, this method is very sensitive to the meshing which determines the accuracy of the solution and is also time consuming. As a consequence, the homemade MIPSE software (Modeling of Interconnected Power SystEms) is chosen to perform the electromagnetic study of the TAPIR technology.
It is based on integral methods  (unstructured PEEC)  (Meunier et al. , 2019; Siau et al. , 2016)  with matrix compression to limit the required computation time and memory space. It also integrates an automatic meshing tool  (Alkama et al. , 2021). In the following paragraph, electromagnetic simulations on a simple geometry will be carried out with MIPSE and a commercial FEM software (Altair Flux 3D ). It will allow validating the use of MIPSE in this study and making a first parametric study.
For studying the current repartition between capacitor rows, the location of the current injection must be modified. Here, a thin opening is made in the middle of one chip to perform the current injection on equipotential surfaces (current lines perpendicular to the surface). The placement of each capacitor row on each DC link heat sink is represented by 7 equipotential surfaces. With the MIPSE software, it is possible to insert the equivalent model of a capacitor between two equipotential surfaces. This tool is thus used to model the capacitance rows between DC link heat sinks as shown in Fig. 10. The equivalent model of a single capacitor is a capacitance C=10 µF in series with a resistance ESR=10 mΩ and an inductance ESL=1nH (values obtained from the datasheet). Since each row is composed by 9 capacitors, a 90 µF capacitance C eq in series with a resistance ESR eq =1.
Inductance of adjacent switching cells The inductance of a switching cell is first estimated as a function of the distance Esp between both cells using the MIPSE software. The modeling principle is presented in Fig. 13a. The current I (frequency f = 100 MHz) is injected on the internal faces of the DC link heat sinks of one switching cell. Voltage V 1 is measured across the DC link internal faces of this cell to obtain the stray inductance L s1 by: L s1 = V 1 2πf ⋅I (4) To estimate the mutual inductance M 1 between them, the circuit of the second cell must be open, therefore the decoupling capacitors are not included, and voltage V 2 is measured: M 1 = V 2 2πf ⋅I = L s1 V 2 V 1 (5) For Esp=0. 5 mm, it can be seen in Fig. 14  that the stray inductance L s1 of a switching cell close to another one is 10% lower than the stray inductance L s of an isolated switching cell (L s =2.
A quantitative description in terms of 2D spatial distribution is needed for more accurate model simulations. To that end, we quantified the 2D spatial distribution of the basal protein pattern from confocal fluorescence images. In particular, we developed a script that allows visualization of the 2D protein patterns of the wing imaginal disc on 3D surfaces (Figs. 6e, 2D profiles) and generation of numerical data (matrices in Fig. 6e ) for the levels of each protein, which have been used in (1) to model cytoneme orientation in wild type conditions. The 2D quantification showed that the wild-type modulation of the protein levels is not the same in all regions (Figs. 6e, 2D profiles), something that could not be deduced from 1D profiles. We then tested if, using our guidance model, the wild-type spatial protein distributions of these proteins could be sufficient to predict cytoneme orientation within the Hh signaling region (Fig.
The ex vivo imaging was performed in standard microscope slides, where the discs were mounted in M3 insect medium and covered with a 15 × 15 mm coverslip. The samples were filmed using 40x magnification; Z-stacks of around 8 μm of thickness with a step size of 0. 62 μm were taken every minute using a LSM800 confocal microscope. Data analysis and statistical study. The data of abdominal histoblast nests are published in  11. The quantification of the number of cytonemes and their orientation angles have been obtained manually using Fiji. The data representation, in boxplots and rose polar diagrams, was performed using Matlab2015a functions. For the statistical study of the data in the figures, we first performed a Shapiro-Wilk test of normality, since the S-W test showed that our data distributions were not parametric, to study the statistical significance between datasets, we used a Wilcoxon rank sum test per pairs in Matlab2015a (See Supplementary excel file for the quantified data and the calculated p-values).
Finally, some cytonemes were marked in ex vivo and in vivo experiments to better show the dynamics and the stabilization of cytonemes, those tracks were performed using the Fiji plugging: Manual Tracking. Quantification of cytoneme orientation. The experimental data of cytoneme length and orientation due to Ihog overexpression in LexA and Gal4 clones were quantified manually using FIJI along 235 cytonemes from different clones (n = 21). In each measurement, we quantified the length (λ) and the angle (β) of a cytoneme and the distance (d) and angle (γ) of the tip of that cytoneme with the closest clone. The study of the effect in the length was performed analyzing λ vs d, and the study of the orientation was calculated using α = γ -β. Please notice that the increase in α means that cytonemes are avoiding the closest confronted clone.
Dlp pattern was quantified using Dlp monoclonal antibody in the wing imaginal disc expressing either Ihog tagged with GFP (Bac. IhogGFP) or Dally tagged with YFP (Dally. trap. YFP). Extracellular staining was performed for Dally tag and Dlp protein to confirm that the same pattern is present in the extracellular matrix where the cytonemes sense the levels of glypicans and Ihog. Since our tissue model works in 2D and Ihog and glypicans proteins are present along all tissue membranes, we obtained the quantitative description of 2D spatial distribution at the basal plane of the imaginal wing disc, plane where cytonemes are present. To that end, the data were treated using a computational script that allows extracting the experimental data from confocal images and visualizing it in a 3D surface the 2D spatial distribution of the particular fluorescence protein pattern along the disc tissue.
Acknowledgements We are grateful to and  Pedro Ripoll  and  Ana-Citlali Gradilla  for comments on the manuscript. We also thank to  Laura González-Méndez ,  Carlos Jiménez-Jiménez ,  David Sánchez-Hernández  and  Eléanor Simon in I. G laboratory  for their help with some experiments, the  Confocal Facilities of the CBMSO and Bloomington and Vienna  stock centers for fly stocks. This work was supported by grants  BFU2017-83789-P ,  PID2020-114533GB-C21  and TENTACLES consortium RED2018-102411-T to I. G from the  Spanish Ministry of Science, Innovation and Universities  and by institutional grants from the  Fundación Areces and Banco de Santander  to the  CBMSO. FPI fellowship  from the  Spanish Ministry of Science, Innovation and Universities supported A. A-T  ( BFU2017-83789-P ). This work was also supported by grants  RTI2018-098850-B-I00  to J.
S from the  MINECO-Feder (Spain) ,  PY18-RT-2422 & A-FQM-311-UGR18  to M. C, D. P and J. S from the  Junta de Andalucia (Spain) ,  MECD (Spain)  research grant  FPI2015/074837  to M. C, and partially supported by the  MECD (Spain)  research grant  FPU14/06304  and the  European Research Council (Europe)  Project  ERC-COG-2019  WACONDY (grant agreement No  865711 ) to D. P.