dataesr/scientific-paragraphs-categorization huggingface dataset:
This work was supported by joint grants awarded to PAD and GC, and to DvE and GC from the  Agence Nationale de la Recherche  ( RETROMET ,  ANR-16-CE12-0020 ;  ActiveLINE ,  ANR-21-CE12-0001 ), as well as other grants awarded to GC from the  Fondation pour la Recherche Médicale  (FRM,  DEQ20180339170 ), the  Agence Nationale de la Recherche  ( Idex UCAJEDI ,  ANR-15-IDEX-01 ;  Labex SIGNALIFE ,  ANR-11-LABX-0028 ;  ImpacTE ,  ANR-19-CE12-0032 ), the  Institut National du Cancer  ( INCa PLBIO 2020-095 ), the  Canceropôle Provence-Alpes-Côte d'Azur ,  INCa  and the  Provence-Alpes-Côte d' Azur Region (Projet Emergence) ,  Inserm  ( GOLD cross-cutting programme on genomic variability) ,  CNRS  ( GDR 3546 ). Equipment acquisition for the GenoMed facility was supported by  FEDER ,  Région Provence Alpes Côte d'Azur ,  Conseil Départemental 06 ,  ITMO Cancer Aviesan  (plan cancer) and  Inserm.
Work in the laboratory of PAD was also supported by  LabEx "Who Am I? " ( ANR-11-LABX-0071 ),  Université Paris Cité IdEx  ( ANR-18-IDEX-0001 ) funded by the  French Government  through its  "Investments for the Future" program ,  Fondation pour la Recherche Médicale , and  Fondation ARC  ( Programme Labellisé   PGA1/RF20180206807 ).
ucsc. edu/cgi-bin/hgTables ENCODE: ENCFF353CZO Browser Annotations: L1 annotation track This study https://github. com/retrogenomics/bs-ATLAS-seq Annotations: Comprehensive gene GENCODE https://www. gencodegenes. org/human/release_29. html annotation (v29) bs-ATLAS-seq (raw data): 12 cell lines This study ArrayExpress: E-MTAB-10895 bs-ATLAS-seq (raw data): aza-treated This study ArrayExpress: E-MTAB-12240 HCT-116 bs-ATLAS-seq (processed data): Full- This study Table S3 length and 3' truncated L1 mapping and methylation tables bs-ATLAS-seq (processed data): This study Zenodo: https://doi. org/10. 5281/zenodo. 7097318 single-molecule methylation patterns of full-length and 3' truncated L1 Bs-ATLAS-seq (processed data): database of full-length and 3' This study Online portal: https://L1methdb.
ircan. org GEO: GSE153250 truncated L1 with position, average methylation and single-molecule Experimental Models: Cell Lines methylation Human: 2102Ep P. W. Andrews RRID: CVCL_C522 RNA-seq: 11 cell lines Human: BJ This study ATCC ArrayExpress: E-MTAB-12246 RRID: CVCL_3653 RNA-seq: H1 Human: HCT-116 ENCODE ECACC ENCODE: ENCLB073SSM RRID: CVCL_0291 RNA-seq: aza-treated HCT-116 Human: HEK-293 This study ECACC ArrayExpress: E-MTAB-12245 RRID: CVCL_0045 WGBS: K-562 cells Human: HEK-293T Scripts to process raw bs-ATLAS-seq ENCODE A. Cimarelli This paper ENCODE: ENCFF660IHA RRID: CVCL_0063 https://github. com/retrogenomics/bs-ATLAS-seq ONT-seq: 125 loci, 4 cell lines (HCT-116, 2102Ep, MCF-7, K-562) Human: HeLa S3 reads This study ECACC ArrayExpress: E-MTAB-12247 RRID: CVCL_0058 ONT-seq (processed data): Human: HepG2 This study ECACC Table S4 RRID: CVCL_0027 methylation table Human: IMR-90 ATCC RRID: CVCL_0347 Database: euL1db Human: K-562 29 ECACC http://euL1db.
unice. fr RRID: CVCL_0004 Database: Unibind Human: MCF-7 90 ECACC https://unibind. uio. no/ RRID: CVCL_0031 ChIP-seq: H3K36me3 (K-562) Human: MRC-5 NCBI ECACC GEO: GSM1782705 RRID: CVCL_2624 ChIP-seq: H2AFZ (HCT-116) Oligonucleotides ENCODE ENCODE: ENCFF193VYC ChIP-seq: H3K27me3 (HCT-116) Oligonucleotides for bs-ATLAS-seq ENCODE This paper ENCODE: ENCFF294LZM Table S1 ChIP-seq: H3K4me3 (HCT-116) and PCR validation ENCODE ENCODE: ENCFF187LLD ChIP-seq: H3K9ac (HCT-116) Primers for meDIP-qPCR ENCODE This paper ENCODE: ENCFF724JXS Table S2 ChIP-seq: H4K20me1 (HCT-116) Antibodies ENCODE ENCODE: ENCFF730VTQ ChIP-seq: H3K27ac (HCT-116) Rabbit anti-human YY1 ENCODE Diagenode ENCODE: ENCFF853VVI Cat# C15410345 ChIP-seq: H3K36me3 (HCT-116) anti-H3K4me3 ENCODE Abcam ENCODE: ENCFF528ZNP Cat# ab8580.
Data were submitted to the ArrayExpress database (www. ebi. ac. uk/arrayexpress) under accession numbers E-MTAB-10895 and E-MTAB-12240 (bs-ATLAS-seq), E-MTAB-12247 (ONT sequencing), E-MTAB-12249 (ChIP-seq), and E-MTAB-12246 and E-MTAB-12245 (RNA-seq). The genomic location and methylation levels of L1 insertions are summarized in TableS3. Single-molecule methylation patterns for each locus are provided in Zenodo (https://doi. org/10. 5281/zenodo. 7097319). All L1 methylation datasets can be interactively queried, filtered and downloaded through the web portal L1MethDB (https://L1methdb. ircan. org/). The scripts written to call L1 insertions and CpG methylation from bs- ATLAS-seq data, as well as useful annotation files used in the course of this study, are available at https://github. com/retrogenomics/bs-ATLAS-seq.
In this paper, we propose a new mathematical formulation of an abstract transformer to convert a LeakyReLU activation layer to an abstract layer. Moreover, we implement and integrate our transformer into the ERAN tool. For validation, we assess the performance of our transformer according to the LeakyReLU hyperparameter, and we study the robustness of the neural network according to the input perturbation intensity. Our approach is evaluated on three different datasets: MNIST, Fashion and a robotic dataset. The obtained results demonstrate the efficacy of our abstract transformer in terms of mathematical formulation and implementation.
This enables the assessment of the robustness of neural networks containing LeakyReLU layers, that is missing in the state-of-theart. To achieve this objective, our strategy consists of the following two contributions 1  : ‚ We propose a new abstract transformer that allows the use of Abstract Interpretation for verifying the robustness of DNN with LeakyReLU activation. The current state of the art does not include this transformer. ‚ We integrate the transformer into ERAN (ETH Robustness Analyzer for Neural Networks), which is one of the most popular formal tools. Then, several several experiments for classification tasks on different datasets are performed. In addition, we note that the formulation of our transformer is generic and could be implemented under any formal tool used for abstract interpretation or interfaced with ERAN as the tool DNNV  [13].
A. DATASETS Our approach was validated on three datasets, including two popular image benchmarks: MNIST  [32]  and Fashion  [33]. The MNIST dataset consists of 60. 000 training and 10. 000 test grayscale images of handwritten digits, whose resolution is 28 ˆ28 pixels. The images show white digits on a black background. The Fashion dataset consists of 60. 000 training grayscale images and 10. 000 test images, with a resolution of 28 ˆ28 pixels. Each example is assigned to one of the following labels: T-shirt/top, Trouser, Pullover, Dress, Coat, Sandal, Shirt, Sneaker, Bag and Ankle boot. The third dataset, named Robotics, is a collection of sensor readings obtained by a robot during its navigation inside a room. For robot navigation, 24 ultrasound sensors (US) were used, and arranged circularly around its waist with an arc distance of 15 degrees.
The second observation concerns the neural network's robustness to input perturbations. In this assessment, one model is chosen and evaluated for each dataset. The results demonstrate that the models trained on the three datasets respond differently to a perturbation of intensity epsilon. The robotic model is the most robust in general. In fact, 90% of robustness is always ensured when epsilon is less than 0. 2. On the other hand, the fashion model is moderately robust; a epsilon value of 0. 03 decreases robustness to 16%. At the same epsilon value (0. 03) for MNIST, the model is not robust. This evaluation demonstrates that our implementation is correct and that no issues were produced for any epsilon value. We recall that the purpose of this work is not to enhance the robustness of already-trained models, but rather to validate their robustness.
Our abstract transformer was tested on three public datasets: MNIST, Fashion and a robotic dataset. The obtained results showed that below a certain value of α, our transformer is effective. However, for large values of α, the approximation is too coarse and should be improved. Moreover, results showed that our implementation is correct and no bugs were generated for all values of ϵ. In future work, we plan to improve the approximation of our abstract domain in the case of large values of α. Then, we will extend our study to other activation func-.
10 and 11  show respectively the obtained results on the three datasets: MNIST, Robotics and Fashion. These figures show the performance of neural networks according to the value of the α hyperparameter of LeakyReLU. These figures include two curves: the blue curve is associated with the performance of the neural network outside ERAN, while the green curve shows its performance inside ERAN. Two evaluation results are presented: 1q a quality evaluation of the abstract domain approximation and 2q a robustness evaluation of the neural network according to the maximal perturbation epsilon. The obtained results are shown on the right side of the figures(9, 10  and 11).
ACKNOWLEDGMENT This research work has been carried out in the framework of  IRT SystemX, Paris-Saclay, France , and therefore granted with public funds within the scope of the  French Program Investissements d'Avenir. This work is a part of the project  EPI  project  (EPI for "AI-based Decision Making Systems' Performance Evaluation "). We would also like to thank  Gwenaëlle BERTHIER ,  EPI  project manager, for her administrative help.
Figures 9 , 9 10 and 11  show respectively the obtained results on the three datasets: MNIST, Robotics and Fashion. These figures show the performance of neural networks according to the value of the α hyperparameter of LeakyReLU. These figures include two curves: the blue curve is associated with the performance of the neural network outside ERAN, while the green curve shows its performance inside ERAN. Two evaluation results are presented: 1q a quality evaluation of the abstract domain approximation and 2q a robustness evaluation of the neural network according to the maximal perturbation epsilon. The obtained results are shown on the right side of the figures(9, 10  and 11).
D. Power consumption In this paragraph, we evaluate the power consumption of the proposed federated learning strategy. We consider two sources of power consumption for each device: local computation and transmission; then, we take into account the power spent for computation at the edge server. At time t, the power spent by device i for local computation is: p c i,t = κ l (f l i,t ) 3 , (22) where κ l is the effective switched capacitance of the processor  [50]. Moreover, given the uplink data rate R u i,t , the power spent for uplink transmission is computed by inverting the Shannon formula, thus obtaining: p u i,t = B u i,t N 0 h u i,t exp R u i,t ln 2 B u i,t -1 , (23) where B u i,t is the bandwidth assigned to device i at time t, h u i,t is the uplink channel power gain, and N 0 is the noise power spectral density.
Moreover, B i =  [2, 4, 8] , and R d i,t = R max i,t for all i, and t. The channels are generated using the ABG model  [54] , with a carrier frequency of 23 GHz and adding a Rayleigh fading with unit variance. The LMS results are obtained with Matlab, using a PC with an Intel Core i7-7700HQ CPU at a frequency of 2. 80 GHz. The data-driven results are obtained using Python and the JAX framework, exploiting an NVIDIA Tesla K80 GPU.
To train the CNN, we use the MNIST dataset  [55] , which is made of 28 × 28 grayscale images of handwritten digits divided in 10 classes. The training data is composed of 6 × 10 4 examples, while the test set is made of 10 4 elements. The loss is the well-known cross-entropy, and the model is trained using a federated ADAM optimizer  [56]. The devices locations are random and the distance of each device from the AP is sampled from a uniform distribution in the interval  [20, 80] , for all i = 1,. , N. Also, the overall bandwidth is 100MHz, O = 10 6 , and N l i = 10 7. The ADAM step-size is set to 0. 008, with forgetting factors β 1 = 0. 9, and β 2 = 0. 99. For this experiment, we use the performance estimate G t in  (47) , and α t in (48) with K = 10. Also, as a surrogate function for the accuracy metric, we exploit: G t = i∈St σ(b i,t -Median{B i }), (52) where σ(   , 3, 7, 14]  for Fig.
In particular, the MNIST dataset is divided into two sub-dataset of 5 classes each; then, the architecture is trained for the first 180 time-slot with one of the two sub-datasets and for the remaining time-slots with the other one (the last dense layer is obviously reduced to a 5 dimensional output). Equivalently, this introduces a nonstationary behavior of the data distribution. Then, at time slot 401, we change the accuracy requirement from G = 0. 8 to G = 0. 9, introducing a further level of non-stationarity. The results are averaged over 10 independent simulations. From Fig. 8 , we can notice that our dynamic strategy is able to react promptly to both changes in the data distribution and in the accuracy requirement, exhibiting powerful learning and adaptation capabilities in a fully data-driven fashion.
A Deep Machine Learning algorithm This Section comes to the core of this Note since by presenting an abstract Deep Machine Learning algorithm endowed with a proof of convergence with respect to the number of layers (so the name Deep Learning). This Deep Learning algorithm can be implemented in one of the Neural Networks/Machine Learning softwares freely available such as Tensorflow/Keras  [1] , Scikit-Learn (Inria 1 ), Pytorch (Facebook 2 ), Julia (MIT licence 3 ). This list is not exhaustive. It is sufficient for this presentation to consider that Neural Networks/Machine Learning softwares have two features: a) they manipulate functions assembled with ReLU like activation functions and composition of functions, b) they perform numerical optimisation to fit the coefficients, in particular with stochastic gradient descent methods  [7, 3].
Then H(e 1,1 (x)) = 32 9 4 x 3 -48 9 4 x 2 + h 1 x + h 2 and H(e 1,2 (x)) = 32 9 4 x 3 - 24 9 4 x 2 + h 3 x + h 4. Making vanish in I 1 the coefficients of the third order and second order monomials in q yields the system β 1,1 + β 1,2 = 4 9 3 = 2 6 3 6 , 2β 1,1 + β 1,2 = 2 4 9 2 = 2 5 3 4. The solution is β 1,1 = 2 5 3 4 -2 6 3 6 and β 1,2 = 2 7 3 6 -2 5 3 4. • Concerning I 3 one notices that the third order Tchebycheff is antisymmetric with respect to the center x = 1/2. It explains why β 1,1 = β 3,2 and β 1,2 = β 3,1. These values can also be obtained after lengthy but elementary calculations. (x) = x -x 2. The training dataset is made with 4000 pairs (x s , y s = H(x s )) 1≤s≤4000 where x s is sampled uniformly between 0 and 1. Around 20% of the pairs are taken outside for validation. The batches are made with 128 pairs.
Acknowledgments We thank  Cédric Troessaert  for important discussions. O. F. is grateful to the  Collège de France  for kind hospitality while this work was completed. This work was partially supported by a  Marina Solvay Fellowship  (O. F. ) and by  FNRS-Belgium  (conventions  FRFC PDRT. 1025. 14  and  IISN 4. 4503. 15 ), as well as by funds from the  Solvay Family.
highest vs lowest score category =29. 0 (23. 4-35. 9), p<0. 001) and the ultraprocessing dimension (OR=174. 3 (151. 4-200. 5), p<0. 001). Trends were similar for cookies, breakfast cereals and ready-to-eat meals. The Nutri-Score V. 2. 0 had a positive effect on purchasing intentions and on the products perceived as the healthiest. Conclusion This randomised controlled trial demonstrates the interest of a front-of-pack label combining the Nutri-Score (informing on the nutrient profile dimension) with an additional graphic mention, indicating when the food is ultraprocessed, compared with a no-label situation. Our results show that a combined label enabled participants to independently understand these two complementary dimensions of foods. Trial registration number NCT05610930.
METHODS Trial design, participants and data collection A two-arm parallel group randomised trial was conducted between April and June 2022. Participants were randomly recruited from the NutriNet-Santé cohort via an emailing campaign and were asked to answer a specific trial questionnaire with two randomly attributed versions, one for the experimental arm and one for the control arm. Briefly, the NutriNet-Santé cohort is an ongoing webbased prospective cohort launched in France in 2009 and aiming to study the relationships between diet and health as well as the determinants of dietary behaviours. 35  Participants aged 18 years or older with access to the internet have been continuously recruited among the general population since May 2009 using multimedia campaigns. Questionnaires are completed online using a dedicated website (www.
Acknowledgements We thank  Thi Hong Van Duong ,  Régis Gatibelza ,  Jagatjit Mohinder ,  Rizvane Mougamadou  and  Aladi Timera  (computer scientists);  Julien Allegre ,  Nathalie Arnault ,  Nicolas Dechamp , (data-manager/statisticians);  Paola Yvroud  (health event validator);  Maria Gomes  and  Mirette Foham  ( Nutrinaute  support) for their technical contribution to the NutriNet-Santé study. We warmly thank all the volunteers of the  NutriNet-Santé  cohort.
II. EMPIRICAL HIGH-ORDER STRUCTURE FUNCTIONS COMPUTED FROM RESTING-STATE FUNCTIONAL MRI DATA SHOW POWER LAWS First, we extracted and bandpass filtered (0. 008-0. 08 Hz) the time series from the 1003 Human Connectome Project (HCP) resting-state functional magnetic resonance imaging (fMRI) recordings, each time series corresponding to the average of a parcel within the Schaefer 1000 parcellation. We adapted the increment of velocity in fluid dynamics, u(r), by computing the difference between BOLD signals at pairs of nodes separated by distance r ± r, where r equals one bin of the spatial grid. To do so, we computed the distances between the geometric centers corresponding to all parcels and then averaged the BOLD signal across all pairs separated by r ± r. For each participant, we calculated the p-order structure functions following Eq.
(  2 ) from p = 1 to p = 8, and then we estimated within the inertial subrange (previously determined by the scaling of the second-order structure function) the power-law scaling exponents corresponding to each order. In Fig. 1 (a) we present the structure functions as a function of the distance in their brain r for each of the 1003 participants of the HCP data set (see Appendix A for detailed explanation on the participants, data acquisition, and preprocessing). We observed that the structure functions are consistent across all participants, with odd structure functions showing a mean around 0. Consequently, we considered only the even functions within the inertial range, with r = 8. 1 to r = 33. 8 mm [highlighted in Fig. 1(a) ] to compute the scaling exponent ζ (n), as is the standard practice in turbulence studies  [18, 20].
Studies of the famous sandpile model proposed by Bak et al. [39]  to capture the behavior of self-organized criticality have shown that the moments of wave size differences present similar scaling to those holding for velocity structure functions in fluid turbulence  [8]. The results presented here push this study to include many different statistical orders, allowing for simultaneous characterization of scale invariance as well as of the deviations from this behavior. The preprocessing of the HCP resting state is described in details on the HCP website. In short, the data are preprocessed using the HCP pipeline which is using standardized methods using FSL (FMRIB Software Library), FREESURFER, and the CONNECTOME WORKBENCH software  [42, 43]. This preprocessing included correction for spatial and gradient distortions and head motion, intensity normalization and bias field removal, registration to the T1-weighted structural image, transformation to the 2-mm Montreal Neurological Institute (MNI) space, and using the FIX artifact removal procedure  [43].
The head motion parameters were regressed out and structured artifacts were removed by ICA + FIX processing (independent component analysis followed by FMRIB's ICA-based X-noiseifier  [44] ). Preprocessed time series of all grayordinates are in HCP CIFTI grayordinates' standard space and available in the surface-based CIFTI file for each participant for the resting state. We used a custom-made MATLAB script using the ft-readcifti function (FIELDTRIP toolbox  [45]  to extract the average time series of all the grayordinates in each region of the Schaefer parcellation, which are defined in the HCP CIFTI grayordinates' standard space. Furthermore, the BOLD time series were transformed to phase space by filtering the signals in the range between 0. 008 and 0. 08 Hz and the lowpass cutoff to filter the physiological noise, which tends to dominate the higher frequencies  [46].
Structural connectivity using diffusion MRI To obtain the structural connectivity we use the HCP database which contains diffusion spectrum and T2-weighted imaging data from 32 participants (acquisition parameters are described in detail on the HCP website). Briefly, the data were processed using a generalized q-sampling imaging algorithm implemented in DSI studio  [47]. The white-matter mask is produced by the segmentation of the T2-weighted anatomical images. The co-register of the images to the b0 image of the diffusion data was carried out using Statistical Parametric Mapping tool (SPM)  [48]. In each HCP participant, 200 000 fibers were sampled within the white-matter mask. Fibers were transformed into MNI space using LEAD-DBS  [49]. We used the standardized methods in LEAD-DBS to produce the structural connectomes for Schaefer 1000 parcellation  [40]  where the connectivity has been normalized to a maximum of 0.
2. The freely available LEAD-DBS software package [50] provides the preprocessing that we implemented and is described in detail in Horn and colleagues  [51]. 2 to 8 accumulated moments Cn (n = 2 to 8) for various separations r p = 22 + 2p, p = 1, 2, 3, 4, 5, and 6. Curves are for p = 1,. , 6 and all values are within the inertial range (see Fig. 4 ). In Fig. 4 , the insets in the odd orders are the accumulated moments computed with the absolute value.
ACKNOWLEDGMENTS The authors acknowledge funding from the  European Union 's  Horizon 2020 research and innovation program  under  Marie Sklodowska-Curie Grant  No. 896354 ; the  Human Brain Project  under Specific Grant Agreement No. 945539 ; the  Spanish national research  project (Ref. No. PID2019-105772GB-I00 MCIU AEI ) funded by the  Spanish Ministry of Science, Innovation and Universities (MCIU) ,  State Research Agency (AEI) ; and  ANID/FONDECYT Regular   1220995  (Chile).
2020)  while the stock status is derived from age-based or surplus production stock assessments  (Tsikliras & Froese 2019). Ecosystem models and stock assessments are thereby required to examine fisheries management and marine policy scenarios  (Piroddi et al. 2022 ) within the context of environmental  (Piroddi et al. 2021) , oceanographic  (Coll et al. 2019 ) and climatic change factors  (Corrales et al. 2018 ), whilst also incorporating economic and social parameters  (Link 2010). The development of ecosystem models demands specific biological data, mainly growth parameters, natural mortality and diet composition per species or functional group of species  (Christensen & Walters 2004) , as well as catch data that are available per fleet through official landings statistics (global and regional databases of the Food and Agricultural Organisation of the United Nations: FAO 2020) and catch datasets (Sea Around Us:  Pauly & Zeller 2016).