dataesr/scientific-paragraphs-categorization huggingface dataset:
For each type of features, a voxel-wise encoding model was constructed to predict brain activity. Model weights were estimated using L2-regularised linear regression. Encoding models also allow the comparison between sparse and latent features in the same brain data using representational similarity analysis (RSA) and feature-brain similarity (FBS)  ( Nakai et al. , 2021 ). The RSA is a region of interest (ROI)-based approach. In contrast, the FBS can directly assess the relationship between latent features and brain representations in each voxel and how such a relationship produces brain activation patterns of mathematical operations modelled by sparse symbolic features. To investigate the relationship between the symbolic and distributed representations underlying mathematical operations in the brain, we used part of a three-hour fMRI dataset  ( Nakai and Nishimoto, 2023 )  where subjects performed a series of mathematical problems with nine different combinations of operators ( Fig.
1 A  ). This dataset is characterised by a relatively large sample size ( N = 3255) per individual, in contrast to existing mathematical fMRI datasets (e. g. N = 430 in Suárez-Pellicioni et al. (  2019 ) ). By using sparse operator features, we constructed a voxel-wise encoding model to predict the brain activity specific to each mathematical operation ( Fig. 1 B  ). We then extracted the latent features from the intermediate layers of an ANN (TP-Transformer)  ( Schlag et al. , 2019 )  and constructed another encoding model based on these latent features. We hypothesised that ANN-based distributed representations can explain the brain activity patterns underlying mathematical operations depicted by sparse features. Alternatively, such a sparse representation could be explained by other features not specific to mathematics.
Stimuli and procedure We selected arithmetic problems with a single operation, addition (Add), subtraction (Sub), multiplication (Mul) and division (Div), and arithmetic problems with two operations, including addition and subtraction (AddSub), addition and multiplication (AddMul), addition and division (AddDiv), subtraction and multiplication (SubMul) and subtraction and division (SubDiv). Each task consisted of 35 instances. Subjects also underwent another math problem-solving condition in word format and a control sentence comprehension condition; these conditions were analysed elsewhere  ( Nakai and Nishimoto, 2023 ). Behavioural data were also analysed in this previous work. In each trial, an arithmetic expression problem (e. g. '3 × 2 = ?') was presented for 4 or 6 s (4 s for single-operator problems, and 6 s for double-operator problems).
8°visual angle at 30 Hz). During scanning, subjects wore MR-compatible ear tips. The experiment was performed over three days, with six runs per each day. A presentation software (Neurobehavioral Systems, Albany, CA, USA) was used to control stimulus presentation and collection of behavioural data. Optic response pads with two buttons were used to measure button responses (HHSC-2 × 2, Current Designs, Philadelphia, PA, USA). Six training and two test runs were conducted. The data from each pair of test runs were averaged to increase the signal-to-noise ratio. Each run contained 45 trials consisting of five trials for each of the nine tasks; the presentation order was randomised within the run. A single run lasted 455 s. At the beginning of each run, we acquired 10 s of dummy scans, during which the fixation cross was displayed; these dummy scans were later omitted from the final analysis to reduce noise.
MRI data acquisition The experiment was conducted using a 3. 0 T scanner (MAGNE-TOM Prisma; Siemens, Erlangen, Germany) with a 64-channel head coil. We scanned 72 interleaved axial slices, 2-mm thick without a gap, parallel to the anterior and posterior commissure line, using a T2 * -weighted gradient-echo multiband echo-planar imaging sequence [repetition time (TR) = 1000 ms; echo time (TE) = 30 ms; flip angle (FA) = 62°; field of view (FOV) = 192 × 192 mm 2 ; resolution = 2 × 2 mm 2 ; multiband factor = 6]. We obtained 465 vol for each run, following 10 dummy images. As anatomical reference, high-resolution T1weighted images of the whole brain were acquired from all subjects with a magnetisation-prepared rapid acquisition gradient-echo sequence (TR = 2530 ms; TE = 3. 26 ms; FA = 9°; FOV = 256 × 256 mm 2 ; voxel size = 1 × 1 × 1 mm 3 ).
fMRI data pre-processing In each run, motion correction was performed using the statistical parametric mapping toolbox (SPM12; Wellcome Trust Centre for Neuroimaging, London, UK; http://www. fil. ion. ucl. ac. uk/spm/ ). All volumes were aligned to the first EPI image for each subject. Low-frequency drift was removed using a median filter with a 120-s window. Slice timing correction was performed against the first slice of each scan. The response for each voxel was then normalised by subtracting the mean response and scaling it to the unit variance. We used FreeSurfer ( https://surfer. nmr. mgh. harvard. edu/ ) to identify the cortical surfaces from anatomical data and register these to functional data voxels. For each subject, identified voxels in the cerebral cortex (59,499-75,980 voxels per subject) were used for analysis.
The other part of the architecture and hyper-parameters of the TP-Transformer is similar to the regular transformer (dimensionality of input and output, d model = 512; dimensionality of feed-forward network, d f = 2048). The model was trained using the Mathematics Dataset  ( Saxton et al. , 2019 ). For each input math expression (e. g. '3 + 5'), we extracted the average query, key, value and roll vectors from each of the six encoding layers. Time points without vector assignments were defined as 0. Although we could use all these vectors, we used the query vectors of the sixth encoding layer as a representative vector based on a previous study  ( Russin et al. , 2021 ). We also extracted query vectors of the sixth encoding layer with each mathematical symbol (e. g. '3', ' + ', etc. ) as input.
ME features We employed a previously described ME model  ( Koide-Majima et al. , 2020 ; Nakai and Nishimoto, 2020 ; Nishimoto et al. , 2011 )  available in a public repository ( https://github. com/gallantlab/motion _ energy _ matlab ). First, movie frames and pictures were spatially downsampled to 96 × 96 pixels. RGB pixel values were then converted into the Commission International de l'Eclairage (CIE) LAB colour space; then, colour information was discarded. The luminance (L * ) pattern was passed through a bank of three-dimensional spatiotemporal Gabor wavelet filters; the outputs of two filters with orthogonal phases (quadrature pairs) were squared and summed to yield the local ME. Subsequently, ME was compressed with a log-transformation and temporally downsampled to 0. 5 Hz. Filters were tuned to six spatial (0, 1.
Word2vec features To quantitatively evaluate the brain representations of the presented semantic information in a data-driven manner, we extracted the semantic features from each narrative stimulus using word2vec  ( Mikolov et al. , 2013 ). Word2vec, based on the skip-gram algorithm, has been used to embed words into distributed representations. We used a text corpus from the Japanese Wikipedia dump on July 9, 2019 ( http://dumps. wikimedia. org/jawiki ) to learn the skip-gram vector space. All math expressions were segmented into words (i. e. symbols) and morphologically parsed using MeCab ( https://taku910. github. io/mecab/ ). Individual word segments were projected into the 300-dimensional space. Timepoints without any word vector assignments were defined as 0. The resultant concatenated vectors were downsampled to 1 Hz.
Encoding model fitting In the encoding model, the cortical activity in each voxel was fitted with a finite impulse response model that captured the slow hemodynamic response and its coupling with neural activity  ( Kay et al. , 2008a ; Nishimoto et al. , 2011 ). The feature matrix F E [ T × 6 N] was modelled by concatenating sets of [ T × N] feature matrices with six temporal delays between 2 and 7 s ( T = number of samples; N = number of features). The cortical response R E [ T × V] was then modelled by multiplying the feature matrix F E by the weight matrix W E [6 N × V] ( V = number of voxels): R 𝐸 = 𝐹 𝐸 𝑊 𝐸 We used L2-regularised linear regression with the training dataset (consisting of 2790 [2790 s] samples) to obtain the weight matrix W E. The optimal regularisation parameter was assessed using 10-fold crossvalidation where the 11 different regularisation parameters ranged from 1 to 2 10.
The test dataset consisted of 465 samples (465 s, repeated twice). Two repetitions of the test dataset were averaged to increase the signalto-noise ratio. Statistical significance (one-sided) was computed by comparing estimated correlations to the null distribution of correlations between two independent Gaussian random vectors with the same length as the test dataset. The statistical threshold was set at p < 0. 05 and corrected for multiple comparisons using FDR  ( Benjamini and Hochberg, 1995 ). For data visualisation on cortical maps, we used pycortex  ( Gao et al. , 2015 )  and fsbrain  ( Schäfer and Ecker, 2020 ).
RSA To compare ANN features with the sparse operator model, we performed RSA based on two different representational similarity matrices (RSMs). First, we calculated a reference feature vector for each operator type using the average features extracted from TP-Transformer for all trials in the training dataset. A feature-based RSM was calculated using the Pearson correlation distance across all combinations of the reference feature vectors for the nine tasks. Second, for each task, we averaged the weight vectors of the operator encoding model for all voxels included in each target anatomical ROI; six-time delays were further averaged. A brain-based RSM was calculated using the Pearson correlation distance across all combinations of the resultant mean weight vectors for the nine tasks. The upper triangular parts of the feature-based and brain-based RSMs were rearranged into single vectors and the Spearman's correlation coefficients between the two vectors were calculated.
Decoding model fitting In the decoding model, the cortical response matrix R D [ T × 6 V] was modelled using concatenating sets of [ T × V] matrices with temporal delays of 2-7 s. The feature matrix F D [ T × N] was modelled by multiplying the cortical response matrix R D by the weight matrix W D [6 V × N]: F 𝐷 = 𝑅 𝐷 𝑊 𝐷 The weight matrix W D was estimated using an L2-regularised linear regression with the training dataset, following the same procedure as for encoding model fitting. To examine the generalizability of our models, we performed three types of novel task decoding. Here, we use the term 'novel' to indicate decoding analyses where data on target tasks are not used in the training samples. (1) First, we performed nine independent model fittings, each using a different task as a target.
From the training dataset, we excluded the time points at which the target task is presented and those within 7 s after its presentation. In the test dataset, we used only the time points at which the target task is presented and those within 7 s after its presentation. This allowed us to assume that the activity induced by the target task (e. g. 'AddSub') and that induced by the other eight tasks ('Add', 'SubDiv', etc. ) did not overlap, and to investigate decoding accuracies for novel tasks. (2) Second, we performed two independent model fittings, where only single-or double-operator problems were used as training dataset; the remaining tasks (double-operators in case of single operators used in model training) were used in the model testing phase. (3) Third, we performed four independent model fittings with tasks containing one of the four operators ('Add', 'Sub', 'Mul' and 'Div') as targets, where tasks without the target operator were used in the model training phase (e.
Latent features extracted from ANN predicted the brain activity induced by mathematical problems To investigate whether the symbolic operator and latent ANN features capture brain representations of math problem solving, we constructed voxel-wise encoding models with both types of features using the training dataset and quantified the prediction accuracy of each model with the test dataset ( Fig. 1 B  ). Both models significantly predicted the activity of large brain regions of the bilateral frontal, parietal and occipital cortices (operator model, prediction accuracy across whole cortex = 0. 040 ± 0. 026 (mean ± s. d. ), 21. 5 ± 9. 4% of voxels were significant; ANN model, prediction accuracy = 0. 045 ± 0. 025, 22. 8 ± 10. 0% of voxels were significant; Figs. 2 A, S1  ). The overall prediction maps between operator and ANN models were similar across all cortical voxels (Spearman's correlation coefficient, 𝜌 = 0.
The ANN model enables decoding novel math problems To further examine the generalizability of the ANN model across different mathematical operations, we performed a series of decoding analyses based on ANN features ( Fig. 5 A  ). While encoding models can quantitatively assess differences between brain regions with respect to feature representations, decoding models have an advantage in quantitatively evaluating differences between stimulus features with respect to brain responses. The decoding approach is thus useful to examine whether certain operators are more easily decodable from brain responses and whether their information can be generalised. First, the generalizability of decoding models was evaluated by training a decoding model using eight of the nine tasks in the training dataset (e.
g. 'Add', 'Sub', 'Mul', 'Div', 'AddMul', 'AddDiv', S'ubMul' and 'SubDiv') and testing it with the remaining operator in the test dataset (e. g. 'AddSub'). Second, decoding accuracy was calculated as the AUC ( Fig. S8  )  ( Nishida and Nishimoto, 2018 ). As a result, mathematical problems were significantly decoded for all subjects (mean decoding accuracy across nine tasks, 0. 724 ± 0. 031; one-sided permutation test for average decoding accuracy, p < 0. 001, FDR corrected; Fig. 5 D  ). Next, we investigated if the generalizability of decoding accuracy was confined to a specific problem structure (i. e. single-or doubleoperators), as math problem structure may affect brain activity patterns  ( Nakai and Sakai, 2014 ). We thus trained decoders using single operators in the training dataset and tested with double-operators in the test dataset; inversely, decoders trained using double-operator problems were applied to single-operator problems in the test dataset ( Fig.
5 B  ). In both cases, the decoding accuracy was larger than chance (0. 5) for all subjects (mean decoding accuracy across nine tasks, 0. 670 ± 0. 044; p < 0. 001, FDR corrected; Fig. 5 E  ). Although the above analysis significantly decoded operators not used for model training, since part of the single operators in the training dataset  ('Add' and 'Mul')  were also used amongst the double-operators in the test dataset (e. g. 'AddMul'), we constructed additional decoding models without a target operator (e. g. without 'Add', 'AddSub', 'Ad-dMul' and 'AddDiv') and tested them with the target operator (e. g. 'Add') ( Fig. 5 C  ). We again found significant decoding accuracy for all four target operators (mean decoding accuracy across nine tasks, 0. 721 ± 0. 034; p < 0. 001, FDR corrected; Fig.
, 2021 ) , the relatively small number of subjects involved may affect the current findings. Indeed, two subjects out of eight showed inconsistent patterns of prediction map similarity ( Fig. 2 C, D  ). These subjects, however, also showed a significant correlation between FBS and operator-weight maps ( Fig. 4 E  ), indicating that the representational relationship between the sparse operator and latent ANN models is robust across individuals. Further research on a larger dataset may clarify individual differences in the distributed brain representations of mathematical operations. The current study is a first step toward ANN modelling of the brain representations of complex human cognitive abilities, such as mathematical thought, bridging the gap between symbolic and distributed representations found in human neuroimaging.
Acknowledgements We thank  MEXT/JSPS KAKENHI  (grant numbers  JP17K13083  and  JP18H05091  in #4903 (Evolinguistics) for T. N. ,  JP15H05311  and  JP18H05522  for S. N. ),  JST CREST JPMJCR18A5 ,  ERATO JPMJER1801  (for S. N. ), and  H2020   Marie Sk ł odowska-Curie Actions  (grant number  101023033  for T. N. ) for partial financial support of this study. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.
For each parameter set, simulations were replicated 10 times, and the average number of diploid TE copies was reported. Average cluster frequencies were calculated by dividing the number of diploid TE copies in pi-clusters by 2k; frequencies could theoretically be slightly > 1 due to rare events in which several TEs could insert simultaneously in the same cluster. The simulation software was implemented in python (version 3. 8. 10 for Linux), with data structures from the numpy library  (Harris et al. 2020 ). The code is available at https://github. com/siddharthst/Simulicron/tree/amodel.
Therefore, future studies that can capture more information on risk of exposure and additional lifestyle factors could help refine the identification of mechanistic correlates of immunity, which could be used to improve vaccine design. Fifth, cytokine release by neutrophils was measured in the absence of complement (due to heat inactivation). Thus, although we do not think that complement affects the interpretation of our data, future studies examining the interaction of simultaneous FcR binding and complement activation would be of great interest. Sixth, data presented in the manuscript do not include the validation sample sets. Due to sample limitation (as a part of a phase 2b/3 trial), most experiments were performed as technical replicates. However, the functional validation by biochemical and molecular assays was implemented to further understand and confirm the unique signatures observed in the initial screening.
A nucleic acid amplification test was used to detect SARS-CoV-2 infection at routine scheduled visits and whenever participants had any symptoms suggestive of COVID-19. Cases were selected as individuals who received two doses of the ChAdOx1 nCoV-19 vaccine and had confirmed COVID-19 more than 14 days post-boost by the positive PCR test result. Controls were randomly selected from a subset of seronegative participants at baseline, based on SARS-CoV-2 nucleocapsid-specific antibody testing and allocated to the vaccination arm, and were demographically matched based on sex (males versus females), age (20-60 years), BMI categories (normal, obese, overweight and underweight) and race (black, mixed, others and white) (Table  1 ). The trial (Clinicaltrials. gov no. NCT04444674; Pan African Clinical Trials Registry no.
Cytokine release assay The yellow-green (505/515-nm) fluorescent beads were coupled with SARS-CoV-2 WT S protein and incubated for 2 h at 37 °C with the diluted pooled samples (1:100 dilution) to form immune complexes. Once the incubation was completed, 5 × 10 5 cells ml -1 of RBC-lysed whole blood were added to the immune complexes and incubated for 18 h at 37 °C. Subsequently, the supernatant was collected and ProcartaPlex Multiplex Immunoassay (Thermo Fisher Scientific) was performed according to the manufacturer's instructions. Briefly, the supernatant was coupled with the cortisol beads, incubated with detection antibody and streptavidin-PE (Thermo Fisher Scientific). The data were acquired on Luminex FLEXMAP 3D (Thermo Fisher Scientific) and analyzed via xPONENT.
LC-MS data processing MzXML files were generated from raw LC-MS spectra. An in-house-developed software, LaCyTools, was used for the alignment and targeted extraction of raw data  96. Alignment was performed based on the average retention time of a minimum of three abundant IgG1 glycoforms. The targeted extraction list included analytes of the 2 + and 3 + charge states and was based on manual annotation of the mass spectra as well as on the literature  97, 98. A pre-COVID-19 plasma pool (Visucon-F) was measured in triplicate to assess method repeatability and used as a negative control. Signals were integrated by covering a minimum of 95% of the area of the isotopic envelope of glycopeptide peaks. The inclusion of an analyte for the final data analysis was based on quality criteria such as signal:noise ratio (>9), isotopic pattern quality (<25% deviation from the theoretical isotopic pattern) and mass error (within a ±20-p.
Statistics Data analysis was performed using R v. 4. 0. 2 (2020-06-22). Comparisons between SARS-CoV-2-infected and -uninfected individuals were performed using a Mann-Whitney U-test test followed by a Benjamini-Hochberg correction. Antigen responses (for example, WT to beta) were compared using Wilcoxon's signed-rank test followed by a Benjamini-Hochberg correction. Classification models were trained to discriminate between infected and uninfected individuals using all the measured antibody responses. Before analysis, all data were normalized using z-scoring. Models were built using a combination of LASSO for feature selection and then classification using PLS-DA with the LASSO-selected features  99  and R package 'ropls' v. 1. 20. 0 (ref. 100) and 'glmnet' v. 4. 0. 2. Model accuracy was assessed using tenfold crossvalidation.
The cocorrelate network was generated using R package 'network' v. 1. 16. 0 (ref. 102). All other figures were generated using ggplot2 (ref. 103 ). To assess the potential confounding effects of the demographics, for each feature null and full linear models were fit. Null models consisted of sex, age, BMI, race, alcohol and smoking status. The full models additionally included the group effect (COVID-19 uninfected or with COVID-19). A likelihood ratio test was then applied using the null and full models to obtain the significance of the group effect as P values. These P values were then plotted against the coefficient of the group effect.
Acknowledgements We thank  N. Zimmerman ,  M. and  L. Schwartz , an anonymous donor (financial support),  T. and  S. Ragon , and the  SAMANA Kay Massachusetts General Hospital (MGH)   Research Scholars  award for their support. We acknowledge support from the  Ragon Institute of MGH, Massachusetts Institute of Technology (MIT)  and  Harvard , the  Massachusetts Consortium on Pathogen Readiness  and the  National Institutes of Health  (grant nos. 1P01AI165072-01 ,  3R37AI080289-11S1 ,  R01AI146785 ,  U19AI42790-01 ,  U19AI135995-02 ,  U19AI42790-01 ,  1U01CA260476-01  and  CIVIC75N93019C00052 ). The  ChAdOx1 nCoV -19  phase 3 study was sponsored by the  University of Oxford  and funded by the  Bill and Melinda Gates Foundation  (grant no. INV-017710 ), the  South African Medical Research Council  (grant no.
This article describes a 30-year data series produced by the SRN ("Suivi Régional des Nutriments" in French; Regional Nutrients Monitoring Programme) network managed by Ifremer. Since 1992, the SRN network has been analysing phytoplankton species and measuring physicochemical (temperature, salinity, oxygen, suspended matter, nutrients) and biological (chlorophyll a, phytoplankton abundance) parameters at 10 different stations distributed along three different transects located in the eastern English Channel and the Southern Bight of the North Sea. This geographic coverage allows for the study of three distinct ecosystems, i. e. three transects (estuary, coastal region under freshwater influence, and coastal region), as well as the investigation of coastal to offshore water gradients. The SRN collects a maximum of 184 samples per year (3687 samples spread over 10 stations during the studied period) and detects up to 291 taxa, including harmful algal bloom species (HABs), with a bi-weekly to monthly sampling frequency (depending on the location and the season).