dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2003; Harmon et al. , 2010). Multivariate models were fitted using the mvMORPH package  (Clavel et al. , 2015). We selected the best fitting model using the Akaike information criterion (AIC), corrected for small sample sizes (AICc). AIC takes into account the number of parameters p in the model: AIC = -2log ( likelihood ) + 2p. This approximation is insufficient when the sample size is small, in which case an additional correction is required, leading to the corrected AIC: AICc = AIC + ( 2p 2 + 2p ) / ( n -p -1 ) , where n is the sample size. The analysis of phylogenetic data is challenging especially when the number of species is reduced, the number of traits studied is large and the models to fit are complex. Cooper et al. , 2016, have  warned in particular about fitting OU models using likelihood-based methods, and the possibility of incorrectly selecting them even when data was generated from a BM process.
Estimation of ancestral phenotypes Fitting of evolutionary models allows us to obtain estimation of the ancestral states of the phenotypes under study. Our phenotypes showed a strong correlation pattern. Instead of estimating ancestral states for each of them independently, we estimated the ancestral state of the first two principal components for all nine phenotypes, and also for a reduced set of phenotypes including only neuroanatomical measurements. All the code necessary to reproduce our analyses is available at https://github. com/neuroanatomy/ comp-cb-folding (copy archived at  Heuer et al. , 2023).
Acknowledgements We thank  Carol MacLeod ,  Fahad Sultan ,  David DiGregorio , and  Maria Castelló  for discussions on cerebellar evolution and cerebellar folding, and  Liam Revell  for help and advice with phylogenetic analyses. Funded by project  NeuroWebLab  ( ANR-19-DATA-0025 ),  DMOBE  ( ANR-21-CE45-0016 ), the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreement No  101033485  ( KH Individual Fellowship ), and the  STIC-AmSud programme  project  STIC-AMSUD+CLANN 22-STIC-03.
ACKNOWLEDGMENTS This work was supported by the  Spanish Ministry of Science and Innovation  (Grant No. MCIN/AEI/10. 13039/501100011033 )through Project No. PID2021-122613OB-I00. J. S. thanks  Rafael Larrosa ,  Darío Guerrero , and  F. Moreno  for the technical support in running the calculations and the  SCBI (Supercomputer and Bioinformatics) of the Univ. Málaga  for computer and software resources.
1a  and b ). We also evaluate the data in a sequence biostratigraphic framework to unravel the dynamics of the depositional environments throughout the section. Additionally, we use bioclimatic analysis to quantitatively reconstruct the climate based on the main climatic variables. We apply the rarefaction method to analyze the sporomorph diversity in the Yaw Formation and compare this with four other middle to late Eocene tropical sporomorph assemblages. This enables us to estimate how climate change and tectonics stimulated plant diversity. Together, these analyses allow us to understand the relation between vegetation, depositional environments, and plant diversity with climate and geological driving factors in the late Eocene CMB.
Palynological analysis and microphotography In total, 56 samples were productive for pollen analysis and with a pollen count of c. 100 specimens or more. The identification of specimens was carried out using the palynological literature from the America, China, Thailand, India, and Vietnam, and particularly from regions in the proximity of the Kalewa section, such as Assam (India) and Tibet (China) (e. g. ,  Germeraad et al. , 1968; Sah and Dutta, 1966; Morley, 1998 Morley, , 2013;; Jaramillo and Dilcher, 2001; Saxena and Trivedi, 2009; Jardine, 2011). All pollen grains from Kalewa were counted using a LEICA DM LB2 LM, and a Zeiss Axiophot Microscope at the Institute for Biodiversity and Ecosystem Dynamics (IBED). Pollen count data are shown in Supplementary Data (Table  S1 ). Pollen diagrams were made in Tilia 2.
1. 1  (Grimm, 1991)  with cluster analysis program CONISS  (Grimm, 1987). LM micrographs were produced with a FUJIFILM X-M1 digital camera (Fujifilm Holdings Corporation, Tokyo, Japan) connected with a Zeiss Axiophot Microscope (Carl Zeiss, Oberkochen, Germany) under the 630× magnification (with oil) at the IBED. We also investigated the morphological details of the sporomorphs under a JEOL JSM•6400 SEM at the DoP, with the singlegrain analysis method  (Zetter, 1989; Halbritter et al. , 2018). The micrographs were then processed in the software CorelDRAW 2019  (Corel Corporation, Ottawa, Canada). Each palynomorph under LM/SEM in Figs. 4  and 5  was referenced with sample number, residue number, and the "England Finder" coordinates if applicable (Supplementary Data, Table  S2 ).
gbif. org). These data were processed to delete duplicated and misplaced points following the methods of  Palazzesi et al. (2014)  and  Zizka et al. (2019). Corresponding climate variables were extracted from the WorldClim Version 2 (https://worldclim. org/version2, 30 seconds in resolution). The modern climate variables in the study area were also derived from WorldClim Version 2 with a resolution of 30 seconds. As currently Kalewa is located at a different latitude (Fig. 1b ; c. 23° N) from the Eocene (Fig. 1c ; c. 5° N;  Westerweel et al. , 2020) , the modern climate variables were also derived from the Phiman area (Fig. 1b ; 6°37′ N, 100°4′ E) in Thailand for comparison. Like for the Eocene Burma Terrane, the Phiman area is located on the eastern shorelines of the broader Bengal Bay and is close to the equator.
We assessed withinsample evenness (a parameter indicating relative abundances of the various sporomorphs in a sample) through the time series with the E var evenness metric of  Smith and Wilson (1996). The Chao1 richness estimator was used to estimate total richness  (Chao and Jost, 2012). R v. 3. 6. 1 (R Core team, 2019) was used to perform diversity rarefaction (sampling standardization and Chao1 metric calculation) with the iNEXT package  (Hsieh et al. , 2014).
However, geochemical proxies yield warmer, not cooler near-equatorial surface temperatures globally (e. g. ,  Peason et al. , 2001; Keating-Bitonti et al. , 2011; van Dijk et al. , 2020) , raising doubts about the accuracy of paleobotanical temperature estimates. We see four possible explanations in the Eocene cooler temperatures found in the monsoonal domain: (1) Mis-identification of the NLRs of fossil taxa can introduce errors in climate reconstructions; this mechanism could explain our results, obtained with BA, but does not explain cooler temperatures found with morphological methods that do not rely on the NLRs (e. g. , CLAMP;  Shukla et al. , 2014; Spicer et al. , 2014; Bhatia et al. , 2021) ; (2) The botanical database on which climatic parameters are extracted is incomplete (GBIF database for BA), and do not contain enough occurrences to fully cover the entire monsoonal domain; this explanation stands for the GBIF database but not for CLAMP approaches, that have been calibrated with many monsoonal stations (e.
10. Abbreviations: tr. = trees, shr. = shrubs. Table  1. Summary of pollen zones. Table  2. Bioclimatic analysis of sporomorphs in the Yaw Formation in the Kalewa section, Central Myanmar Basins and the modern-day levels of Kalewa area and Phiman area (Thailand) estimated based on their coordinates via the WorldClim Version 2 database (https://worldclim. org/version2). Note that as Kalewa area is situated in the foothills of the Indo-Burman Ranges (IBR), it constitutes a transitional region between the central dry belt and the IBR; The estimated mean temperature of coldest quarter (MTCQ) of the modern-day level (18. 9 °C) is much lower than that in the late Eocene (24. 6 °C), which may be because there are mountainous areas nearby, that were incorporated in the WorldClim. Based on information from adjacent climate stations, its MAP should be 900-1700 mm, of which Kalewa climate station shows 1641 mm  (Lai Lai Aung et al.
Acknowledgements We are indebted to all members of the  Myanmar Paleoclimate and Geodynamics research group  for sample collection. We thank  Annemarie Philip  and  Malcolm Jones  for processing palynological samples;  Friðgeir Grímsson  and  Reinhard Zetter  for assistance on microphotography and identification of palynomorphs;  Shufeng Li  and  He Tang  for help on bioclimatic analysis;  Phillip Jardine  for support on rarefaction analysis and helpful comments on an initial draft. We also thank the two anonymous reviewers for their constructive comments that helped us to improve the manuscript. H. H. was supported by the  China Scholarship Council  ( CSC grant   201604910677 ) and the  University of Amsterdam ; A. L. , G. D. -N. , and J. W. acknowledge the  European Research Council   Consolidator Grant  ( MAGIC 649081 ); A.
Ar/Ar Ages Excellent to acceptable Ar/Ar ages were obtained from most VESPA samples. A summary of the preferred Ar/ Ar age for each of the 33 dated samples is presented in Table  1 , and associated age spectra are shown in Figure  6. A tabulated summary of results for all 49 dated mineral and groundmass separates is given in Supporting Information S5 and all raw data and spectra in Supporting Information S6. The methods used to obtain reported ages and age uncertainties vary. For samples that yield straightforward plateaus, where well over 50% of the 39 Ar is released in consecutive steps that are concordant (i. e. , lie within 2σ analytical uncertainty of each other), we follow the widely accepted convention (e. g. ,  McDougall & Harrison, 1999)  of calculating a weighted mean plateau age (WMPA), with each step weighted according to its analytical uncertainty, and calculate an uncertainty in the age (2σ, 95% confidence) from the weighted mean uncertainty of all steps used in the calculation.
Acknowledgments We thank the captain and crew of  N/O l'Atalante  for a productive and enjoyable cruise. We also thank  Walter Roest ,  Rick Herzer ,  Gilles Chazot ,  Méderic Amann ,  Claire Bassoullet ,  Charline Guérin ,  Nina Jordan ,  Caroline Juan ,  Mathieu Mengin ,  Mathilde Pitel ,  Clément Roussel , and  Fanny Soetaert  for project discussions and/or onboard geological assistance. John Simes ,  Ben Durrant ,  Belinda Smith Lyttle ,  Brent Pooley ,  Matt Sagar , and  Malcolm Reid  gave post-cruise technical help. This manuscript benefitted from comments by internal reviewers  Wanda Stratford ,  James Conrad  and  Michael Clynne , and journal referees  Scott Whattam ,  Sebastien Meffre , and an anonymous reviewer. The VESPA cruise was funded by the  Commission Nationale Flotte Hauturière of the French Ministry of Research and Higher Education , with support from the governments of  New Zealand and New Caledonia.
Data Availability Statement All eight Supporting Information files for this paper are available on the SEANOE website at https://doi. org/10. 17882/89740. The whole rock geochemical analyses of VESPA rocks are available in a data file at https://doi. org/10. 17882/90050. Additional information about the VESPA cruise, including the  Mortimer and Patriat (2016)  voyage report, can be found at https://doi. org/10. 17600/15001100.
Methods The simulations were performed using Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software  [23] , and the Embedded Atom Method (EAM) potential, developed by Pan et al. for the Ag-Ni binary system  [24]. The structural parameters (lattice parameter and cohesive energy) and thermodynamic properties (melting temperature) are reported in Table  1. The calculated values of melting temperature are close to the experimental ones. The temperature evolution of the lattice parameter a 0 was evaluated and results are reported in Appendix A. Bimetallic interfaces can be classified according to their crystal structure and mismatch between the two lattices  [1]. At coherent interfaces, two metals in contact have identical crystal structures with similar values of lattice parameters.
Ni 2d = p 2 δp + p ( 4 ) where p and p + δp are the periods of the two 1D lattices. The atoms arrangement at the (001) interface is displayed in Figure  2b , in the case of the bilayer Ag-Ni system. As expected, we observed pale and dark zones, typical of Moiré fringes. In dark area, we observed Ag unit cells in the Ag layer and Ni unit cells in the Ni layer. We expect that atoms keep their fcc structure in dark zones. For system B, we considered a bilayer system with two grains in the Ni layer, as shown in Figure  3a. The atomic configuration corresponds to a Σ5(310)[001] symmetric tilt grain boundary that was built using Atomsk software  [26]  by rotating the two lattices by an opposite angle of magnitude 18. 435 • (Figure  3b ). The corresponding grain boundary energy was evaluated in  [27]  for the Pan potential: γ GB = 1.
Acknowledgments This work was funded by the  TOAD  (The  Origin of Aeolian Dunes ) project (funded by the  Natural Environment Research Council, UK  and  National Science Foundation, USA ;  NE/R010196NSF-GEO-NERC ,  NSF-GEO-1829541 , and  NSF -GEO-1829513 ). Research was undertaken at GSD under a Scientific Research and Collection permit  GRSA-2018-SCI-004 , and we are very grateful for support from  A. Valdez  and  F. Bunch. For the Huab fieldwork, we acknowledge  Gobabeb Namib Research Institute ,  J. Kazeurua ,  I. Matheus ,  L. Uahengo , MET and NCRST (permits 1913/2014; 2051/2015;  2168 /2016 ,  RPIV00022018 ),  RPIV00022018 ). Data processing used the  IRIDIS Southampton Computing Facility. J. M. Nield  was supported by a  Department of Geology and Geophysics, Texas AM University ,  Michel T   Halbouty Visiting  Chair during the GSD field campaign.
Data Availability Statement The data used in this manuscript can be found in the NERC National Geological Data Center: Huab river valley data set (https://doi. org/10. 5285/99e4446f-c43a-492d-83c9-e896206649c0, Nield et al. , 2022a)  and Great Sand Dunes National Park data set (https://doi. org/10. 5285/46e9ff95-27ca-4d3b-b587-fc9ce22c5781,  Nield et al. , 2022b). Supplementary figures and text can be found in Supporting Information S1.
Contrary to 2D FFT, which requires this interpolation step for data reduction to a common altitude, the RHA modeling can also deal with measurements acquired at different altitudes. This represents a valuable advantage over the 2D FFT because there is no need to remove the average field value for each survey, but only to remove the average field for all surveys. This better preserves the large wavelengths and opens a way to iteratively incorporate new UAV surveys to the full dataset. This possibility also shows that RHA can deal with measurements acquired over (reasonably) large geographical extensions for which constant altitude measurements in a geographic reference frame correspond to non constant altitudes in the Cartesian reference frame. Therefore, RHA as it is defined here is not a planar approximation because the geographical coordinate system can be converted into the Cartesian one while accounting for the curvature of the Earth in the variations of z.
The weighting matrix W is then updated according to the misfit residuals following the implementation advocated by Huber ([11], chapter 7), and successive inversions are performed until the model parameters converge. Once the model parameters p are obtained, the forward problem is computed on a regular grid and at a constant altitude. In this paper, magnetic field component maps are displayed at the minimum altitude of the full dataset, but this could be modified in the code. During this forward computation on the regular grid, we address the well-known drawbacks occurring with periodic functions. When the functions to be represented (here, the magnetic field components) are themselves not periodic, the solutions are convergent in the mean square sense, subject to ringing near the boundaries, and prone to the Gibbs effect (e.
Computation of Synthetic Datasets We test the efficiency of RHA and its ability to model the Earth's magnetic crustal field. Three closed-loop numerical experiments are carried out. In the first test, we consider the original aeromagnetic grid of the French metropolitan territory  [22]  and compute a total field intensity for the main and the lithospheric fields. The original French anomaly intensity grid, not in the public domain, was included in the World Magnetic Anomaly Map (WDMAM-2,  [23] ). We compute the Earth's core vector field with the CHAOS-7 model  [21]  expanded to spherical harmonic (SH) degree 15 at epoch 2023. 0 in decimal year. The vector crustal field contributions are computed from SH degree 16 to 1319 using the extended dedicated lithospheric field model derived with the WDMAM-2 map and the European Swarm satellite measurements  [24].
The maximum spatial resolution of the combined core and crustal field models is about 30 km at the Earth's mean radius. The anomaly intensity is then computed by subtracting the total intensity of the core field from the combined core and crust intensity values. For this synthetic dataset, hereafter named SYN-AERO-PERFECT, we do not assign any weight and the measurements are perfect (no noise added). The locations of the synthetic data anomaly intensity projected in the Cartesian reference are shown in Figure  3a. For the second analysis we use a series of UAV real surveys to generate a realistic data distribution. Part of these surveys were acquired over the Puy de Dôme volcano (Massif Central, France) by our group during the validation/calibration phase of UAVs as an efficient platform for magnetometry  [25].
However, we purposefully stretch both the altitudes and the areas in order to test the efficiency of RHA to model significant altitude differences over dimensions larger than individual surveys. This is also a way to test the ability of RHA to patch together small-dimension surveys in a consistent way, and to secure wavelengths larger than the dimensions of the individual surveys. The full dataset, hereafter named SYN-UAVS-PERFECT, contains 24 surveys covering altitudes between 5. 2 and 20. 0 km. The total intensity measurements are computed in a similar way to before. The synthetic measurements have no weight and contain no noise. The data locations are displayed in the Cartesian reference frame in Figure  3b. Finally, we simulate a series of noisy scalar measurements by adding a geophysical noise to the SYN-UAVS-PERFECT dataset.
The noise is computed by selecting the time series of the permanent magnetic ground station installed at Clermont-Ferrand in November 2021 (International Association of Geomagnetism and Aeronomy code "CMF" available at Bureau Central de Magnétisme Terrestre-BCMT: http://www. bcmt. fr, accessed on 13 September 2023, located in Figure  3 ). This station delivers minute vector and scalar measurements. We extract from the database the intensity channel between 23 April 2023 0:00 LT and 24 April 2023 23:59 LT. This corresponds to a period during which a magnetic storm classified as severe was measured worldwide (G4, following the National Oceanic and Atmospheric Administration classification). The intensity signal is high-pass filtered in order to remove the global magnetospheric field variations with periods larger than 20 min, which is typically the duration of a UAV survey.
The remaining rapid geophysical variations considered as the natural noise (Figure  4 ) are then added to the crustal field signal computed at each data location and altitude. This noise that is correlated in time and not stationary is more realistic than pure random noise. When superimposed to the crustal field signals it introduces magnetic field variations along the UAV trajectory that mimic well noise contamination and flight-line offsets. The corresponding dataset is hereafter named SYN-UAVS-NOISED.
Results and Discussion RHA models are derived from the three datasets described above. For the test case computed with the dataset SYN-AERO-PERFECT, we derive a model over France from the regular scalar anomaly grid to maximum expansion indices N = M = 30 in the infinite series (Equations 9a-9c). For the inversion of datasets SYN-UAVS-PERFECT and SYN-UAVS-NOISED, the maximum truncation indices are set to N = M = 15. According to Equation (  8 ), the maximum spatial resolution for all three cases is about 30 km in the east and north directions. We remind the reader that the synthetic measurements were also computed with a global model to the maximum spatial resolution of about 38 km. Therefore, these RHA truncation indices correspond to the spatial information content of the synthetic measurements.
One primary conclusion of this test is that RHA, which is a Cartesian representation, can be used to derive magnetic field models in the geocentric reference frame even when the curvature of the Earth cannot be neglected over extensions as large as 1000 km. Regarding the realistic UAV data location experiments, the standard deviation between the synthetic measurements at their actual location and the RHA model predictions derived from the SYN-UAVS-PERFECT and SYN-UAVS-NOISED datasets are 0. 2 nT and 1. 5 nT, respectively. The misfit value for the RHA model based on the noisy dataset corresponds to the level of noise introduced in the dataset (Figure  4 ). The scalar and vector field models are then predicted on a regular grid at a constant altitude of 5 km above the Earth's mean radius. Both residual maps between the intensity anomaly RHA predictions and the expected synthetic anomaly field values computed with the global spherical harmonic model  [24]  are displayed in Figures  6a  and 7a , respectively.
The residuals show almost identical misfit patterns, with a comparatively larger amplitude for the model obtained with the noisy measurements. The vector field model derived from the SYN-UAVS-NOISED dataset is slightly noisier than the vector field model obtained with the SYN-UAVS-PERFECT one. Figure  8a  shows the initial geophysical noise (displayed as a time series in Figure  4  bottom) in the geographical frame that was added to the intensity data for the numerical simulation with the SYN-UAVS-NOISED dataset. This noise manifests itself as rapid spatial variations, along-flight errors, and data incompatibility in overlapping areas, but the algorithm identifies and downweights most of the noisy data (Figure  7b ) during the inversion process. It should be noted that the geophysical noise we added comes from a magnetic field time series during a magnetic storm.
With this signal being a time varying potential field, some of its contributions leak into the crustal field model in the geographic reference frame. For both cases on UAV real trajectories there is no spatially coherent residuals between the model and the expected field, except near the edges where no measurement was available to build the RHA models. This indicates that the RHA models did not miss either large-or small-scale structures contained in the data. We remind the reader that intensity anomaly and vector field maps are leveled at the constant altitude of 5. 2 km over a regular interpolation grid. The leveling altitude corresponds to the minimum altitude present in the dataset. Since the initial data altitudes comprise between 5. 2 km and 20 km according to Figure  3b , the computation of the vector model corresponds to a downward continuation in all locations except for a small part of the southwest quadrant.
Data Availability Statement: The lithospheric magnetic field used for the synthetic analyses is available at https://swarm-diss. eo. esa. int/#swarm/Level2longterm/MLI/SW_OPER_MLI_SHA_ 2E_00000000T000000_99999999T999999_0801. ZIP, accessed on 13 September 2023. The auxiliary core field model CHAOS-7 is available at https://www. space. dtu. dk/english/research/scientific_ data_and_models/magnetic_field_models, accessed on 13 September 2023. The synthetic datasets generated for this study and the code are available as an archive at https://www. opgc. fr/DOI/ DataSoft/1qg6-qh39/RHA_optim_final. zip, accessed on 13 September 2023, under the Creative Commons licence with doi: https://doi. org/10. 25519/1QG6-QH39, accessed on 13 September 2023.