dataesr/scientific-paragraphs-categorization huggingface dataset:
In this example, the desired output of the model is the class of magnetism exhibited by the material. For magnetic propagation vector classification, we collected 1,562 material structures with known magnetic properties from experiments to train and validate the model. NN was chosen as the model architecture due to its ability to incorporate complex interactions present in the materials. For magnetic order classification, a larger density-functional-theory (DFT)based database from Materials Project  [Jain 2013 ] is used. Compared to other methods such as decision trees, NNs can capture intricate relationships between input features and output labels, even in cases where it is challenging to separate the contributions to magnetism from different factors. In particular, we utilized a specialized NN called GNN for their model architecture.
GNNs are well-suited for modeling material structures as crystal graphs, and in this particular case, with added symmetry to the GNN, it allows for the inclusion of Euclidean symmetry considerations. The results demonstrate the effectiveness of the developed model in predicting the category of magnetism with an average accuracy of 77. 8%, and with 73. 6% for propagation vector prediction. By training the model on a large dataset of material structures, it achieved high accuracy in correctly classifying the magnetic properties of new materials. This suggests that the model is capable of capturing the complex relationships between material structures and their magnetic behaviors, though there is still room for further improvement. The findings contribute to the field of materials science by providing a valuable tool for predicting magnetism in various materials, thereby facilitating the discovery and design of new magnetic materials.
B. Topological Properties Topological insulators (TIs) or topological semimetals (TSMs) are condensed matter systems exhibiting robust edge or surface modes and quantized bulk response functions due to the topological properties of their electronic wavefunctions. The advent of symmetrybased indicators probing topology or topological quantum chemistry allowed the creation of large catalogs of topological materials  [Vergniory 2019 ], with high throughput DFT calculations  [Vergniory 2022 ]. The graphical user interface (GUI) is shown in Fig. 3(a). Predicting topology through ML faces several challenges: a relatively small dataset (in this study 38,298 stoichiometric unique compounds), the outcome being a label rather than an "energetic" quantity and the usage of unstructured features. Our results  [Claussen 2020 ] use a simplified approach based on GBTs, an improved version of the binary tree classifiers depicted in Fig.
E. New Permanent Magnets A method similar to case study D was used in the first part of this study. It involved using regression and principal components for dimensionality reduction to create a model. This model (ML1), partial least squares regression  (PLSRegression [Höskuldson 1988 ), could predict the intrinsic material properties of permanent magnet materials, spontaneous magnetization µ0MS and uniaxial anisotropy constant Ku, based on the chemical formula of the 2-14-1 system  [Marinescu 2002 ]. The training data came from an experimental database and was further enhanced with a large database of DFT calculations for different chemical combinations of the elements, Nd, Pr, La, Ce, Ni, Fe, Co and B, within the same system. When a magnet engineer/developer needs to find the most suitable material combination for their application, they can use this trained model inversely.
ACKNOWLEDGMENT R. O. and M. L. acknowledge the support from  U. S. Department of Energy (DOE), Office of Science (SC), Basic Energy Sciences (BES) , Award No. DE-SC0021940. Y. I. was supported by  Japan Science and Technology Agency (JST) Core Research for Evolutionary Science and Technology (CREST)  (Grant No. JPMJCR21O1 ). M. S. and A. H. also thank the financial support by  JST-CREST  (Grant No. JPMJCR17J5 ). A. K. and T. S. gratefully acknowledge the financial support by the  Austrian Federal Ministry for Digital and Economic Affairs , the  National Foundation for Research, Technology and Development, Austria , the  Christian Doppler Research Association, Austria , and  Toyota Motor Corporation. Data of first-principles computations of permanent magnet properties used in this work was computed using the facilities of the  Supercomputer Center of the Institute for Solid State Physics at the University of Tokyo , and computational resources of supercomputer Fugaku provided by the  RIKEN Center for Computational Science  (Project ID:  hp220175 ).
In contrast, when only focusing on a particular application, one may develop associated specific data models and unmixing methods. This is especially what we did for coastal water remote sensing in the framework of the HypFoM project (see https: //anr. fr/Projet-ANR-15-ASTR-0019, accessed on 1 February 2023). We took various physical phenomena into account, including the influence of adjacent pixels, often referred to as the "adjacency effect"  [48]  (this effect was also considered in the literature, for instance in  [49] , but in the atmosphere). We thus derived the data model reported in  [50]. We then developed a corresponding unmixing method  [50] , which is "not blind" or "only partly blind", in the sense that it assumes various parameters of the above mixing model to be known and it then only estimates the other parameters.
These vectors depend on the considered water quality (clear or standard) and on the depth d i of the considered pixel i. We set these depths by creating a synthetic sea bottom profile, first defined by a reference depth d re f and where each pixel depth d i is randomly and uniformly drawn in an interval ranging from -∆ to +∆ around depth d re f. The vectors k 1 and k 2 were first computed by the OSOAA software only for depths equal to 1, 2, 3, 4, 5 and 10 m. For any considered sea profile, these results from OSOAA were then used to derive the values of k 1,i and k 2,i for any depth d i of a pixel i of the considered scene. To this end, the following linear interpolation was used: k 1,i = (0. 5 -α)k 1 (d - i ) + (0. 5 + α)k 1 (d + i ) ( 13 ) k 2,i = (0. 5 -α)k 2 (d - i ) + (0. 5 + α)k 2 (d + i ) ( 14 ) where di and d + i are the pixel-dependent closest depths, respectively, below and above d i , for which OSOAA results are available (i.
00 • , as compared with the maximum values 4. 15 • and 5. 54 • obtained in the previous two cases. One may relate these values to the fact that the SAM-based classification method available in the commercial ENVI software, version 2019,  [59]  considers that spectra from a class have a SAM lower than 0. 1 rad 5. 73 • , with respect to the representative of that class. Therefore, for the maximum value ∆ = 0. 25 m, IP-NMF can hardly separate the considered classes of materials for the low signal magnitude faced in the difficult conditions considered in the present section. For the water depth variability defined by ∆ = 0. 25 m, IP-NMF is therefore of main interest for moderately deep water. However, when considering ∆ ≤ 0. 2 m, IP-NMF remains satisfactory even in the difficult conditions considered here, since the maximum SAM is then 5.
When wall effects are negligible, i. e. when D∕d → ∞ , the pressure drop depends only on Re and. In this case, the Ergun model  (Ergun 1952 ) is generally used to describe the pressure drop of random arrangements of spherical particles for low fluid volume fraction, and new correlation has been recently derived in  Dixon (2023)  by considering different datasets. Nevertheless, this model is not suitable for cases where the wall effects are evident, particularly when D∕d < 10 (  Eisfeld and Schnitzlein 2001; Erdim et al. 2015; Hill et al. 2001b; Clavier et al. 2015; Foumeny et al. 1993; Flaischlen et al. 2021). It has also been reported that, in the laminar regime with walls, the Ergun model underestimates the pressure gradient because of the additional reactor wall friction in the low-Re regime, whereas in the higher-Re case the pressure drop is less than that of Ergun since the effects of the local porosity near the walls increase ( ≈ 1 ), therefore acting as a less resistant path for the flow to go through  (Eisfeld and Schnitzlein 2001).
Pressure along the bed is measured using an array of ten pressure sensors, flushmounted along the column, and equidistantly distributed from each other at positions z i , where z = 0 corresponds to the bottom of the bed. The pressure probes are high-precision piezo-resistive sensors with a sensibility of 150mV/bar and a linear deviation of 0. 05%∕bar. In order to increase the signal-to-noise ratio, the signal is amplified by a homemade voltage amplifier with a gain G = 10 and digitized using a high precision data acquisition system (NI Dacq 4472: 8 channels, 21 bits, 100 kHz from National Instruments). As a consequence, signals from the flow meter and seven pressure sensors are recorded at a time with a 20 kHz sampling frequency, so that eventual pressure fluctuations due to fluidization or turbulence can be detected.
Computational Approach Similarly to experiments, the fixed bed generation is addressed numerically using a vertical cylindrical domain (for D∕d = 5 and D∕d = 8, 10 , respectively) and periodic boundary conditions at the top and bottom. The random arrangements of beads in the cylindrical container are built using the Discrete Element Method (DEM) software Grains3D  (Wachs et al. 2012). The fixed beds are done in three successive steps: first, the particles are dropped into a non-periodic cylindrical container with a fixed bottom. During this first step, the spheres are driven by gravitational and contact forces until they form a packed bed with a random arrangement. Afterwards, the two periodic ends of the bed are set at the minimum and maximum positions of the settled particles (these will be the inlet and the outlet of the system), and they are given an initial random velocity so that they can move inside the now periodic domain.
Acknowledgements This work was supported by  H2020 -MSCA-ITN-EJD/ED-ARCHMAT  action under the  Marie Sklodowska-Curie grant  agreement no. 766311. Partial support is obtained from  Gobierno de Aragón  (research group  T54_20R ). The use of  Servicio General de Apoyo a la Investigación at the University of Zaragoza  is acknowledged. This work has been performed in the framework of the  Unidad Asociada de I + D + I al CSIC "Vidrio y Materiales del Patrimonio Cultural (VIMPAC) ", by  INMA (CSIC-University of Zaragoza)  and  University of Burgos.
For bacteria growth monitoring (Section 3. 4. 1), the reference spectrum was acquired using a cuvette containing LB; for all the other experiments (bacteria spectral shape description (Section 3. 1), mixture analysis (Section 3. 4. 2) and contamination description (Section 3. 4. 3)), the reference spectrum was acquired with PBS. Suspensions of the bacteria alone and of the mixture, in case of contamination, were homogenized using several gentle inversions before each spectroscopy measurement. The spectra were recorded in transmission, in the wavelength range 177 nm-892 nm with a step of 0. 22 nm using OceanView software (Ocean Insight, USA, supplier Paris, France). Preliminary remark. Speaking strictly from an optical perspective, the spectral dat presented in this paper result from two main light-matter interaction processes: absorp tion and diffusion (from particles of sizes similar to wavelength).
Spectral Data Processing A total of 395 bacteria spectral data were recorded into a text file and then transposed to Excel. The data obtained from transmission were converted into absorption percentages and all calculations were performed using Matlab™ R2020b software (Matlab™, Natick, MA, USA, supplier, Meudon, France). Only wavelengths between 330 nm and 860 nm were considered to remove measurements with high background noise. Artifacts due to the energetic emission peaks of the deuterium lamp were numerically removed. Regularly, the absorption spectra of neutral densities (Thorlabs, Newton, NJ, USA, NE05B and NE10B) were recorded and compared to the supplier's data to ensure correct absorption spectra measurements. Only spectra containing useful information for the considered spectral range were kept; they approximately corresponded to spectra with absorption values between 3% and 94% at a 600 nm wavelength.
= 0. 14 (in log units), about 2% at center range. Bias = -0. 01 (in log units), virtually zero. Note that the dispersion estimated when measuring the concentrations with a seeder is of the order of 0. 12 in log units. Considerations regarding the dispersions and actual spectral method accuracy will be discussed in Section 4. 4 and in the supplementary data SD1. Indeed, the dispersion calculated here was not a measurement of the spectral method's accuracy but an estimation of the spectroscopy cuvette's variability and of the difficulty in cultivating and enumerating the bacteria. The lower validity bound for the E. coli function was measured at 7. 05 log units. The upper validity bound was set to the value of the maximum E. coli concentration used in this experiment, i. e. , 8. 63 log units.
Monitoring of Bacteria Cultivation without Seedings/Enumeration The E. coli function was used to monitor a 30 h cultivation experiment. This cultivation was performed in a RPMI medium, which is not the normal cultivation medium for E. coli. Originally, the goal was to monitor a co-culture of CEM-E. coli since these studies were conducted in the framework of ATMP production. The choice of RPMI as the culture medium was due to the fact that priority was given to the growth of CEM. Figure  12  shows the spectra recorded during this experiment. An additional signal around 410 nm was observed and its possible origin is discussed in Section 4. 7. This additional signal was removed numerically as explained in the supplementary data SD2. Figure  12b  shows the spectra after extraction of the E. coli signal.
7. This additional signal was removed numerically as explained in the supplementary data SD2. Figure  12b  shows the spectra after extraction of the E. coli signal. The spectra recorded during the 30 h experiment were then exploited. Results are shown in Figure  13. A PCA analysis was performed with the spectra from Figure  12  (Figure  13a ). Figure  13b  shows the evolution of the E. coli concentration with time (red stars). The lag period, the exponential phase and the stationary phase are clearly visible. The lag time is measured in Figure  13c , where the natural logarithm of the concentration is plotted versus time and estimated at 5 h 40. This value is discussed in Section 4. 8. A black linear regression of the exponential phase, shown in Figure  13c , allowed for the determination of the bounds for the exponential fitting shown in Figure  13b  (blue solid line) and for the calculation of a generation time of 1 h 40.
Describing a Probably Contaminated CEM Cultivation Observing Contamination and Evaluating with PCA Unusual spectra shapes were observed during a CEM culture (Figure  16a ). They were similar to the shapes observed in mixtures (in the previous section) and contamination was suspected. A PCA analysis was performed to study this CEM culture (Figure  16b ). The CEM concentrations in the spectroscopy cuvettes were not measured with an automated cell counter. Only the dilution factors corresponding to each cuvette were known (legend of Figure  16a ). As for the PCA performed on the mixture, the data corresponding to the unusual spectra were located between the CEM and bacteria areas. This confirmed that a contamination occurred. The next step was to measure the CEM and bacteria concentrations. The trends of mixtures were not perfectly homothetic to bacteria representation because the CEM concentration was not constant among the measurements.
Measuring Species Concentrations At the time of this experiment, only E. coli and L. lactis were used in our laboratory and two hypotheses were established for the contamination's origin. Equation  (10)  was used to optically measure the CEM and bacteria concentrations for both hypotheses using the CEM function and corresponding bacteria function (Figure  17 ). As for the PCA performed on the mixture, the data corresponding to the unusual spectra were located between the CEM and bacteria areas. This confirmed that a contamination occurred. The next step was to measure the CEM and bacteria concentrations. The trends of mixtures were not perfectly homothetic to bacteria representation because the CEM concentration was not constant among the measurements.
In Table  2  is shown a summary of the γ 100 γ 110 energetic ratio obtained by GISAXS. We can evaluate the γ 100 γ 110 ratio as 1. 03 ± 0. 03 by GISAXS. The simulated Wulff bubble shape corresponding to this ratio is given in Fig. 6 , the visualisation is performed using the Wulffpack software  [46].
Acknowledgments This work has been carried out within the framework of the  EUROfusion Consortium , funded by the  European Union  via the  Euratom Research and Training Programme  (Grant Agreement No  101052200 -EUROfusion ). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the  European Commission. Neither the  European Union  nor the  European Commission  can be held responsible for them. This work has been also carried out within the framework of the French Federation for Magnetic Fusion Studies (FR-FCM). In particular, we are grateful to  D. Chaudanson  and  A. Altié  for their help in SEM and TEM characterizations. We gratefully acknowledge the helpful discussions with  Dr. T. Swinburne ,  Dr J Mougenot  and  Dr M-F Barthe.
The purpose of the paper is to identify Mach-number effects on pressure fluctuations p in compressible turbulent plane channel flow. We use data from a specifically constructed (Re τ , MCL x )-matrix direct numerical simulation (DNS) database, with systematic variation of the centreline streamwise Mach number 0. 32 MCL x 2. 49 and of the HCB (Huang et al. , J. Fluid Mech. , vol. 305, 1995, pp. 185-218)  friction Reynolds number 66 Re τ 1000. Strong MCL x effects (enhanced by the increasingly cold-wall condition) appear for MCL x 2, for all Re τ , very close to the wall (y 15). Compared with incompressible flow at the same Re τ , the wall root-mean-square [p rms ] + w (in wall-units, i. e. scaled by the average wall shear stress τw ) strongly increases with MCL x. In contrast, the peak level across the channel, [p rms ] + PEAK , slightly decreases with increasing MCL x.
In previous work  (Gerolymos & Vallet 2014 , 2018)  the simultaneous variation of both (Re τ , MCL x ) in the database hindered the unambiguous identification of the effect of each parameter. For this reason we constructed a (Re τ , MCL x )-matrix database. The other important parameter in wall turbulence, namely Tw /T r , is not controlled in the present simulations of canonical compressible TPC flow  (Coleman et al. 1995) , but depends on (Re τ , MCL x ), because there is no artificial source term in the energy equation. The wall gets increasingly colder with increasing MCL x. Although closer-to-adiabatic wall-temperature conditions are relevant in practical high-Mach-number applications  (Zhang et al. 2017 ) TPC flow data are particularly useful for the study of thermodynamic turbulence structure  (Gerolymos & Vallet 2018)  and the transport of thermodynamic quantities in the inner layer  (Gerolymos & Vallet 2014)  including temperature  (Bowersox 2009) , especially as the exact streamwise invariance of the flow allows, via streamwise averaging, for much larger statistical samples in a given observation time.
The purpose of the paper is to study the effects of (Re τ , MCL x ) on the fluctuating pressure field p , and to identify similarities and differences with incompressible flow data. We use the term compressible in a generic sense, making no distinction between mean flow stratification effects  (Morkovin 1962)  or compressible turbulence effects directly related to the fluctuating density ρ  (Gerolymos & Vallet 2014 , 2018)  either via the compressible terms in the Poisson equation for fluctuating pressure p  (Pantano & Sarkar 2002; Foysi et al. 2004; Tang et al. 2020)  or identified in relation to the dilatation-induced velocity  (Yu et al. 2019). In § 2, we briefly describe the construction of the database, summarize available data and introduce the three systems of units (defining the non-dimensionalisation scales) used in the paper.
(Re τ , MCL x )-scalings and database Compressible TPC flow between two isothermal walls  (Coleman et al. 1995)  is characterised by mean temperature stratification, which strongly increases with increasing Mach number (figure  1 ), because of viscous heating S ij τ ij , especially near the wall  (Coleman et al. 1995). Mean pressure p( y) = pw -ρv v (under the condition of streamwise invariance in the mean of plane compressible turbulent channel flow) varies little across the channel (increasingly so with increasing MCL x , but never exceeding 3 %; figure  1 ). Therefore, because of the perfect gas EoS p = ρR g T =⇒ p = ρR g T, density ρ( y) varies almost inversely proportionally to temperature T( y). Finally, dynamic viscosity μ( y), being a function of temperature  (Gerolymos & Vallet 2014, (2.
2020; Yu et al. 2019 Yu et al. , 2020;; Yu & Xu 2021)  and incompressible  (Kim, Moin & Moser 1987; Moser et al. 1999; Hu & Sandham 2001; Hoyas & Jiménez 2006; Lee & Moser 2015; Hoyas et al. 2022). Computational resolution in wall-units (table  1 ) is typical of compressible TPC flow DNS computations, in line with grid-resolution studies  (Gerolymos et al. 2010; Modesti & Pirozzoli 2016; Trettel & Larsson 2016). Some early computations in the database  (Gerolymos & Vallet 2014 , 2018)  were initialised following the procedure described in  Gerolymos et al. (2010, (44) , p. 790). However, most of the computations were initialised by thermodynamic rescaling and linear interpolation of an instantaneous turbulent flow field at different (Re τ , MCL x )-conditions. Computational experience shows that p rms reaches statistical convergence much slower than velocity covariances and other statistics.
Database The target during the construction of the database was to obtain a matrix of (Re τ , MCL x ) values, where Re τ is the HCB friction Reynolds number (2. 1b) and MCL x := u CL a CL (2. 4) is the average streamwise centreline Mach number. Note that the often used approximations MCL MCL x ũCL /a( TCL ) are confirmed by the data with good accuracy because v CL u CL w CL and (T rms / T) CL ≪ 1. We use the exact average (2. 4) in our work. In general, Re τ is adopted by workers in the field ( § 2. 1), because it is the proper parameter for the scaling of the Reynolds shear stress -ρu v and, hence, controls the mean velocity ũ profile  (Trettel & Larsson 2016). We chose the centreline Mach number MCL x for the matrix construction because it allows comparison with boundary-layer data which are always referenced to the external flow Mach number, and because its physical significance is clear.
Furthermore the coefficients of variation CV (•) := (•) rms /(•) of the thermodynamic fluctuations {p , ρ , T , s } scale with M2 CL x  (Gerolymos & Vallet 2014 , 2018). Neither Re τ nor MCL x are fixed in the computations, the flow conditions being determined by the set {ρ B , ṁB , Tw }  (Gerolymos et al. 2010) , where ρ B := ρxyzt is the bulk density, ṁB := L y L z ρ B u B := L y L z ρu xyzt is the mass flow, and T w = const. is the wall temperature (as a consequence the bulk-wall Mach number M B w := u B /ā w is fixed). However, we took particular care in the construction of the database to obtain the closest possible target MCL x ∈ {0. 33, 0. 80, 1. 50, 2. 00} and Re τ ∈ {75, 100, 110, 250, 340, 1000} (table  1 ). The cost of the computations strongly increases with MCL x if nearly constant resolution in standard wall-units is sought (this is the most stringent resolution assessment), as a result of the rapid increase of the ratio Re τ w /Re τ with increasing MCL x.