dataesr/scientific-paragraphs-categorization huggingface dataset:
Data on Bentheimer sandstone Alizadeh (2013) performed a series of steady-state flow experiments on water-wet Bentheimer sandstone to obtain two-phase and three-phase rela1ve permeabili1es. The absolute brine permeability and porosity of the core sample whose data were used in our study were 2. 66 D and 0. 24, respec1vely  (Alizadeh and Piri, 2014b). The physical proper1es of the fluids used in the flow experiments are provided in Table  2. (#)  2. 526 1. 144  Oak, 1990  The two-phase rela1ve permeabili1es obtained during primary drainage in oil-water, gas-water, and gas-oil systems are ploBed in Fig. 3  and compared to the simulated two-phase rela1ve permeabili1es using the MVG model. To quan1fy the input parameter for the MVG model, we used the experimentally determined endpoint weQng-phase satura1ons and the associated nonweQng-phase rela1ve permeability as known.
Data on Berea sandstone Oak (1990) performed a series of steady-state flow experiments on water-wet Berea sandstone to obtain twophase and three-phase rela1ve permeabili1es. The absolute permeability and porosity of the core sample whose data were used here were 0. 2 D and 0. 22. The physical proper1es of the fluids used in his experiments are provided in Table  3. The two-phase rela1ve permeabili1es obtained in Experiments 2, 8, and 13 were conducted in oil-water, gaswater and oil-gas systems. The measured and numerically simulated two-phase rela1onships are presented in Fig. 4. The capillary pressure-satura1on curves determined in Oak's experiments in a gas-water, water-oil and oil-gas system were analysed numerically with the Van Genuchten model (Fig. 4 ). All fit parameters and characteris1cs of the op1miza1on process are summarized in Table  C2  (Appendix C).
1, the predicted permeabili1es are significantly higher than those observed, aBaining kr values 10 1mes or more. For measured oil rela1ve permeabili1es higher than 0. 1, the oil rela1ve permeabili1es predicted by the mechanis1c model are about 60 and 25% lower than the measured kr values in the case of Berea sandstone and Bentheimer sandstone, respec1vely. However, the average rela1ve errors were quan1fied to 3. 25 (±4. 75) for Berea sandstone and 1. 27 (±2. 78) for Bentheimer sandstone, respec1vely. The obtained global overes1mate of measured oil rela1ve permeabili1es is clearly aBributed to the weight of the large number of experimental data with oil rela1ve permeabili1es lower than 0. 1. Analyzing the fiBed regression line of the cross-plot shown in Fig. 16 , one could again conclude that the predicted gas rela1ve permeabili1es underes1mated the measured data of the Berea sandstone and Bentheimer sandstone by about 10 and 30%, respec1vely; but the average rela1ve error of about 1.
69 (±6. 71) quan1fied for the experimental data of Berea sandstone does not give the same conclusion. Apparently, the mechanis1c model overes1mates the low rela1ve permeabili1es measured in the experiment, even by factor of 10 and more. The large number of data close to the origin does not strongly influence the slope of the regression line but have a strong impact on the average rela1ve error. In the case of Bentheimer sandstone, the maximum rela1ve errors observed for the predicted gas rela1ve permeability do not exceed 1. 5 for the extremely low gas rela1ve permeabili1es measured in the experiment.
15) can be ignored. AHer extrac1ng the global mobili1es corresponding to the experimental data of the seven DDI flow experiments, the numerical results were compared with the experimentally determined global mobili1es (Fig. 20 ). The same general trend was observed for Bentheimer sandstone: the predic1ons overes1mate the observa1ons, and with increasing gas satura1ons, the differences become acceptable. For low gas satura1ons, up to 30 or 35%, the simulated global mobili1es strongly overes1mate the experimental data by a factor of 2 and more. For example, in the case of DDI Experiment 15, the maximum rela1ve error was quan1fied to about 8. 3 for a measured gas satura1on of about 13%, whereas for a gas satura1on of 59% the rela1ve error decreased to about 0. 3. The highest average rela1ve error was quan1fied for the predic1on of global mobili1es of Experiment 25 (RE=24.
In order to constrain our interpola1on method, we used one third of the experimental data available for the Bentheimer and Berea sandstone DDI experiments to measure local global mobility uniformly distributed within the ternary diagram. The resul1ng "improved" global mobili1es will then be used, based on Equa1on 4, to predict the three-phase rela1ve permeabili1es (water, oil, gas) for Bentheimer sandstone and Berea sandstone (Sec1on 4. 2. 3).
Therefore, as in the case of Bentheimer sandstone, the rela1ve oil permeabili1es in the three-phase system is not likely to be determined. The only possible interpreta1on is therefore limited to the quan1fica1on of rela1ve water permeabili1es (using Equa1on 4) as the water frac1ons determined represent physical values, except for a small area in the diagram. The calculated water rela1ve permeabili1es are compared with the experimental data of DDI Experiments 15 (Fig. 24 ) and Experiments 18 (Fig. 25 ). The detailed comparison of predicted water rela1ve permeabili1es for Experiments 16, 17, 19 and 25 with those experimentally measured is documented in Appendix E (Figs. E6  and E7 ). Generally, the measured water rela1ve permeabili1es are largely overes1mated by the TD compa1ble model. The majority of the predicted values clearly exceed the physical upper limit of 1, which is mainly due to the water frac1onal flow determined, some of which are two orders of magnitude higher than the experimental frac1onal water flows.
04, the predicted values closely approaches the measured rela1ve permeabili1es. However, model op1on Pc-S strongly underes1mates the measured water rela1ve permeabili1es (RE=-0. 96±0. 02) for the whole set of experimental data. In the case of Bentheimer sandstone, model op1on kr-S also seems as the beBer op1on to predict the measured water rela1ve permeabili1es. Here, both op1ons overes1mate the experimental data (RE=0. 85±1. 85 (kr-S), RE=4. 72±3. 86 (Pc-S)). The devia1on from the 1:1 line is high for measured water rela1ve permeabili1es lower than 0. 01; in the case of modeling op1on Pc-S the maximum rela1ve error achieves values higher than 15. The oil rela1ve permeabili1es predicted for the Berea sandstone (Fig. 29 ) show the same general trend as observed for the water rela1ve permeabili1es: modeling op1on kr-S overes1mates and modeling op1on Pc-S underes1mates the measured rela1ve oil permeabili1es.
Three-phase oil rela1ve permeability Using the mechanis1c model, the predicted oil rela1ve permeabili1es are par1ally acceptable. For measured oil rela1ve permeability below 0. 1, the predicted permeabili1es are significantly higher than those observed, aBaining kr values 10 1mes or more. For measured oil rela1ve permeabili1es higher than 0. 1, the oil rela1ve permeabili1es predicted by the mechanis1c model are about 60 and 25% lower than the measured kr values in the case of Berea sandstone and Bentheimer sandstone, respec1vely. However, the rela1ve errors were quan1fied to 3. 25±4. 75 for Berea sandstone and 1. 27±2. 78 for Bentheimer sandstone, respec1vely. The obtained global overes1mate of measured oil rela1ve permeabili1es is clearly aBributed to the weight of the large number of experimental data with oil rela1ve permeabili1es lower than 0.
1. The oil rela1ve permeabili1es predicted for the Berea sandstone using the Parker-Lenhard model show similar trend as those for the water rela1ve permeabili1es: modeling op1on kr-S overes1mates and modeling op1on Pc-S underes1mates the measured rela1ve oil permeabili1es. However, here, modeling op1on kr-S strongly overes1mates the experimental data characterized by a large spreading around a high mean rela1ve error whereas modeling op1on Pc-S seems as the best op1on for predic1ng the experimental data. In the case of Bentheimer sandstone, both modeling op1ons again overes1mate the measured oil rela1ve permeabili1es. It should be noted here that the devia1on of predicted oil rela1ve permeabili1es from the experimental data is also high for very low oil rela1ve permeabili1es (<0. 01). They aBain maximum rela1ve errors of up to 80 and 40 for modeling op1on kr-S and modeling op1on Pc-S, respec1vely.
Three-phase gas rela1ve permeability Using the mechanis1c model, the predicted gas rela1ve permeabili1es underes1mated the measured data of the Berea sandstone and Bentheimer sandstone by about 10 and 30%, respec1vely; but the average rela1ve error of about 1. 69±6. 71 quan1fied for the experimental data of Berea sandstone does not provide the same conclusion. Apparently, the mechanis1c model overes1mates the low rela1ve permeabili1es measured in the experiment, even by factor of 10 and more. In the case of Bentheimer sandstone, the measured gas rela1ve permeabili1es are well represented by the model predic1ons. The maximum rela1ve errors do not exceed 1. 5 for the extremely low gas rela1ve permeabili1es measured in the experiment. The TD compa1ble model provided only reliable predic1ons for the Bentheimer sandstone.
The difficul1es described in sec1on 4. 2, the very high capillarity of Berea sandstone, poses problems in the interpola1on of the global capillary pressure and its deriva1ves with respect to water satura1on (s1) and gas satura1on (s3). Using the Parker-Lenhard model, the gas rela1ve permeabili1es predicted for Berea sandstone and Bentheimer sandstone strongly overes1mate the measured gas rela1ve permeabili1es. The maximum rela1ve errors are observed for very low rela1ve permeabili1es (<0. 01). In the case of Berea sandstone, the maximum rela1ve errors aBain values of 1000 (op1on kr-S) and 100 (op1on Pc-S) whereas for Bentheimer sandstone values of about 26 (op1on kr-S) and 14 (op1on Pc-S) are achieved. Even for higher rela1ve permeabili1es measured for both sandstones, the predicted gas rela1ve permeabili1es overes1mate the experimental data globally by at least a factor of 2.
Conclusions and future work In this study, two recent and two classical models were evaluated against experimentally measured threephase permeabili1es. Experimental data generated on two different water-wet sandstones were selected from the literature to evaluate and compare the four mathema1cal models. Experimentally determined cons1tu1ve rela1onships in two-phase systems were used as input parameters to numerically predict rela1ve permeabili1es (kr) in three-phase systems, and then the es1mated results were compared with experimental three-phase permeabili1es measured along decreasing water satura1on/decreasing oil satura1on/increasing gas satura1on (DDI) paths.
Our study showed that the global mobili1es predicted by C0 finite element interpola1on significantly overes1mate the experimentally quan1fied global mobili1es. Predic1on improved when experimental data were used to locally impose the global mobility. Our numerical study also revealed weaknesses in the TD compa1ble model. The main issue is the fulfillment of the required condi1on of frac1onal flows of water, oil and gas predicted by the PDE-TD interpola1on algorithm, which should be bounded by the physical limits of 0 and 1 everywhere in the ternary diagram. This condi1on was respected in the case of negligible residual weQng phase satura1on, low capillary porous medium and smooth varia1ons of associated capillary pressure gradients, as shown in the study of di  Chiara et al. (2010). In our case, however, it appears that the very high capillarity of both the Bentheimer and Berea sandstones contributes to numerically interpolated water and gas frac1onal flows in the ternary diagram that locally fall below the physical lower limit of 0 and exceed its upper limit of 1.
It should be noted that at least one set of experimental three-phase rela1ve permeability data (for one satura1on path) for all three fluids is required to tune these characteris1c coefficients. To reduce the degree of uncertainty,  Shahverdi and Sohrabi (2017)  suggested employing more measured data of three-phase rela1ve permeabili1es for calibra1on of the six characteris1c coefficients. In the case of Bentheimer sandstone, using two experimental data sets instead of one for tuning the characteris1c coefficients, only slightly improved the predicted kr values. The use of different input data sets also revealed the absence of a unique solu1on for the calibra1on of these six characteris1c coefficients. This resulted in different quali1es in the subsequent predic1on of the rela1ve permeabili1es.
As complete datasets on capillary pressure-satura1on curves are available for both sandstones, it could be interes1ng to implement the effect of capillarity in the evalua1on of ellip1c zones under the given experimental condi1ons. In the case of the TD compa1ble model, our study revealed that the interpola1on of the global capillary pressure and its deriva1ves exposes unphysical frac1onal phase flows; the Total Differen1al compa1ble = -" ˜1 , 1 , " K X K ™ ! (A6) = ,K1Z -1 , " ˜1 , " K X ™ !K where krow,max is the maximum rela1ve oil permeability achieved at irreducible water satura1on Swi in the water/oil system. mwo and mow correspond to the MVG parameter for water and gas, respec1vely. In a two-phase oil/gas system, the corresponding rela1ve permeabili1es can be expressed by = ,K1Z -1 , " ˜1 , " K X ™ !K (A7) = -" ˜1 , 1 , " K X K ™ ! where krgo,max is the maximum rela1ve gas permeability achieved at residual oil satura1on in the oil/gas system Sor.
Acknowledgment This research was granted from  January  to August, 2019 by the  French-American Fulbright commission  and the Ins1tute of  Interna1onal Educa1on/Council for Interna1onal Exchange of Scholars (IIE/CIES ),  US Department of State. Gerhard Schäfer  is also grateful for the financial support by the  University of Strasbourg  during his sabba1cal leave at the  Center of Innova1on for Flow through Porous Media, University of Wyoming  and the administra1ve and technical support by the  University of Wyoming.
S 11 Measurement Results. e simulation results compared to the measurement results in free space in terms of S 11 with respect to 50 ohms are represented in Figure  7. e measurement results confirm the results of simulation done with CST Studio software where all the target frequency bands fit the simulation resonance bands with small shift for the lowest frequencies up to 0. 2 GHz. e first main reason is the line added in the manufactured design and one of the possible reasons explaining the larger bandwidth obtained in measurements is the multipath effect obtained by the environment where the measurements are performed and which is absent in the simulations. e results prove that the antenna meets perfectly the requirements in all the frequency bands discussed previously. e radiation pattern of the gain in 2D plot (Phi � 0 and Phi � 90) is presented for each frequency at elevation view in Figure  8 , and at azimuth view in Figure  9.
01 W/kg higher than the SAR value calculated in skin tissue. is can be explained by electrical properties ε r and σ (S/m) of the fat tissue that are lower than the electrical properties of the skin tissue. In the other hand, the maximum SAR value decreases from the fat tissue to muscle tissue, and then from the muscle tissue to the bone tissue. We notice that the maximum SAR within the same tissue decreases as the frequency increases. In average, the maximum SAR decreases from 2. 3 GHz to 5. 8 GHz by 70% at the skin, fat, and muscle layers and by 45% at the bone layer. Figure  16  shows the three-dimensional distributions of the SAR (W/kg) averaged over a mass of 10 g simulated inside the hand wrist model at the frequencies of 2. 3 GHz, 2. 4 GHz, 2. 6 GHz and 3. 500 GHz, 5. 2 GHz, and 5. 8 GHz with 5 mm spacing, using software CST MWS.
Antenna next to SAM Mouth. In this configuration, the antenna is placed next to SAM mouth. We selected three values of the separation between the antenna and SAM mouth: d � 1 mm, d � 5 mm, and d � 9 mm. e simulated values of the maximum SAR averaged over a mass of 10 g of the tissues of the head for the SAM phantom head, at selected frequencies, using CST MWS software, are summarized in Table  6. From the results of electromagnetic simulations, we notice that the maximum SAR values for 10 g of the head model tissue decreases when the spacing between the antenna to SAM mouth changes from d � 1 mm to d � 9 mm. In average, the SAR value decreases by 60% from d � 1 mm to d � 9 mm. It is also noticeable that the SAR value is higher at higher frequencies 3500 MHz, 5200 MHz, and 5800 MHz. We notice from the plots of SAR distribution inside SAM head that for the lowest frequencies 2300 MHz, 2400 MHz,.
For apoptosis analysis by flow cytometry, control and treated cells were collected and labelled with propidium iodide as per manufacturer's instructions (ThermoFischer Sci. , Madrid, Spain) or processed for cleaved caspase-3 staining as follows: cells were fixed with 1% paraformaldehyde, permeabilized with 0. 1% Triton-X100, and stained with a rabbit polyclonal anti-cleaved caspase 3 antibody (1/600, Cell Signaling Technology, Danvers, MA, USA), followed by Alexa Fluor 647-conjugated goat anti-rabbit IgG secondary antibody (1/500, Invitrogen, Carlsbad, CA, USA). Nuclei were counterstained with DAPI (Life Technologies). Flow cytometry was conducted in a FACSCanto II and DNA histograms were fitted into cell-cycle distributions using the BD FACSDiva software (Beckton Dickinson, Madrid, Spain).
3). For each experiment, identical background subtraction and scaling was applied to all images. Pearson correlation and Mender's coefficients from 10-12 images (4-5 cells per images) from 3 independent experiments were calculated using JACoP plugin ImageJ software  [41]. Quantification of the colocalized pixels in cell periphery or in perinuclear region (Figure  2B  and supplemental figure 5B) were performed using home-made Image J plugin. Briefly, using segmentation tools, a first region of interest (ROI) "total cell" corresponding to the cell contour is previously defined. A second ROI "cell periphery" is then defined as a regular inner region of 13 pixels following the cell contour. The third ROI "perinuclear region" is derived from the subtraction of the first two and the elimination of an ROI corresponding to the nucleus (DAPI labelling).
Spheroid migration assays Single cell suspension was mixed in EMEM/10% FBS containing 10% of methylcellulose. All the spheroids were made with 1000 cells by hanging drop method in a 20 μL drop as previously described  [40]. Tissue culture plates were coated with fibronectin (20 µg. mL -1 in DPBS solution) for 2 h at 37 °C. Two-day-old spheroids were allowed to adhere and migrate in complete medium +/-gefitinib (EMEM, 10% FBS). Twenty-four hours later, cells were fixed with paraformaldehyde 3. 7% (Electron Microscopy Sciences) and stained with DAPI. Nucleus were picturized under the objective 5x in the fluorescence microscope ZEISS-Axio (ZEISS). Image analysis to evaluate the number of cells that migrated out of the spheroid was performed with ImageJ software using a homemade plugin  [40]. Alternatively, phase-contrast time-lapse images were acquired using a Leica DMIR2 microscope (5xNPlan 0.
Immunoblot Equivalent amount of proteins were separated on precast gradient 4-20% SDS-PAGE gels (Bio-Rad) and transferred to PVDF membrane (GE Healthcare). Membranes were probed with primary antibodies; anti-EGFR antibody (D38B1), anti-5 integrin (H104) at 1µg/ml and anti-GAPDH at 0. 2µg/ml in blocking solution (PBS-5% non-fat dry milk). Immunological complexes were revealed with anti-rabbit or anti-mouse IgG coupled peroxidase antibodies using chemoluminescence (ECL, Bio-Rad) and visualized with LAS4000 image analyser (GE Healthcare). Quantification of non-saturated images was performed with ImageJ software. GAPDH was used as the loading control for all samples.
Ultimately, all methods boil down to a canonical polyadic decomposition (CP decomposition) of the constructed tensor to retrieve a decoupled representation in which the nonlinearities occur as univariate polynomial mappings. The benefit of using a tensor-based approach for decoupling is twofold. First, 'tensorization' procedures often lead to (essentially) uniquely decomposable tensors  [8] , i. e. , ensuring that identifiable structures can be retrieved. Second, by solving the decoupling problem as a CP decomposition, one can use recent widely available and robust numerical tools, such as Tensorlab for MATLAB  [27]  (or alternatives  [28, 29] ). This paper specifically focuses on the two tensorization methods  [26]  and  [24]. Although both associated tensors have a particular structure, both approaches seem quite different in nature, and each of the methods has distinct advantages over the other one.
The CP rank r is defined as the (minimal) number of terms that is required to represent T as a sum of r rank-one terms. To refer to elements of matrices or tensors, or subsets thereof, we may use MATLAB-like index notation (including MATLAB's colon wildcard): for instance, T i,j,k,ℓ is the element at position (i, j, k, ℓ) of a fourth-order tensor T , and T :,:,2 is the second frontal slice of a third-order tensor T. The mode-n product is denoted by "• n " and is defined as follows. Let X be an I 1 × I 2 × • • • × I N tensor, and let u be a vector of length I n , then we have X • n u ⊤ i1•••in-1in+1•••iN = In in=1 x i1i2•••iN u in. Notice that the result is a tensor of order N -1, as mode n is summed out. Similarly, for an I 1 × I 2 × • • • × I N tensor X and a matrix M ∈ J × I n , the mode-n product is defined as X • n M ⊤ i1•••in-1jin+1•••iN = In in=1 x i1i2•••iN m j,in.
Acknowledgements This work was supported in part by the  ERC   AdG-2013-320594 grant  " DECODA ", by the  Flemish Government  (Methusalem), by the  ERC Advanced Grant SNLSID  under contract  320378 , and by the  Fonds Wetenschappelijk Onderzoek -Vlaanderen  under  EOS  Project no  30468160  and  FWO projects G. 0280. 15N  and  G. 0901. 17N.
Acknowledgements This work was financially supported by the project SMOSCs, ID:  37_220 ,  Cod MySMIS :  103509  funded by the  Romanian Ministry for European Funds  through the  National Authority for Scientific Research and Innovation (ANCSI)  and co-funded by the  European Regional Development Fund/Competitiveness Operational Program   2014-2020 (POC) Priority Axis 1/Action 1. 1. 4.
Jianghan Basin Based on our provenance interpretation and chronological results obtained on the Yichang Gravel Layer sediments, a drainage evolution model of the Yangtze River can be proposed (Fig. 10 ). In this model, we cannot give details prior to the early Pleistocene because the Yichang Gravel Layer does not go deep enough in western hilly area of Jianghan Basin, leading to a stratigraphic gap between the Yichang Gravel Layer and the underlying Neogene bedrock. However, our results clearly demonstrate that the Three Gorges was incised before 1. 12 Ma. This proposal is supported by the data derived from the study of the Zhoulao Core (Core ZL, Fig. 8.
RNA sequencing and bioinformatics tools. RNA extraction and sample preparation were performed as described  49. RNA sequencing was performed using stranded strategy. Bioinformatics analyses were performed as previously described (bioinformatics pipelines for gene expression  50  ). From curated BAM files, SAMtools and BCFtools (v0. 1. 19) detected mismatches at any position with a minimum depth of five reads where alternative bases were above 30%  51, 52. Then, all mismatches were investigated in all samples (possibly below 30% of alternative bases). Variants were then annotated with the different databases using ANNOVAR (v2017/07;  53. We excluded known variants in the 1000 Genomes Project or in the dbSNP, non-exonic or synonymous variants. www. nature. com/scientificreports/ Differential gene expression (DGE) was performed on raw counts, then normalized and analysed using DESeq2 (v1.