key: cord-0847712-mamouhk7 authors: Hagita, Katsumi; Aoyagi, Takeshi; Abe, Yuto; Genda, Shinya; Honda, Takashi title: Deep learning-based estimation of Flory–Huggins parameter of A–B block copolymers from cross-sectional images of phase-separated structures date: 2021-06-10 journal: Sci Rep DOI: 10.1038/s41598-021-91761-8 sha: 955e2b4333fdcf12b5037c9ed6eaed9b38668781 doc_id: 847712 cord_uid: mamouhk7 In this study, deep learning (DL)-based estimation of the Flory–Huggins χ parameter of A-B diblock copolymers from two-dimensional cross-sectional images of three-dimensional (3D) phase-separated structures were investigated. 3D structures with random networks of phase-separated domains were generated from real-space self-consistent field simulations in the 25–40 χN range for chain lengths (N) of 20 and 40. To confirm that the prepared data can be discriminated using DL, image classification was performed using the VGG-16 network. We comprehensively investigated the performances of the learned networks in the regression problem. The generalization ability was evaluated from independent images with the unlearned χN. We found that, except for large χN values, the standard deviation values were approximately 0.1 and 0.5 for A-component fractions of 0.2 and 0.35, respectively. The images for larger χN values were more difficult to distinguish. In addition, the learning performances for the 4-class problem were comparable to those for the 8-class problem, except when the χN values were large. This information is useful for the analysis of real experimental image data, where the variation of samples is limited. www.nature.com/scientificreports/ ally, it is considered that a highly symmetric structure can be obtained by using a sufficiently large system size or by optimizing the system size. From another point of view, the images shown in Fig. 1 can be regarded as structures trapped in the metastable state during the phase separation process. Although these images are not trivial and have certain complexities, they have features that are governed by the interaction parameter, χN. Although the highly symmetric structure under TPMS can be classified by a mathematical index such as the Betti number, there is no mathematical index to classify and express these metastable features. This absence may reveal a case where ML is difficult but DL may prove to be successful. As a result, these images were considered to be suitable to evaluate the potential of estimating χN from their morphology information and density profiles. For understanding the basic characteristics of the examined data system, image classification was performed before regression. We performed the image classification using Keras 96 and TensorFlow 97 packages based on the VGG-16 network. For performance comparison, we performed several ML-based image classifications using Scikit-learn 98 . In the ML-based image classifications, we used support vector machine (SVM) with a radial basis function (rbf) kernel for two features: (1) the histogram of brightness and (2) the histogram of oriented gradients (HoG). In the DL-based image classifications, binarized images were also examined for comparison. To summarize, the present work performed the following image classifications: (1) ML with SVM for histogram of brightness 28, 30, 32, 34, 36, 38 , and 40 . To avoid redundancy, results for the 6-and 8-class problems are presented in Section S1 of the Supplementary Information. Figure 2 shows the learning curves of the trainings performed. We found that 100 epochs are enough to obtain a reasonable accuracy. Comparisons among f and N suggest that training for f = 0.2 is less difficult than training for f = 0.35 . For f = 0.35 , training with N = 20 appears to be more difficult than that with N = 40. Table 1 presents confusion matrices of the 4-class problem at 100 epochs. For confusion matrix M i,j , accuracy A = i M i,i / i,j M i,j and error rate E = 1 − A . For f = 0.2 , E = 1.25 × 10 −4 and 0.0 for N = 20 and 40 , respectively. When f = 0.35 , E = 1.13 × 10 −2 and 1.63 × 10 −3 for N = 20 and 40 , respectively. It was found that E for f = 0.2 is lower than that with f = 0.35 . This tendency is also found in the 6-and 8-class problems presented in Section S1 of the Supplementary Information. These behaviors suggest that the images for f = 0.35 are more difficult to learn than for f = 0.2. The results of the 8-class problem, presented in Section S1of Supplementary Information, suggest that the accuracy for a larger χN is lower when f = 0.2 . This tendency is maintained for (f , N) = (0. 35, 20) , although it is not clear for (f , N) = (0. 35, 40) because of the large error. This tendency is consistent with that of the 4-class problem in Table 1 . We expect that the accuracy of each class group on χN in the image-classification problems corresponds to the error of the estimated χN values in the regression problems. Next, for comparison, we performed ML-based image classifications. Table 2 presents the error rates of the 4-class problem with SVM for the histogram of brightness and the HoG features. Here, 6000 and 2000 images for each χN class were used for the training and evaluation of generalization ability, respectively. Moreover, DL-based image-classification results for binarized images are presented for later consideration. The results for the 8-class problem are also presented in Table 3 . The confusion matrices for the 4-and 8-class problems are presented in Sections S2 and S3 of the Supplementary Information. The DL-based image classification exhibits highly superior performance (low error rate) compared to that achieved with ML. Therefore, we consider that regression by ML is not realistic for these datasets. Moreover, it is clear that DL for binarized images outperforms ML. ML results for the brightness histogram suggest that the prepared images for f = 0.35 are more dependent on brightness than the images for f = 0.2 . The error rate of ML for the HoG feature for these images is worse than that for the histogram of the brightness. These ML models exhibit inferior performance because the area of each image is small. The image-classification performance improves for larger image sizes in both ML and DL models. One of the authors 99 investigated the effect of image size on generalization ability of image classification for morphologies of nanoparticles in rubber matrices, where the morphologies were modeled based on the ultra-small X-ray scattering spectrum 100 . These image-classification results confirm that the prepared dataset has some features that can be distinguished by DL; however, the performance of ML was not good. In the next section, we have used these datasets for the regression problem in the estimation of the Flory-Huggins χ parameter. Regression to estimate the Flory-Huggins parameter. As mentioned previously, to investigate the characteristics of regression to estimate the Flory-Huggins χ parameter, we performed regression using the VGG-16 model. When preparing training images via electron microscopy for actual materials, such as stained phased-separated diblock copolymers, the number of prepared materials for the observations is limited to a small value (e.g., less than a few tens of specimens). Thus, in turn, the number of χN classes is limited to a small value. Therefore, in the present regression problem, discrete χN rather than continuous χN is used for the training images. Here, we considered the 8-class problem with training images of χN = 26, 28, 30, 32, 34, 36, 38 , and 40 . In the classification problem, the generalization ability was evaluated from independent images that belonged to the same χN classes and were independent of the training images. For the regression problem, two types of www.nature.com/scientificreports/ generalization abilities can be evaluated from (1) independent images generated with the same χN value (the 8-classes) and (2) independent images with unlearned χN value. Here, we selected χN = 27, 29, 31, 33, 35, 37, and 39 as the unlearned χN values. In this study, we evaluated these two generalization abilities. As a first test, we performed training with 100 epochs. Figure 3 presents the learning curves until 100 epochs. At f = 0.35 , a discrepancy between training MAE and validation MAE was observed, although a similar discrepancy was not observed for f = 0.2 . We consider that learning from the given training images was saturated (i.e., overfitting tendency). In the learning curve of the validation MAE, the trend comprising the minimum and a subsequent increment can be considered as an indicator of overfitting. In the cases of Fig. 3c and d, the curve around 60 epochs appears to be the minimum. For comparison with the learned network before overfitting, we present the results of an independent run with 50 epochs in Section S4 of the Supplementary Information. Figure 4 presents distributions of the estimated χN for independent images whose χN values are the same values as those for the training images. The distribution proceeds differently at f = 0.2 and 0.35 . These tendencies are the same as those in the image-classification problem as mentioned in the previous section, and they are considered to be related to the difficulty encountered in estimating the χN value. The behavior is similar to that of an independent run with 50 epochs presented in Section S4 of the Supplementary Information. Table 4 presents the average and standard deviation values of the estimated χN for each χN class. In all cases, the absolute value of the difference from the true value is approximately 0.1. The standard deviation values are approximately 0.1-0.2 and 0.2-0.8 for f = 0.2 and 0.35 , respectively. The standard deviation values become larger for larger χN values, as presented in Fig. 4 . Figure 5 and Table 5 present www.nature.com/scientificreports/ Cases with long learning times and transfer learning. In some cases, to obtain small MAEs, long learning times (epochs) and/or transfer learning are applied. In this study, we also attempted to perform learning with large epochs and transfer learning. However, both the cases showed overfitting and poor generalization ability. The detailed results are presented in Sections S6-S9 of the Supplementary Information. These results indicate that it is a realistic solution to use a trained network, wherein overfitting does not occur in the generalization-ability evaluation of the unlearned χN. To confirm the effects of interfacial density gradients on the regression problem and feasibility of χN estimation for stained specimens, we investigated the regression per- Table 1 . Confusion matrices of the 4-class problem at 100 epochs. www.nature.com/scientificreports/ formance for binarized images. Tables 6 and 7 present the average and standard deviation values of the estimated χN for each χN class, as detailed in Section S10 of the Supplementary Information. We consider that DL-based χN estimation for binarized images is learning the characteristics of morphology in the binary images without density gradients. The distributions of the estimated χN for the binarized images are much wider than those for the gray-scale images. Absolute differences from the true values of χN are also larger than those for the grayscale images. Therefore, we conclude that the gray-scale images have essential information for χN estimation. This suggests that χN can be evaluated accurately without using DL if an arithmetic calculation method for estimating χN from a cross-sectional image is developed. However, at present, such a method is unknown; thus, DL is an effective tool. It should be noted that the χN estimation for the binarized image is predictable as an average, although the error is large. In TEM observations of polymer materials, staining such as by OsO4 is currently essential owing to the limited detector ability. The observed images of the stained sample are considered to correspond to the binarized images. The confirmation that the binarized image has a certain estimation ability is useful information in the future analysis of TEM images of the actual materials. To clarify the effects of the number of classes and step size of χN on the error, we investigated the cases of training using the 4-class training images with χN = 25, 30, 35, and 40 . Figure 6 shows the learning curves for the 4-class training images. The MAEs at 100 epochs in the 4-class problem were smaller than those in the 8-class problem. Figure 7 presents the distribution of the estimated χN for the 4-class problem. Except for the cases of (f , N) = (0.2, 40) , we find that there is no discriminating ability for χN = 37.5 . In particular, for the cases of Except for the large χN, it was found that the estimation with the 4-class training images was as accurate as that with the 8-class training images. This finding is supported by the behaviors of the average and standard deviation values presented in Table 8 . We consider that this knowledge is useful in the analysis of actual experimental images. DL-based methods were studied to estimate the Flory-Huggins χ parameter of A-B diblock copolymers from 2D cross-sectional images generated from SCF calculations, assuming them to observation images from electron microscopes. In this study, we aimed to estimate χN for images created by a particular process. Note that χN estimation, independent of the material processes, cannot be discussed because we used only one image-generation method in this study. Through SCF calculations, 10,000 images for each χN were obtained from cross-sectional views of the 3D phase-separated structures in random directions at randomly selected positions. Here, the 3D density field data were obtained by real-space SCF simulations in the 25-40 χN range for f = 0.2 and 0.35 and N = 20 and 40 . For DL, we used VGG-16 38 . www.nature.com/scientificreports/ To show that the generated images can be classified systematically, DL-based image classification was performed. The accuracy for f = 0.2 was found to be better than that for f = 0.35 because of the difficulty encountered in distinguishing owing to the resemble images. It was clarified that the accuracy for a larger χN is lower when f = 0. 35 . In addition, we investigated image classification performance of ML with SVM for the histogram of brightness and the HoG features as well as DL for binarized images. The error rates of ML were considerably larger than those of DL. Thus, regression via ML was found to be difficult for these prepared datasets. We also confirmed that the image classification performance by DL for binary images was inferior to those for gray-scale images. The binarization also affected the regression performance. In addition, we found that the DL-based χN estimation for the binarized image was predictable as an average, although the error was large. This is an important finding to extend χN estimation for images in TEM observations of stained polymer materials. 26, 28, 30, 32, 34, 36, 38, and 40 . To evaluate the generalization ability, MAEs for the following two image groups were estimated: (1) independent images generated with the same χN value as that for the training images and (2) independent images with unlearned χN value such as χN = 27, 29, 31, 33, 35, 37, and 39. We investigated the distribution of the estimated χN of independent images with the unlearned χN values. Large χN values could not be accurately estimated, which can be ascribed to the difficulty encountered in image classification. For (f , N) = (0. 35, 20) , the image classification for the 3-class problem for χN = 38, 39, and 40 failed to distinguish images for χN = 38 and 39 . Except when χN was large, we obtained accurate average values of χN for the examined images, and the standard deviation was approximately 0.1 and 0.5 for f = 0.2 and 0.35 , respectively. To improve the accuracy of estimation for large χN, we require high-resolution images wherein the density gradient at the phase-separation interface can be recognized. Studies in this direction, including experimental observation data, are underway. Moreover, we found that the learning performances for the 4-class problem were comparable to those for the 8-class problem except when χN was large. This information is useful for the analysis of experimental image data. On the other hand, given that the estimation with the 8-class teacher dataset was more accurate than that with the 4-class dataset, the performance could be improved with the incorporation of smaller χN intervals into the teacher data. For example, it is difficult to prepare specimens that have a wide χN range with 0.1 intervals even in simulations; however, it may not be impossible. Research that provides insights into how small an χN interval is required for more accurate estimations, would be an important next step in this field. To estimate χN from experimental images, in addition to the effects of binarization associated with observations of stained specimens, we should train a regression network model that is robust to the effects of noise and image adjustments (including focus) of experimental data. To investigate random local noises and variations in image contrast and brightness, a large amount of experimental image data must be analyzed and pseudo image data must be generated accordingly. Recently developed electron-microscope automation techniques can be applied to observe a large area of images from one stained specimen at one observation. Research in these directions is also being conducted. In this study, we considered images created solely from a particular process of phase separations. This limits our ability to estimate χN only for that specific material process. Although the effectiveness of the learned network was limited to a specific process, we expected the estimation ability of the physical parameters governing phase-separation to be utilizable not only for polymers but also for metals. In the research and development of real materials, χN is expected to be estimated from structures obtained from various material processes. Further prospects in this field include an investigation into the feasibility of χN estimation, independent of material processes. Table 6 . Averages and standard deviations of estimated χN for each χN class for the binarized images. Here, the χN class was same value of the teaching image. N) = (0.2, 20) (f, N) = (0.2, 40) (f, N) = (0.35, 20) (f, N) = (0.35, 40 Table 7 . Averages and standard deviations of estimated χN for each unlearned χN class for the binarized images. 52, 53 . The theoretical background is briefly explained in Section S11 of the Supplementary Information. The system size was set at 128 × 128 × 128 under PBCs, and a regular 128 × 128 × 128 grid mesh was used. In the present study, the following cases were examined:N = 20 and 40 . According to the mean field prediction 94 , the boundary value, χN, of the order-disorder phase transition is approximately 23.5 for f = 0.2 and 12.5 for f = 0.35 . Thus, we generated images for χN ≥ 25 , as presented in Fig. 1 . In practice, we obtained the 3D field data with an χN interval of 0.5. All the images were obtained from cross-sectional views of the 3D density field data of the A domain in random directions at randomly selected positions. A total of 10,000 input images with 64 × 64 pixels were prepared for each class. In generating a cross-sectional view with 64 × 64 pixels from 3D field data of 128 × 128 × 128 grids under the PBCs, we performed linear-weight interpolation. Here, the images were 8-bit gray-scale images. We placed the same data in 3 RGB channels for generality in preliminarily tests such as transfer learning using the weight data trained by ImageNet 38 . Learning with the same data on three channels did not have any significant effect, except for a slight difference in convergence behaviors. This differs from the method of obtaining highly symmetric structures from SCF calculations. To construct ordered structures in the shape of lamellae, cylinders, and gyroids, artificial initial estimate and cell-size optimization-a parameter search of the box size to minimize the free energy 95 -are effective. The initial value and search range are important to obtain a reasonable solution. If we start from uniformly mixed initial states, hydrodynamic effects are essential to obtain ordered structures 101 . By contrast, to obtain random network of phase-separated domains, spatially uncorrelated fields were used as initial density profiles and cell-size optimization was not used. Image classification by DL. In the image-classification problem, the labels of the training images are learned and the trained model outputs the estimated probability of each label for an arbitrary image. CNNs are well known to have high image-classification ability [38] [39] [40] [41] [42] [43] [44] . Keras 96 provides all popular network models for image classification including VGG-16 model, which is one of the more successful CNN models. Comparisons among popular network models provided by Keras 96 are presented in Section S12 of the Supplementary Information. www.nature.com/scientificreports/ The VGG-16 model has 16 layers, including five convolutional blocks (13 convolutional layers), as shown in Fig. 8 . To determine the parameters of the VGG-16 model, we used TensorFlow 97 as the backend for Keras. For image classification, 6000 and 2000 images per χN class were used as training and testing images, respectively, for the learning and for evaluating the generalization ability. The stochastic gradient descent (SGD) method was used as the optimizer for the classification problem; a standard learning rate of 10 -4 and momentum 0.9 was used for simplicity. In the regression problem, the values of the training images are learned and the trained model outputs the estimated values for an arbitrary image. For the regression problem, we used a network based on the VGG-16 model, as presented in Fig. 8b . Compared to the classification problem, in the regression problem, the last block is different, as shown in Fig. 8 . Figure 8 . Schematic images of network architectures for (a) image-classification problem and (b) regression problem based on the VGG-16 model. The first five convolutional blocks are the same, but the last block is different. For the image-classification problem, the output is a vector whose number of elements equals the number of classes. For the regression problem, the output is a scalar. Here, the numbers at the lower right of each block denote the number of elements of the output tensor of each block. Deep learning Deep learning in neural networks: An overview Reducing the dimensionality of data with neural networks Imagenet large scale visual recognition challenge End to end learning for self-driving cars Mastering the game of Go with deep neural networks and tree search AI systems aim to sniff out coronavirus outbreaks Artificial intelligence-enabled rapid diagnosis of patients with COVID-19 Application of deep learning technique to manage COVID-19 in routine clinical practice using CT images: results of 10 convolutional neural networks Machine learning in materials informatics: recent applications and prospects Recent advances and applications of machine learning in solid-state materials science Machine learning for composite materials Challenges and opportunities of polymer design with machine learning and high throughput experimentation Recent advances in machine learning towards multiscale soft materials design Materials by design for stiff and tough hairy nanoparticle assemblies Machine learning-aided analysis for complex local structure of liquid crystal polymers Autonomous molecular design by Monte-Carlo tree search and rapid evaluations using molecular dynamics simulations Machine-learning-assisted discovery of polymers with high thermal conductivity using a molecular design algorithm Machine learning enables polymer cloud-point engineering via inverse design Deep materials informatics: Applications of deep learning in materials science Advanced steel microstructural classification by deep learning methods Extracting dislocation microstructures by deep learning Deep learning for semantic segmentation of defects in advanced STEM images of steels Optimizing convolutional neural networks to perform semantic segmentation on large materials imaging datasets: X-ray tomography and serial sectioning Big-data science in porous materials: Materials genomics and machine learning High throughput quantitative metallography for complex microstructures using deep learning: A case study in ultrahigh carbon steel Deep learning model for predicting phase diagrams of block copolymers Super-resolution for asymmetric resolution of FIB-SEM 3D imaging using AI with deep learning CT-image of rock samples super resolution using 3D convolutional neural network Enhancing images of shale formations by a hybrid stochastic and deep learning algorithm General resolution enhancement method in atomic force microscopy using deep learning High-speed piezoresponse force microscopy and machine learning approaches for dynamic domain growth in ferroelectric materials 0.7 Å resolution electron tomography enabled by deep-learning-aided information recovery Application of deep learning to inverse design of phase separation structure in polymer alloy Three-dimensional study of cylindrical morphology in a styrene-butadiene-styrene block copolymer Transmission electron microtomography in polymer research Transmission electron microtomography and polymer nanostructures ImageNet classification with deep convolutional neural networks Very Deep Convolutional Networks for Large-Scale Image Recognition Deep residual learning for image recognition Going deeper with convolutions Xception: Deep learning with depthwise separable convolutions Mobilenetv2: inverted residuals and linear bottlenecks. Proc. IEEE Conf. Comp. Vis. Patt. Recogn Densely connected convolutional networks Introduction to Polymer Physics The Equilibrium Theory of Inhomogeneous Polymers Unifying weak-and strong-segregation block copolymer theories The gyroid: A new equilibrium morphology in weakly segregated diblock copolymers Direct measurement of interfacial curvature distributions in a bicontinuous block copolymer morphology Stability of the A15 phase in deblock copolymer melts Density functional theory for block copolymer melts and blends Stable and unstable phases of a diblock copolymer melt Statistical Physics of Polymers: An Introduction Polyisoprene-polystyrene diblock copolymer phase diagram near the order-disorder transition Chain architecture and asymmetry in copolymer microphases Morphology and domain size of a model graft copolymer Morphologies and domain sizes of microphase-separated structures of block and graft copolymers of different types Cyclic block copolymers for controlling feature sizes in block copolymer lithography Sub-10 nm nano-organization in AB2-and AB3-type miktoarm star copolymers consisting of maltoheptaose and polycaprolactone Well-organized dense arrays of nanodomains in thin-films of poly(dimethylsiloxane)-b-poly(lactide) diblock copolymers Producing small domain features using miktoarm block copolymers with large interaction parameters Branched block copolymers for tuning of morphology and feature size in thin film nanolithography Using block copolymer architecture to achieve sub-10 nm periods Microphase separation of carbohydrate-based star-block copolymers with sub-10 nm periodicity Impact of cyclic block copolymer chain architecture and degree of polymerization on nanoscale domain spacing: A simulation and scaling theory analysis Lamellar domain spacing of diblock copolymers of ring and 4-arm starreal-space self consistent field method versus dissipative particle dynamics simulation Directed self-assembly of block copolymers for next generation nanolithography Directed self-assembly of block copolymers for nanocircuitry fabrication High quality sub-10 nm graphene nanoribbons by on-chip PS-b-PDMS block copolymer lithography Using block copolymers as infiltration sites for development of future nanoelectronic devices: Achievements, barriers, and opportunities Advances in nanoimprint lithography Nanofabrication by electron beam lithography and its applications New generation electron beam resists: A review Optimization and control of large block copolymer self-assembly via precision solvent vapor annealing Morphology evolution of PS-b-PDMS block copolymer and its hierarchical directed self-assembly on block copolymer templates Development of ordered, porous (sub-25 nm dimensions) surface membrane structures using a block copolymer approach Polarity-switching top coats enable orientation of sub-10-nm block copolymer domains 10 nm scale cylinder-cubic phase transition induced by caramelization in sugar-based block copolymers Relationship between microphase separation structure and physical property of thermoplastic elastomer mixtures Structure analyses of the mixture of thermoplastic elastomers having different symmetry in stretching process Equilibrium behavior of symmetric ABA triblock copolymer melts Equilibrium behavior of asymmetric ABA triblock copolymer melts The standard Gaussian model for block copolymer melts Asymmetric PS-block -(PS-co-PB)-block -PS block copolymers: morphology formation and deformation behaviour Molecularly asymmetric triblock copolymers as a single-molecule route to ordered bidisperse polymer brushes Morphology re-entry in asymmetric PS-PI-PS' triblock copolymer and PS homopolymer blends Dissipative particle dynamics of triblock copolymer melts: A midblock conformational study at moderate segregation Microstructural study of mechanical properties of the ABA triblock copolymer using selfconsistent field and molecular dynamics Scattering patterns and stress-strain relations on phase-separated ABA block copolymers under uniaxial elongating simulations Recoverably and destructively deformed domain structures in elongation process of thermoplastic elastomer analyzed by graph theory Theory of the interface between immiscible polymers. II Computer simulations of nano-scale phenomena based on the dynamic density functional theories: Applications of SUSHI in the OCTA system Computer Simulation of Polymeric Materials. Application of the OCTA System Theory of microphase separation in block copolymers Epitaxial transition from gyroid to cylinder in a diblock copolymer melt TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems Scikit-learn: Machine learning in Python A study of image classification based on deep learning for filler morphologies in rubber materials Large-scale reverse Monte Carlo analysis for the morphologies of silica nanoparticles in end-modified rubbers based on ultra-small-angle X-ray scattering data Hydrodynamic effects on the disorder-to-order transitions of diblock copolymer melts A method for stochastic optimization The authors declare no competing interests. Supplementary Information The online version contains supplementary material available at https:// doi. org/ 10. 1038/ s41598-021-91761-8.Correspondence and requests for materials should be addressed to K.H.Reprints and permissions information is available at www.nature.com/reprints.Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.