dataesr/scientific-paragraphs-categorization huggingface dataset:
g. , subvertical cliffs without long slopes). The value of the energy line angle will depend on the morphology of the surface; therefore, INRAE and BRGM  [58]  compiled an inventory of rockfall events and developed tools to obtain energy line angles that correspond to the individual surface slope's characteristics. In order to compare the morphology of various topographic profiles, Levy et al. [59]  defined the dimensionless areas under the topographic profile (DAP) (Figure  5 ) that will only provide the change in length/height (L/H 0 ). To validate this model's concept, a database on past rockfall events needed to be expanded. The authors of this method collected over 2800 events  [60] , and the databases were later enriched within the ROCKtheALPS project (Interreg-Alpine Space project), where more than 3600 events across the Alps were added  [14, 61].
The distributions of rock deposits and energy line angles were statistically quantified using the following: (i) non-linear regression, (ii) transformation of the variables for reductions into classic linear regressions, (iii) regression on extreme quantiles (with power transformation), and (iv) the calibration of the probability law of the logit-normal type. Following these statistical evaluations, an ELANA mapping tool was developed  [60]. ELANA is used to spatially map the probability of rockfall propagations in 2D. It uses DTM with a defined source area, and it obtains the values of energy line angles for high, medium, and low rockfall hazard risks from the proposed empirical laws. The software interpolates profiles around each starting pixel in order to determine the location of rockfall propagation limits for each profile.
The final results are fixed on the rockfall probability that presents the worst-case angle value for all profiles intercepting the pixels. Based on the rockfall activity, three homogeneous probability zones are defined  [58] : (i) high (at least one rockfall event every year), (ii) medium (rockfall event every 10 years), and low (rockfall events every 100 years). Based on the profiles of rockfalls in this study (Figure  6 ), the ELANA tool was used to obtain values of ß for each site for high, medium, and low rockfall propagation probabilities (Table  2 ). To validate this model's concept, a database on past rockfall events needed to be expanded. The authors of this method collected over 2800 events  [60] , and the databases were later enriched within the ROCKtheALPS project (Interreg-Alpine Space project), where more than 3600 events across the Alps were added  [14, 61].
The distributions of rock deposits and energy line angles were statistically quantified using the following: (i) nonlinear regression, (ii) transformation of the variables for reductions into classic linear regressions, (iii) regression on extreme quantiles (with power transformation), and (iv) the calibration of the probability law of the logit-normal type. Following these statistical evaluations, an ELANA mapping tool was developed  [60]. ELANA is used to spatially map the probability of rockfall propagations in 2D. It uses DTM with a defined source area, and it obtains the values of energy line angles for high, medium, and low rockfall hazard risks from the proposed empirical laws. The software interpolates profiles around each starting pixel in order to determine the location of rockfall propagation limits for each profile.
The measurements on the field were performed with a measuring tape, and for each dimension, we aimed for the maximum geometrical length, which was estimated based on the visual inspection. The measurements in both photogrammetric and LiDAR point clouds were performed in two steps. Firstly, each rock was extracted from the common point cloud. This was carried out with segmentation in the CloudCompare software  [61]. In this step, the outlier points were eliminated in order to reduce potential overestimations of dimension.
The measurements on the field were performed with a measuring tape, and for each dimension, we aimed for the maximum geometrical length, which was estimated based on the visual inspection. The measurements in both photogrammetric and LiDAR point clouds were performed in two steps. Firstly, each rock was extracted from the common point cloud. This was carried out with segmentation in the CloudCompare software  [61]. In this step, the outlier points were eliminated in order to reduce potential overestimations of dimension calculations. Secondly, the dimensions of single rocks were automatically extracted with an algorithm named minimum bounding volume in ArcGIS Pro  [62]. This algorithm creates multipatch features, which represent the volume of space occupied by a set of 3D features (Figure  8 ).
Maximum Runout Zones The modeled maximum runout zones between the different methods of obtaining the dimensions of rock input data were evaluated using a Rockyfor3D simulation model and examining the propagation probability. This modeling result represents the most realistic spatial distribution of the current rockfall event, and it is used for the calculation of spatial calculation probability, which is often used in rockfall hazard analyses  [11]. To compare the modeling results of rockfall runout areas to an actual rockfall area, goodness-of-fit (GOF) indexes  [73]  were used. GOF indexes are based on pixel-by-pixel comparisons between the observed rockfall area (OR) and predicted rockfall area (PR), and the comparisons are made with rockfall modeling. Rockfall modeling is carried out by comparing OR and PR results in a binary map with positive values that correspond to the actual rockfall area and negative values that correspond to areas without rockfall areas.
Conclusions This study has shown the application of UAV-acquired LiDAR and photogrammetric point clouds for measuring rock dimensions in order to provide input parameters for modeling rockfall propagation areas. The purpose of the study was to show that these datasets can be used as an alternative to the traditional approach of measuring rock dimensions on the field by using a measuring tape. With UAV surveys, it is possible to cover larger areas and obtain data at larger scales, with decreased fieldwork efforts and most importantly improved safety conditions for fieldwork at rockfall areas. This study provided a comparison of measurement methods with respect to rock dimensions (width, length, and height) between field, LiDAR, and photogrammetric survey methods. The results of this study show that the minimum bounding volume method can be used for extracting the dimensions of rocks from LiDAR and photogrammetric point clouds since the measured values are comparable to those on the field.
Funding: The authors express their gratitude to the Pahernik Foundation for providing funds to prepare this paper. This research was also supported by the Slovenian Research Agency project J1-3024 (Deciphering the sensitivity of rock faces to climatic changes and freeze-thaw cycles in permafrost-free regions) and Interreg Alpine Space projects "ROCKtheALPS" (ASP 462) and "GreenRisk4ALPs" (ASP 635). The third author acknowledges the financial support from the Slovenian Research Agency (research core funding No. P4-0059).
22 mm 2 /year). Progression rates in eyes were significantly higher in diffuse trickling pattern as compared to eyes without hyperfluorescent abnormalities (p = 0. 003) and other diffuse patterns (p = 0. 024). No statistically significant difference was found in progression rates between the banded and diffuse trickling (p = 1. 01) or diffuse nontrickling (p = 1. 0). However, eyes with the banded pattern had a significantly higher progression rate than eyes without any hyperfluorescent abnormalities (p = 0. 038)  [6]. Biarnés et al. (2015)  also assessed the role of increased hyperfluorescence as a risk factor for GA progression (ClinicalTrials. gov identifier NCT01694095). They found a statistically significant relationship between GA growth and hyperfluorescence patterns, which were categorized as none, focal, banded, diffuse and undetermined.
e. , we can easily identify the color ranges in HSV). Color ranges representing hyperfluorescent areas were manually identified using the open-source graphic editor GIMP v2. 10. 4 (https://www. gimp. org/ (accessed on 1 April 2021)). Specifically, the Color Picker tool was used to scroll over the newly colored regions and identify the HSV values for hyperfluorescent areas. These values were used, along with the Python OpenCV inRange() function to extract and create both colored and binarized masks for the hyperfluorescent regions. Hyperfluorescent regions extracted from FAF images were classified into major transitionary groups (i. e. , early to late) in accordance with their changes in intensity and proximity to lesions in FAF images.
Cluster Tendency Testing for cluster tendency is a preliminary step to identify whether the data can form meaningful clusters based on different properties or characteristics  [16]. This process involves the application of statistical tests to evaluate the data structure and assesses whether the data are uniformly distributed. A uniform dataset would suggest there is an absence of structure or pattern and any clustering method tested will be unlikely to yield significant results. To evaluate cluster tendency, the Hopkins statistical test for spatial randomness of a variable can be used  [16]. The Hopkins test is denoted as  [17] : H = ∑ m j=1 u d j ∑ m j=1 u d j + ∑ m j=1 w d j (1) where [X = (x i |i = 1 to n] refers to a collection of patterns, n, in the dimensional space, d (i. e. , x i = [x i1 , x i2 ,.
, x id ], Y = [j = 1 to m], where m are sampling origins placed at random in space d. In the Hopkins statistic, two distances are used: u j refers to the minimum distance from y i to its nearest pattern in X, and w j is the distance from a randomly selected pattern in X to its nearest neighbor  [17]. The null hypothesis for the Hopkins test is that the data contains no clusters and is uniformly distributed. The alternative hypothesis is that the dataset is not uniformly distributed and contains meaningful clusters. The values for the Hopkins test range from 0 to 1. To reject the null hypothesis, the value of H would be larger than 0. 5 and close to 1 for well-defined clusters. For H values less than 0. 5, this would suggest the data are regularly spaced and data cannot be clustered. In instances where the space d is uniformly distributed, the distances u j and w j would be close to each other, whereas if clusters are present, it is anticipated that u j distances would be substantially larger than w j.
Note on Software: To execute the Hopkins test in the Python language, the pyclustertend package was used (https://pypi. org/project/pyclustertend/ (accessed on 16 April 2021)). The package uses the formula 1 -H so that clusterability is interpreted as being a value close to 0. For the pyclustertend package, a high score (i. e. , 0. 3 and above) suggests that the data cannot be clustered.
Unsupervised Clustering Methods A diverse range of clustering algorithms was investigated as part of this analysis. These included Affinity Propagation, Agglomerative Clustering, Balanced Iterative Reducing and Clustering (BIRCH), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), k-Means, Mini-Batch k-Means, and Spectral Clustering. These approaches are described in more detail as follows. The Affinity Propagation clustering approach identifies samples in the data that are most representative of a cluster, and measures similarities between data samples  [18]. Agglomerative Clustering begins by partitioning the data into single nodes and, step by step, merges paired data which are the closest nodes into a new node, until only a single node is left (i. e. , the entire dataset)  [19].
The BIRCH approach takes large datasets and converts them into more compact, summarised versions that retain as much data distribution information as possible, and uses the data summary in lieu of the original dataset  [20]. The DBSCAN approach proposed for spatial databases with noise finds cluster points that are close together within specified distances, and considers points which are far away from the other points as outliers  [21]. The k-Means approach relies on the distance between points and calculates cluster centers or centroids, and thus partitions that data around these centroids  [22]. The Mini-Batch k-Means approach is similar to the more traditional k-Means approach. However, rather than using an entire dataset, it uses small batches making this a faster algorithm than its traditional counterpart  [23].
Visualization of Clusters Two types of plots were used in the analysis for graphical visualization of clusters: scatter plots and silhouette plots. Scatterplots are used to visualize the placement of datapoints and the clusters using the first and second order statistical features of the datasets showing lesions and hyperfluorescence. Silhouette plots, on the other hand, show how the data are distributed into the respective clusters (i. e. , total number of images that go into each cluster), and they also determine whether each assigned cluster exceeds or falls beneath the average silhouette score. In addition to the above, following the identification of the optimal number of clusters, the original images (i. e. , hyperfluorescence segmentation outputs) are automatically labelled according to the specifications of the clustering model.
Data Transformation Prior to testing the various clustering algorithms, the following transformations were taken to ensure there was no skewness in the data: (1) Standardization of feature data. This involves removal of the feature mean (average) value and dividing non-constant features by their standard deviation to scale the data, which is equivalent to the statistical z-score  [25]. In Python, this is achieved using the StandardScaler() function in the package sklearn (https://scikit-learn. org/stable/ (accessed on 20 April 2021)). (  2 ) Reducing the complexity of the data using Principal Component Analysis (PCA), which transforms the collections of correlated features extracted from the images and condenses them into smaller, uncorrelated variables named principal components  [26]. This is achieved using the Python sklearn function PCA().
Cluster Evaluation Metrics There are different metrics which can be used for evaluation of meaningful clusters. The choice is contingent on whether we use an intrinsic (i. e. , internal) cluster quality measure or an extrinsic (i. e. , external) measure. The analysis presented here is for unsupervised clustering methods where there is no prior knowledge (unlike supervised learning). Therefore, to assess the quality of the clustering method, we adopt an intrinsic approach and evaluate the properties of the data itself. For this analysis, internal validation measures were used, such as the Silhouette Coefficient (SC), the Davies-Bouldin Index (DBI), and the Calinski-Harabasz Index (CHI). The SC is a proximity measure, assessing both the compactness of clusters as well the separation of clusters from one another.
5 and higher. In fact, the higher the value, the more we can validate that good clustering has been identified (i. e. , data points are well matched to their cluster and poorly matched to neighboring clusters). The DBI is a cluster separation measure and possesses the following qualities: (1) it can be applied to hierarchical datasets, (2) it is computationally feasible for even large datasets, and (3) can yield meaningful results for data of arbitrary dimensionality  [28]. The objective of DBI is to identify whether clusters are well-spaced from each other, and whether each cluster is very dense and likely to be a good cluster. It calculates the ratio of the sum of the average distances between two clusters and between cluster centers  [29]. The formula for the DBI is: DBI = 1 n ∑ n i=1 max j =i σ i + σ j d c i , c j (3) where n is the number of clusters, σ i is the average distance of all points in cluster i, σ j is the average distance of all points in cluster j, and c i and c j are the cluster centroids for clusters i and j, respectively.
4. Late-stage hyperfluorescent development: The hyperfluorescent regions of greatest intensity are classified as late stage. These are the areas thought to be precursors to lesion development. These regions are clearly highlighted in Figure  3. To extract the different hyperfluorescent stages and regions from the pseudocolored images, the following values were identified (using GIMP software) and were used in the extraction of varying hyperfluorescent regions: 1. Early The values were extracted as ranges to ensure extraction of the lower and upper limits of the colors in the pseudocolored images. While we have identified several hyperfluorescent development stages, the one with the greatest importance to lesion formation is the late-stage (i. e. , red) regions, given that the dark red regions represent high-intensity areas (i.
The lowest number of clusters identified was k = 92 clusters for lesions, k = 95 clusters for early-stage hyperfluorescence, k = 102 clusters for intermediate-stage hyperfluorescence, and k = 119 clusters for late-stage hyperfluorescence. These values were achieved by using a damping factor of 0. 9, and the preference option excluded. Another method which does not require the input of a potential cluster number is DBSCAN. DBSCAN also requires the modification of appropriate parameters to optimize and identify the most appropriate clusters for a dataset. The most prominent parameter for DBSCAN is referred to as epsilon. Epsilon is defined as the maximum distance between two datapoints. Rahmah and Sitanggang (2016)  proposed an automated method of tuning epsilon  [31]. The processing involves finding the shortest distance between each data point and its nearest neighbor, then sorting these distances in ascending order, and plotting the results on a curve.
The point at which maximum curvature takes place on a curve is where the optimal epsilon value for the dataset can be found. Optimal epsilons were calculated for all hyperfluorescent regions (Table  2 ). For early-hyperfluorescence, an epsilon value of 10 was found to be the most appropriate. Optimal epsilon value for intermediate-stage hyperfluorescence was 31 and 16 for late-stage hyperfluorescence. Despite the automated method of selecting optimal epsilon values for each hyperfluorescence region, there was an inconsistency in the results. While some SCs were good (i. e. , intermediate-stage hyperfluorescence had a SC of 0. 829), the DBI and CHI were not ideal (i. e. , DBIs were larger than expected, and CHIs smaller). As a result, the DBSCAN was ruled out as an appropriate clustering technique.
Another method that was ruled out early in this study was Spectral Clustering. Unlike DBSCAN and Affinity Propagation, the user can specify different cluster numbers and determine the quality of the output. Using Spectral Clustering, typically 2-3 clusters would be identified at most (Table  3 ). However, any attempts at looking at clusters larger than 2-3 would yield warnings and produce identical results, irrespective of the cluster being tested. There could be several reasons for this, namely: (1) Spectral Clustering is sensitive to change in the similarity map, and (2) Spectral Clustering works well with balanced datasets (i. e. , datasets with even occurrences of different classification categories), and falter if there are large differences between the datapoints within the clusters  [32].
Given the similarity in quantitative results and scatter plots, an additional approach was taken to discern one method from the other: to visually assess how the shapes and patterns of lesions and hyperfluorescence areas were being categorized (i. e. , to see how the 524 images were being divided into their respective clusters), and if the categorization looked consistent. The k-Means produced more consistent categorization (Figures  4 5 6 7 ), as patterns and shapes of hyperfluorescent areas within the clusters assigned seemed consistent, whereas Agglomerative had some inconsistencies (i. e. , some cluster groups had mixed shapes that did not seem to belong together). Therefore, the k-Means clustering method was chosen as the most appropriate for this dataset. The most appropriate number of clusters per hyperfluorescent region is shown in Table  8.
The repetitiveness of results with the use of Spectral Clustering can have many factors, but one which may be most probable for this dataset is that the dataset is not balanced (i. e. , there is not an equality of cases for each cluster). Among the remaining algorithms, k-Mean and Agglomerative clustering were the main contenders. They both had favourable SC, DBI, and CHI outcomes, and showed more distinguishable and separable clusters in the scatter plots. However, when it came to seeing how each image was clustered, the shapes and patterns within each cluster as produced by k-Means was much more consistent than Agglomerative, with the latter having the tendency to mix-in different shapes and patterns into one cluster group. As a result, the k-Means, a simple partitioning cluster method, was chosen as the best unsupervised clustering method (in combination with pre-processing techniques, such as scaling and PCA) for GA feature data.
Even though attempts were made to automate the selection of the epsilon parameters for DBSCAN, the results can change given their sensitivity to parameter changes. Proper settings can only be established by trial-and-error, and the analysis presented here was no exception  [28]. From establishing the most appropriate data transformations, to testing the different algorithms, and the selection of parameters, there is a still a component of human error in unsupervised clustering that needs to be addressed. Another potential limitation exists with the cases available in this cohort. The clustering was based on the shapes and patterns of the data in the trial. However, this dataset may not be representative of all GA cases and future research could investigate further applications to new data sets.
Computational modelling The angular-dependent spectral reflectivity map of the planar 1DPC is calculated by means of a MATLAB implementation of the transfer matrix method. The illumination is assumed as a TE-polarized plane wave incident on the 1DPC from the glass substrate at specific angles and wavelengths. As the surface pattern is introduced, we neglect the presence of the grating coupler and consider the resonant cavity only (i. e. the DBR and the inner spacer), leaving the design of the grating as a mere application of the Bragg law. Two approximate methods have been adopted. In a first approach, the freely available MATLAB package implementing the rigorous coupled waves analysis (RCWA) RETICOLO  [58, 59]  is used to model the full multilayer and the cavity on top, assumed as a one-dimensional (1D) corrugation with a defect spacer, along the two orthogonal xand y-direction (see Supplementary Figure  S2  and related description).
Acknowledgements: Computational resources were provided by  HPC@POLITO , a project of Academic Computing within the  Department of Control and Computer Engineering at the Politecnico di Torino  (http://hpc. polito. it). Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding:  M. C. Giordano  and  F. Buatier de Mongeot  acknowledge financial support by  Ministero dell'Università e della Ricerca , within the project ' Dipartimento di Eccellenza 2018-2022 ' art. 1 , c. 314-337 ,  Legge 232/2016. M. C. Giordano acknowledges financial support by  Ministero degli Affari Esteri e della Cooperazione Internazionale (MAECI)  within ' Progetti di Grande Rilevanza 2021-2023'bilateral project Italy-Vietnam 'Large-area 2D/plasmonic heterostructures for photocatalysis and energy storage (H2D )'.