dataesr/scientific-paragraphs-categorization huggingface dataset:
Analysis of trait relationships. All analyses were conducted in R (v. 3. 3. 3). Code is available at github. com/hjdthomas/Tundra_trait_variation. We performed principal component analysis (PCA) on plant traits for all global species, and for tundra species only using the R package 'prcomp'. As far as possible, we replicated the methods outlined in Diaz et al. (2016)  8  , though this was not always possible due to the use of gap-filled traits and additional data not included in TRY in Diaz et al. (2016)   8. We log transformed trait values to account for log-normal distributions, which is considered appropriate for data with different measurement scales  8. To test whether the inclusion of SSD altered results, and for comparison with Diaz et al. (2016)  8  , we performed supplementary analysis using a conversion from SSD to LDMC based on the correlation between these two traits  8, 145  , since LDMC and SSD individually have fewer trait observations than other traits at the global scale.
Although only an approximate conversion, this greatly increases the number of species available for the analyses and does not affect the distribution of trait-space or direction of trait loadings (Supplementary Figs. 8-10). We did not use converted values in the main analysis to avoid introducing additional sources of variation. To visualise trait-space, we plotted the first two PCA axes and direction and weighting of trait loadings. We performed PCA on the full global dataset (including tundra data) and highlighted tundra species within the overall distribution to identify the location of tundra species within global trait-space. We repeated PCA using tundra species only to compare global trait relationships with tundra trait relationships. We compared all pairwise trait correlations for both global and tundra species (Supplementary Fig.
2 ) to investigate consistency in trait-trait relationships, and investigated the strength and direction of trait loadings for global and tundra analyses to compare the location and relative importance of PCA axes (Supplementary Fig. 3 ). Finally, we calculated the contribution of traits loadings to each PCA axis using the 'fviz_contrib' function in the R package 'factoextra' (Supplementary Fig. 4 ). To investigate whether the location of species within tundra trait-space or along the two major axes of variation was influenced by climate, we categorised species according to temperature class (point colour). We plotted the distribution of species along PCA axes for each temperature class to test whether trait variation within multivariate trait-space was influenced by the species' thermal range (Supplementary Fig.
1 ). Variance partitioning. To investigate the sources of trait variation in the tundra, we conducted variance partitioning by fitting a generalised linear mixed-effects model to the variance across nested classification hierarchy (functional group/ species) using the R package 'nlme'. We then conducted a variance component analysis on this model using the 'varcomp' function in the R package 'ape'. Partitioning was performed on a trait-by-trait basis, so does not account for co-variation between traits. We used unexplained variance to represent the within-species variation (including within-individual variation), though some unexplained variation could also arise from measurement error. Variance partitioning was conducted for each site with greater than three observations per trait per species, and at least three sampled species, and summarised using the mean of all sites.
12, 13). For a given trait sampling site, we conducted variance partitioning analysis at the site scale (scale = 0). We then added data from the nearest site (shortest geographical distance) and conducted variance partitioning analysis on this expanded dataset (geographic scale = distance from starting site to most distant site). We added sites iteratively until all sites were included i. e. , the biome-scale was reached. We repeated this analysis across all trait sampling sites. To examine whether sources of trait variance were affected by differences in species richness at different geographical scales, we also calculated the species richness (number of unique species for which we have trait measurements, i. e. , size of the measured species pool) of the dataset at each sampling step. To summarise the relationship between variance explained, geographic scale and species richness, we performed a breakpoint analysis using the R package 'segmented' with one break point.
To calculate errors, we grouped trait observation sites into 5 km or 1 species bins and calculated the 95% intervals of the spread of values. These were plotted as error bounds using a second-order polynomial smooth. We visualised all analyses with geographic scale and species richness presented on a log 10 scale to highlight change at local scales. For non-logged figures see Supplementary Figs. 6, 7. To investigate if differences in the contribution of within-species and among-species variation to total trait variation were significant, we additionally grouped data into 10 equal bins, and tested the significance of source of variance using linear models, with a significance threshold of 0. 05. We highlighted insignificant bins on figures as grey shaded areas, which indicate scales at which the amount of within-species variation is not significantly different among-species variation.
Acknowledgements Additional data and contributions were provided by  L. Andreu-Hayles ,  O. Atkin ,  A. Blach Overgaard ,  J. Dickie ,  S. Dullinger ,  B. Enquist ,  J. Fang ,  K. Fleischer ,  H. Ford ,  G. Freschet ,  E. Garnier ,  R. Halfdan Jørgensen ,  K. Harper ,  S. Harrison ,  M. Harze ,  J. Hille Ris Lambers ,  R. Jackson ,  R. Klady ,  S. Kuleza ,  A. Lavalle ,  F. Louault ,  B. Medlyn ,  R. Milla ,  J. Ordonez ,  C. Pladevall ,  H. Poorter ,  C. Price ,  P. Semenchuk ,  F. Schweingruber ,  B. Shipley ,  A. Siefert ,  L. Street ,  J. Tremblay ,  E. Weiher ,  C. Wirth ,  I. Wright  and the  Royal Botanic Gardens Kew Seed Information Database (SID). We thank innumerable field technicians, logistics teams, graduate and undergraduate assistants for help with data NE/M016323/1 [I. M. -S.
, H. T. , A. B. ] and  NERC  doctoral training partnership grant  NE/L002558/1  [H. T. ]), and the  Synthesis Centre of the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig  ( DFG FZT 118 ; sTundra working group). The study has been supported by the TRY initiative on plant traits (http://www. try-db. org). The TRY initiative and database is hosted at the  Max Planck Institute for Biogeochemistry, Jena, Germany. TRY is currently supported by  DIVERSITAS/Future Earth  and the  German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig. Authors were supported by:  Academy of Finland  [A. E. ], ArcticNet  [E. F. , E. L. , L. H. , O. G. ],  Arctic Research Centre, Aarhus University  [J. N. N. ],  BBSRC   David Phillips Fellowship  [F. d. V. ],  Carl Tryggers Stiftelse för Vetenskaplig Forskning and Qatar Petroleum  ( QUEX-ESC-QP-RD-18/19  [J.
We then apply the method to the probabilistic absolute hypocenter catalog KaKiOS-16, which contains three decades of southern Californian seismicity. To reduce data size and increase computation efficiency, the new approach builds upon the previously introduced catalog condensation method that exploits the heterogeneity of the hypocenter uncertainties. We validate the obtained fault network through a pseudo prospective spatial forecast test and discuss possible improvements for future studies. The performance of the presented methodology attests to the importance of the non-linear techniques used to quantify location uncertainty information, which is a crucial input for the large-scale application of the method. We envision that the results of this study can be used to construct improved models for the spatiotemporal evolution of seismicity.
Method description The method shares the basic principles of agglomerative clustering  (Rokach and Maimon, 2005)  with additional improvements to suit the specifics of seismic data, such as the strong anisotropy of the underlying fault segments. We illustrate the method by applying it to a synthetic dataset obtained by sampling hypocenters on a set of five plane segments, and potentially adding uncorrelated background points which are uniformly distributed in the volume (see Fig. 2 ). The implementation follows the successive steps described below: i. For a given dataset featuring N hypocenters, we first construct an agglomerative hierarchical cluster (AHC) tree based on Ward's minimum variance linkage method  (Ward, 1963). Such a tree starts out with a cluster for each data point (i. e. , with zero variance) and then progressively branches into an incrementally decreasing number of clusters (see Fig.
2c, d ). At any step, the merging of two clusters is based on a criterion involving the minimum distance D w criterion given by D w C i , C j = x∈C ij x -r ij 2 - x∈C i (x -r i ) 2 - x∈C j x -r j 2 , (1) In this equation, C ij is the cluster formed by merging clusters C i and C j , x represents the set of hypocenters, and r (with proper subscript) is the centroid of each cluster. Hence, clusters i and j are merged if the sum of squares in Eq. (  1 ) is minimized after they are merged  into a single cluster ij. The number of branches in the tree is thus reduced by one, and the remaining clusters are used to decide which ones will be merged at the next iteration. This merging of clusters (i. e. , branches) continues until there remains only a single cluster. "Cut-ting" the AHC tree at the D w level corresponding to the desired number of branches allows one to choose the number of clusters (from 1 to N ) used to represent the original dataset.
We then continue our traverse along the tree down replacing each cluster that has more than four points by a Gaussian kernel. At each level on the tree, we count the number of these non-singular Gaussian kernels. The results are illustrated in Fig. 2b  where we consider two cases: the first considering only the five planes, the second one including a set of uniformly distributed background points. In the first case, we see that the maximum number of Gaussian kernels (  76 ) is obtained when we cut the tree so that the total number of clusters is 117. In the second case, in the presence of background points, the maximum number of Gaussian kernels (  77 ) is obtained when we cut the tree at a level of 214 clusters. We refer to this maximum number is as the "holding capacity" of the dataset, and the corresponding configuration defines the starting point of the following iterative and likelihood-based clustering algorithm.
The process of finding this optimum set of initial Gaussian proto-clusters (all containing more than four points) is coined as "atomization". iii. Once we determine the holding capacity, all points that are not associated with any Gaussian kernel are assigned to a uniform background kernel that encloses the whole dataset. The boundaries of this kernel are defined as the minimum bounding box of its points. The uniform spatial density of this background kernel is defined as the number of points divided by the volume (see Fig. 3 ). The Gaussian kernels together with the uniform background kernel represent a mixture model where each kernel has a contributing weight proportional to the number of points that are associated with it  (Bishop, 2007). This representation facilitates the calculation of an overall likelihood and allows us to compare models with different complexities using the Bayesian information criteria (BIC)  (Schwarz, 1978)  given by BIC = - N i log(L) + k 2 log(N ), (2) where L is the likelihood of each data point, k is the number of free parameters of the mixture model and N is the total number of data points.
The value of k is calculated as k = 10N C -1 (where N C is the number of kernels in the mixture) since each kernel requires 3 (mean vector) +6 (covariance matrix) +1 (weight) = 10 free parameters. The same parameterization is also used to describe the background kernel, which is a uniformly dense cuboid with a size and orientation prescribed by its covariance matrix. The number of free parameters (k) is reduced by 1 because the weights have to sum to unity and hence knowing N C -1 of them is sufficient. iv At the holding capacity, the representation with the large number of kernels is likely to constitute an overfitting model for the dataset. Therefore, we iteratively merge pairs of the Gaussian kernels until an optimal balance between fitness and model complexity is reached. We use the measure of information gain in terms of BIC to select which pair of kernels to merge.
To make our approach feasible for large seismic datasets, we introduce a preliminary check that considers clusters as candidates for merging only if they are overlapping within a confidence interval of σ √ directions. The factor √ 12 is derived from the variance of an hypothetical uniform distribution over a planar surface (for details see  Ouillon et al. , 2008). During all steps of the merging procedure, the data points are in the state of soft clustering, meaning that they have a finite probability to belong to any given kernel. A deterministic assignment can be achieved by assigning each point to the kernel that provides the highest responsibility (as per the definition of a mixture model), which is referred to as hard clustering. This dichotomy between stochastic and deterministic inference gives rise to two different implementations for the merging criteria: (1) local criterion, considering only the two candidate clusters and the data points assigned to them through hard clustering, and (2) global criterion, considering the likelihood of all data points for all clusters.
In essence, the local criterion tests the information gain for the case of two kernels versus one kernel on a subset, whereas the global criterion considers N c versus N c -1 kernels on the whole mixture and dataset. Figure  4  shows the resulting final reconstructions for the two criteria. For this synthetic dataset, we observe that both the local and global criteria converge to a similar final structure. The global criterion yields a model with the same number of clusters as the input synthetic, while the local criterion introduces four additional clusters in the under-sampled part of one of the faults. For most pattern recognition applications that deal with a robust definition of noise and signal, the global criterion may be the preferred choice since it is able to recover the true complexity level.
The Rand index measures the similarity between different clusterings and is expressed by the following equation: R = 2 (a + b) n (n -1) , ( 4 ) where a is the number of pairs that are in the same cluster in the two clusterings, b is the number of pairs that are in different clusters in the two clusterings and n is the number of points in the dataset. A Rand index of 1 indicates total match between the two groupings while a value of 0 indicates that all pairs are in disagreement. In our case, we are comparing the ground truth clustering, which is given by the 20 fault planes and the uniform background, and the clustering obtained by our method. Figure  5a  shows the Rand index obtained using the local and the global criteria as a function of increasing sampling density for the three levels of background noise.
The results are shown in Fig. 5b , where we see no drop off in the Rand index. These synthetics indicate that the method is robust in the presence of uniform background noise and that it is able to recover structures that are sufficiently sampled. In the presented case, the performance saturates around 0. 5 points per square kilometer; however, this value can change based on the particular setting. For instance, if faults are very closely spaced and intersecting, higher sampling may be needed. On the other hand, if the structures are isolated, similar performance can be achieved at lower sampling. The MATLAB code used for generating the synthetics and evaluating the reconstruction's Rand index is provided. Users may prefer to create synthetic cases that are informed by the properties of the actual data they are working on (such as numbers of points, spatial extent, etc.
Application to seismicity In this section, we apply our method to observed seismicity data. For this purpose, we use the KaKiOS-16 catalog  (Kamer et al. , 2017)  that was obtained by the probabilistic absolute location of nearly 479 000 southern Californian events spanning the time period 1981-2011. We consider all events, regardless of magnitude, as each event samples some part of the fault network. Before tackling this vast dataset, however, we first consider the 1992 Landers sequence as a smaller dataset to assess the overall performance and computational demands.
Small-scale application to the Landers aftershocks sequence We use the same dataset as  Wang et al. (2013)  that consists of 3360 aftershocks of the 1992 Landers earthquake. The initial atomization step produces a total of 394 proto-clusters that are iteratively merged using the two different criteria (local and global). The resulting fault networks are given in Fig. 6  together with the fault traces available in the community fault model of southern California  (Plesch et al. , 2007). Comparing the two fault networks, we observe that the local criterion provides a much detailed structure that is consistent with the large-scale features in the global one. We also observe that, in the southern end, the global criterion produces thick clusters by lumping together small features with seemingly different orientations.
Thus, by disregarding the kernel weights we are considering only the potential loci of earthquakes, not their activity rates. Another important aspect, in the case of such a large-scale application, is the uniform background kernel. The assump- tion of a single background kernel defined as the minimum bounding box of the entire dataset seems to be suitable for the case of Landers aftershocks; however, it becomes evident that for whole of southern California such a minimum bounding box would overestimate the data extent (covering aseismic offshore areas) and would thus lead to an underestimated density. In addition, one can also expect the background density to vary regionally in such large domains. We thus extend our approach by allowing for multiple uniform background kernels. For this purpose, we make use of the AHC tree that is already calculated for the atomization of the whole dataset.
We then cut the tree at a level corresponding to only a few clusters (5 or 30 in the following application), which allows the original catalog to be divided into smaller subcatalogs represented by each cluster. Each of these subsets is then atomized individually yielding its own background kernel. The atomized subsets are then brought together, to be progressively merged. Naturally, we have no objective way of knowing how many background kernels a dataset may feature. However, in various synthetic tests, involving cuboid backgrounds with known densities, we observe that inflating this number has no effect on the recovered densities, whereas a value that is too low causes underestimation. Apart from this justification, we are motivated to divide this large dataset into subsets for purely computational reasons as this allows for improved parallelization and computational efficiency.
Our fault reconstruction uses all events in the Y. Kamer et al. :  Fault network reconstruction using agglomerative clustering KaKiOS-16 catalog, regardless of their magnitude. The last event in this catalog occurred on 30 June 2011. For target events, we consider all routinely located events by the southern California Earthquake Data Center between 1 July 2011 and 1 July 2015 with magnitudes larger than M2. 5. We limit our volume of interest arbitrarily to the region limited by latitudes  [32. 5, 36. 0] , longitudes  [-121, -115]  and depths in the range 0-20 km. The likelihood scores of the target events are calculated directly from the fault network, which is essentially a weighted mixture of Gaussian PDFs and uniform background kernels. The only modification done to accommodate the forecast is aggregating all background kernels into a single cuboid covering the volume of interest.
The weight of this cuboid is equal to the sum of all aggregated background kernel weights. To compare the spatial forecasting performance of our fault network we consider the simple smoothed seismicity model (TripleS) (Zechar and Jordan, 2010) that was proposed as a forecasting benchmark. This model is obtained by replacing each event with an isotropic, constant bandwidth Gaussian kernel. The bandwidth is then optimized by dividing the dataset into training and validation sets. As already pointed out by Zechar and Jordan (2010) the construction of the model involves several choices (e. g. , choice of optimization function, choice of candidate bandwidths). To sidestep these choices we construct the TripleS model by optimizing the bandwidth parameter directly on the target set. Allowing this privilege of foresight, which would not be possible in a prospective setting, makes sure that the TripleS method is at its maximum attainable forecast skill.
Conclusion We presented an agglomerative clustering method for seismicity-based fault network reconstruction. The method provides the following advantages: (1) a bottom-up approach that explores all possible merger options at each step and moves coherently towards a global optimum; (2) an optimized atomization scheme to isolate the background (i. e. , uncorrelated) points; (3) improved computation performance due to geometrical merging constraints. We were able to analyze a very large dataset consisting of 30 years of southern Californian seismicity by utilizing the non-linear location uncertainties of the events and condensing the catalog to ∼ 20 % of its initial size. We validated the information gain of the reconstructed fault network through a pseudoprospective 3D spatial forecast test, targeting 4 years of seismicity.
Figure12. Average negative log likelihood for the target dataset limited to events above M2. 5 (light gray), M3. 0 (dark gray) and M3. 5 (black). Performance of the TripleS models is evaluated as a function of the isotropic kernel bandwidth (dotted lines). The fault network performance is plotted with constant level solid lines. The performance of a single uniformly dense cuboid is plotted with a dashed line.
Code and data availability. The MATLAB implementation of the agglomerative fault reconstruction method and the synthetic tests can be downloaded from https://doi. org/10. 5281/zenodo. 4274628 (Kamer, 2020). The KaKiOS-16 catalog can be downloaded from https://doi. org/10. 5281/zenodo. 4355424 (Kamer et al. , 2017). The MATLAB implementation of the condensation method can be downloaded from https://doi. org/10. 5281/zenodo. 4356218 (Kamer, 2014). Author contributions. All authors conceived and designed the research. YK wrote the paper with major contributions GO and DS. YK developed the computer codes.
Appropriate secondary Alexa Fluor Abs (Thermo Fisher Scientific) were used. DNA was marked with 4′,6-diamidino-2-phenylindole (DAPI) in Vectashield. Slides were analyzed with a confocal microscope system (Zeiss LSM 710) and images were acquired using the interfaced software ZEN 2010: both microscope hardware and software configuration were always maintained. Technical parameters fixed in our acquisition procedure were pinhole size, at 1 AU (Airy unit), laser power at 2%, and digital gain at 1. 0. Images were then processed using ImageJ software, in order to merge channels from monochrome acquisitions and make montage, when serial microscope scans of the specimen were performed along z axis. Plasmid and siRNA Transient Transfection. For transient protein expression, plasmid DNA was added to the cells for 48 h using Xtreme gene 9 reagent (Roche).