dataesr/scientific-paragraphs-categorization huggingface dataset:
Composite gene gain and loss events are concentrated at specific nodes on the phylogeny In order to determine the tempo of CHG gain and loss across the animal phylogeny we analysed a subset of 10,829 (from a total of 13,632) CHGs where we could categorise the CHG as single or multiple origin. For the 5,198 CHGs of single origin we analysed their evolutionary history using the irreversible Dollo model of evolution  (45)  implemented in the R package Claddis  (46, 47). For the 5,631 CHGs of multiple origin we used the reversible Mk model  (48)  implemented in the RevBayes software program  (49). We used the species tree shown in Figure 4  (50) (51) (52) , the most appropriate model as described above, and applied time calibrations extracted from the TimeTree database  (53). Using TimeTree as a source for divergence times allowed us to use a detailed phylogeny including all taxa of interest.
Acknowledgements This work was undertaken on ARC3, part of the  High-Performance Computing  facilities at the  University of Leeds, UK. We thank  Martin Callaghan  and all members of the  ARC team  for their excellent technical support. PM was funded through a  University Academic Fellowship  to MOC at the  University of Leeds. RM was funded by the  IRCSET PhD scholarship  ( GOIPG/2014/306 ). The authors wish to acknowledge the  Irish Centre for High-End computing (ICHEC)  for the provision of computational facilities and support. EB and JP were supported by a  FP7/2007-2013  Grant Agreement #  615274 , category LS8). C. J. C. wishes to acknowledge funding from the  European Commission  via  Horizon 2020  ( 818368 , MASTER with K. S. T. and  101000213  HoloRuminant); FJW was supported by a  Marie Skłodowska-Curie Individual Fellowship  (GA no.
Again, some success of the predictive power of dynamic facilitation was found  20, 21. Quantitative analysis contrasting the key objects of RFOT (e. g. the cooperatively rearranging regions) and dynamic facilitation (i. e. the elementary excitations) in the relevant regime of deep supercooling is lacking to date, and this is the focus of the present work. We exploit two new techniques to obtain dynamic particleresolved data in the regime beyond the mode-coupling crossover T < T mct to probe the predictions of thermodynamic and dynamic theories. The first of these developments is highly-efficient GPU simulations using the Roskilde University Molecular Dynamics (RUMD) package  22  on dedicated graphical processing units. The simulations provide a complete static and dynamical picture that forms much of our analysis.
The simulations allow us to study both the microscopic timescales of excitations and longer timescales associated with cooperative rearrangements. The colloidal data provide an experimental comparison of the spatial features of the cooperative rearrangements. The simulations are performed at a largeto-small particle composition of 2:1 and 3:1 for their enhanced stability against crystallisation compared to the often-used 4:1 composition  23. Unless otherwise specified, we present data from the 2:1 composition and N = 10,002 system size. Throughout, we use Lennard-Jones units for the larger particles for simulation data. For the experiments, we express time in Brownian times τ B and length in diameter σ. Experiment and computer simulation details are in the materials and methods and supplementary information (SI).
For these analyses, we require particle-resolved data sampled at differing rates. The excitations are identified on microscopic timescales, and we run short simulations for this purpose. For the CRRs, the timescales are much longer. In the case of the experimental data that we present, we have optimised the data acquisition for CRRs, and thus the limited number of frames accessible (around 100 per dataset) means that these are sampled at a timescale rather longer than that associated with excitations, and so, therefore, we focus the analysis of our experimental data on the CRRs. The string analysis also requires a higher frame rate, so here too, we focus on the simulation data. We furthermore compute the configurational entropy for the simulations data via thermodynamic integration  26.
Simulation and model details We study the binary Lennard-Jones Kob-Andersen (KA) mixture with 2:1 and 3:1 compositions in the NVT ensemble at a number density ρ = 1. 400 using the Roskilde University Molecular Dynamics (RUMD) package  22. The interactions of the KA mixture are defined by u ij ðrÞ = ϵ αβ ½ð σ αβ r Þ 12 À ð σ αβ r Þ 6 with parameters σ AB = 0. 80, σ BB = 0. 88 and ϵ AB = 1. 50, ϵ BB = 0. 50 (α, β = A, B). We employ a unit system in which σ AA = 1, ϵ AA = 1, and m A = m B = 1 (we refer to this as LJ units). We study system sizes N = 10,002 and 100,002 for KA 2:1 and N = 10,000 for KA 3:1. The temperature is in the range T = [0. 48, 2. 00] for KA 2:1 and T = [0. 68, 2. 00] for KA 3:1. For the lowest temperature it took well over 1 year to equilibrate on an Nvidia 1080 GTX card.
Acknowledgements We thank  Ludovic Berthier ,  Giulio Biroli ,  Jeppe Dyre ,  Paola Gallo ,  Rob Jack ,  Walther Kob ,  Andrea Liu ,  Itamar Procaccia ,  Camille Scalliet ,  Shiladitya Sengupta ,  Perfrancesco Urbani  and  Matthieu Wyart  for insightful suggestions and discussions. CPR and FT acknowledge the  European Research Council  ( ERC consolidator  grant  NANOPRS , project  617266 ) and the  EPSRC  ( EP/H022333/1 ) for financial support. CPR acknowledges the  ANR  project  DiViNew  for financial support. T. S. I. is supported by the  VILLUM Foundation"s Matter  grant (No. 16515 ).
, 2019)  and biogeochemistry  (Dentith et al. , 2020). We added Nd isotopes ( 143 Nd and 144 Nd) as optional passive tracers into the ocean component of FAMOUS, using a version of the model with the Met Office Surface Exchange Scheme (MOSES) version 1  (Cox et al. , 1999: FAMOUS-MOSES1). It was a pragmatic choice to avoid the more recent FAMOUS-MOSES2. 2 configuration  (Essery and Clark, 2003; Valdes et al. , 2017; Williams et al. , 2013; Essery et al. , 2001) , because evaluation of our new Nd scheme would be hindered by the collapsed Atlantic Ocean convection and strong deep Pacific MOC produced by FAMOUS-MOSES2. 2 under pre-industrial boundary conditions (see  Dentith et al. , 2019). Nonetheless, the Nd isotope code implementation presented here is directly transferable to other versions of the UK Met Office Unified Model (UM) version 4.
FAMOUS does contain an optional ocean biogeochemistry module (Hadley Centre Ocean Carbon Cycle; HadOCC), which includes simplified nutrient-phytoplankton-zooplankton-detritus (NPZD) classes  (Palmer and Totterdell, 2001)  and could instead be used as the basis for predicting vertical particle fluxes in the ocean (which was the approach adopted by  Arsouze et al. , 2009; Gu et al. , 2019; and Rempfer et al. , 2011). We favoured satellite-derived estimates in order to improve the accuracy of particle-associated cycling of Nd and reduce biases inherent to the intermediate complexity biogeochemistry model  (Dentith et al. , 2020; Palmer and Totterdell, 2001). This approach also optimises the computational efficiency of our scheme, since the added ecosystem and geochemistry tracer fields in HadOCC slows the model down.
Code Availability The code detailing the advances for the marine Nd isotope scheme (ND v1. 0) described in this manuscript is available via the Research Data Leeds Repository (Robinson 2022: https://doi. org/10. 5518/1136) under a Creative Commons Attribution 4. 0 International (CCBY 4. 0) license. These files are known as code modification (i. e. 'mod') files and should be applied to the original FAMOUS model code, which is protected under UK Crown Copyright and can be obtained from the National Centre for Atmospheric Science (NCAS) Computational Modelling Services (CMS): https://cms. ncas. ac. uk/, with specific FAMOUS documentation available at: https://cms. ncas. ac. uk/miscellaneous/um-famous/. All files and corresponding information that needs to be applied to configure each individual simulation presented here are available from the same DOI (above); note that to complete the setup of these simulations, line 4909 in each simulation's tracer.
A. Experimental Setup We validate the proposed approach in a realistic simulation environment implemented in MATLAB/Simulink. The environment simulates the platform shown in Fig. 3  with the corresponding actuator dynamics. The platform is a modification of the dual-tilt quadrotor platform from  [7]  with a higher thrust to weight ratio such that ū/m B g = 1. 05. With the current configuration, each propeller can generate thrust in a semi-sphere to avoid propellers' collision with the platform's arms. As such, the platform's constraints can be written as follows: u x,1 ≥ 0, u y,1 ≥ 0 (24) u x,3 ≤ 0, u y,4 ≤ 0 (25) 0 ≤ u i 2 ≤ ū2 i ∀i = {1, 2, 3, 4} (26) where we assumed u = 0. The force set of the platform while applying zero moment is shown in Fig. 4. It is easy to see that, it is difficult to fit a cylinder or a cone into the force set (similar to  [15] ,  [16] ) without either reducing the reachable force set, or breaking the actuation constraints.
Pauline Pounds  upon evaluation of the reviewers' comments. The work of  Mahmoud Hamandi  was supported by the  NYUAD Center for Artificial Intelligence and Robotics , funded by  Tamkeen  through the  NYUAD Research Institute  Award  CG010. The work of  Antonio Franchi  was supported by the  H2020 Research and Innovation Program  under Grant  871479  ( AERIAL -CORE ). This work was supported by the  Khalifa University of Science and Technology  under Award  RC1-2018-KUCARS  and Project  CIRA-2020-082.
We integrate UF into a merging methodology that combines similar clusters within a partition, allowing us to determine the number of clusters without the need to run the clustering algorithms iteratively as other CIVIs require. We undertake a comprehensive evaluation of our proposal on 5,250 convex, 36 non-convex synthetic datasets, and five benchmark real datasets. In addition, we apply UF in a real-world scenario that involves high uncertainty: Passive Acoustic Monitoring (PAM) of ecosystems, which aims to study ecological transformations through acoustic recordings. The results show that UF exhibits notable performance in synthetic and real-world scenarios, obtaining an Adjusted Mutual Information (AMI) score higher than 0. 88 for normal, uniform, gamma, and triangular distribution datasets.
External indices compare the clustering results with prior data labels or cluster prototypes  (Halkidi et al. , 2002b). CIVIs are used to measure different characteristics of data and are based on different assumptions. Numerous studies have evaluated CIVIs for crisp  (Arbelaitz et al. , 2013; Halkidi et al. , 2002a,b) , density  (Agrawal et al. , 2015a) , and fuzzy clustering  (Wang and Zhang, 2007). It is widely accepted that no single CIVI can perform well in all applications  (Iglesias et al. , 2020). Instead, the validation paradigm has shifted towards using specific CIVIs for particular applications based on the assumptions of each index. For instance, CIVIs have been developed for social networks  (Campo et al. , 2016) , pharmacological datasets  (Rivera-Borroto et al. , 2012) , bioinformatics  (Handl et al.
In this work, we propose a novel CIVI, named Uncertainty Fréchet index (UF), which uses a modified Wang's Type 2 fuzzy Gaussian Mixture Models (T2FGMM) uncertainty function  (Wang and Zhang, 2007)  and a Fréchet Distance inspired by the research field of optimal transport  (Panaretos and Zemel, 2019) , which has been never used in CVI. To evaluate UF's performance, we apply a CVI assessment methodology  (Gurrutxaga et al. , 2011)  that employs various metrics to compare UF with other established CIVIs. We extensively evaluate UF using 5,250 synthetic datasets with different convex distributions, such as normal, uniform, logistic, gamma, and 36 non-convex datasets such as triangular, moon shape, and ring shape, as well as real-world benchmark datasets (Iris, Wine, Breast cancer, Liver, Digits, Haberman, Ionosphere SwedishLeaf, Wafer, ArrowHead, BeetleFly, Car) from the UCI repository  (Dua and Graff, 2017)  and UCR  (Chen et al.
, 2015)  repository and the PAM application dataset  (Rendon et al. , 2022a). Although UF was initially designed for Gaussian non-isotropic data, our evaluations demonstrate that it achieves remarkable results for uniform, triangular, and non-convex distributions. Our findings indicate that UF outperforms or performs similarly to well-established CIVIs in terms of accuracy, robustness, and stability across a range of datasets. The proposed UF index stands out from other CIVIs in the literature due to two notable features: First, A Footprint Of Uncertainty (FOU) of partitions is quantified, measuring the uncertainty associated with each cluster; Secondly, our proposal measured inter-cluster distances through the Fréchet distance, considering the relationships among variables. Both metrics incorporate the underlying geometry of the space, which has not been explored before in cluster validation research.
Previous works Several CIVIs estimate the intra-similarity and inter-separation among the clusters in the literature. Cohesion and separation-based indices examine the relationship between within-group scatter/dispersion and between-group scatter/dispersion distances. These metrics are based on cluster centers and typically do not consider the shape of the cluster, thereby failing to capture non-convex clusters. Some authors have addressed this limitation with graphical models such as ideogram methodologies  (Iglesias Vázquez et al. , 2021) , but these methods introduce additional hyperparameters that increase the algorithm's complexity. Cohesion and separation-based CIVIs, such as Silhouette (SI), Davies Bouldin (DB), Gamma (G), and Calinski-Harabasz (CH), have demonstrated the best results for normally distributed datasets.
However, SI and CH tend to produce clusters formed by noise  (Arbelaitz et al. , 2013). Similarly, G, DB, and Dunn Index (DI) penalize noisy cluster behavior at the expense of struggling with nonglobular densities. Dispersion-based CIVIs that rely on the dispersion of data are not necessarily the optimal choice for finding convex partitions. Nevertheless, these CIVIs are commonly used with dense, sparse, and arbitrarily shaped datasets. Some cohesion and separation CIVIs, including Partition Coefficient (PC), Partition Entropy (PE), and Interclass Contrast Coefficient (ICC), use only fuzzy membership degrees, considering those clusters with high degrees of membership for data close to the cluster prototype and low degrees for data far from the prototype. These indices are useful when it is not feasible to work with the data directly but with their degrees of belonging to each class  (Isaza, 2007).
Only Two CIVIs, Relative Uncertainty (RU)  (Sirmen and Üstöndag, 2022)  and -stable  (Ozkan and Türkşen, 2012) , have been proposed in terms of Type-2 fuzzy clustering, which allows working with a higher level of uncertainty regarding the variables. However, these indexes are only proposed for fuzzy partitions. The performance of CIVIs generally depends on dataset properties. For instance, as the degree of overlapping increases, the performance of most CIVIs tends to decrease, except for Dunn and DB indices. Noise level is the factor that has the greatest impact on CIVIs, degrading their performance by an average of three times  (Arbelaitz et al. , 2013; Iglesias et al. , 2020). Furthermore, non-convex clusters usually pose greater challenges for most CIVIs  (Lee et al. , 2018). Although CIVIs can be adjusted by varying the number of clusters within a lower and an upper bound, alternative methodologies have been proposed, specialized in dissolving irrelevant and unrepresentative clusters commonly generated by noisy data  (Gurrutxaga et al.
Achieving these characteristics is critical for the effective deployment of CIVIs in real-world scenarios. Thus, in the proposed methodology, we incorporate properties of the Fuzzy Type-2 theory to obtain information for measuring the quality of partitions. Previous work stresses the importance of developing new methodologies and evaluating the performance of new CIVIs across various applications  (Arbelaitz et al. , 2013; Xu et al. , 2020). To address these challenges, we propose the Uncertainty Fréchet (UF) index, which can identify both convex and non-convex clusters under uncertain data assumptions. UF is based on Type-2 fuzzy sets, but it is designed to handle a large number of data points and clusters without relying on the membership degrees of the data. To find the number of clusters, we propose a merging methodology based on UF, as a metric to establish the number of clusters.
Experimental framework This section details the testing of UF on multiple datasets with varying data distributions, including both convex and non-convex types. To evaluate UF's effectiveness, we conduct tests on different data features, such as noise, compactness, and overlapping. By manipulating these features, we sought to thoroughly evaluate the performance of UF across a range of scenarios. In summary, we test our proposal with three case studies: synthetic datasets, the real-world case study of Passive Acoustic monitoring datasets, and the case study with publicly available real-world data. We explain each of these case studies in the following subsections.
Synthetic datasets We test UF with synthetic convex and non-convex datasets. We generate the data using combinations of the parameters presented in Table  4  and Table  5  to generate 5,250 convex and 36 non-convex synthetic datasets respectively. Each generated dataset has 5,000 samples each with different distributions uniform, normal, logistic, gamma, triangular, ring-shape, and moon-shape. For data generation, we used the MDCenpy framework  (Iglesias et al. , 2019)  and Scikit-learn with make-moons and make rings functions  (Pedregosa et al. , 2011).
Benchmark datasets We test our methodology in common real-world datasets as benchmarks commonly used to test CIVIs. We use Iris, Wine, Breast cancer,    (Xing et al. , 2022; Guo et al. , 2017)  See Table  6  to see the principal characteristics of each one. In the case of time-series data, there are usually local and global patterns. New algorithms, such as Deep Temporal Clustering Representation (DTCR)  (Guo et al. , 2017) , and Robust Temporal Feature Network (RTFN) for feature extraction related to time series classification  (Xiao et al. , 2021a) , have been able to deal with this type of data. However, one of the challenges for recent functional clustering algorithms for time series  (Guo et al. , 2017)  is to increase the performance and deal with missing data. Therefore, we employ the recently proposed Clustering Method Representation Learning on Incomplete time-series data  (Guo et al.
Passive acoustic monitoring application Passive Acoustic Monitoring (PAM) is a particular application that needs to consider uncertainty metrics to evaluate the obtained partitions. PAM uses recordings of soundscapes collected at ecosystem sites that are analyzed through clustering algorithms for analyzing community dynamics and landscape transformation. The recorded soundscape is composed of an amalgam of sounds such as anthrophony: humangenerated sources, geophony: earth sounds such as rain, wind, and  thunders, and biophony: biologically generated sounds. Particularly, there are data for biological phenomena, that clustering could confuse with outliers, noise, or vice versa, as well as high uncertainty for ecologists to identify the type of transformation of a point. Therefore, in this application a CIVI based on uncertainty is crucial.
Some CIVIs were tested on PAM studies  (Rendon et al. , 2022b) , finding that none has shown good performance to define a good evaluation. Consequently, we decided to test UF in a PAM dataset of 23,540 acoustic recordings supplied by the Alexander von Humboldt Biological Resources Research Institute of Colombia. The acoustic recordings were collected between 2015 and 2017 in the Bolivar department of Colombia's Caribbean region as part of the Global Environment Facility (GEF) project  (Rendon et al. , 2022a). The study locations are located in a tropical dry forest ecosystem, which is situated below 1,000 meters above sea level, highly seasonal in its rainfall with dry periods of at least three months. Twelve sites were sampled over a landscape transformation gradient in the Arroyo Grande (Bolivar) area as shown the image 3.
However, there has been evidence that clustering algorithms do not always determine the correct partitions (complex environments such as noisy datasets, and over-sampled clusters). In 2011,  Gurrutxaga et al. (2011)  proposed a new evaluation methodology, where the best partition must be chosen using different similarity metrics depending on the criteria evaluation. In this work, we use the three following metrics: 1. The Adjusted Mutual Information (AMI)  (Vinh et al. , 2010)  measures the degree of similarity of two labels for the same data set independently of the label values. While other metrics like the Rand index score are available, some studies like Romano et al. (  2016 ),  Guo et al. (2017)  have shown that such measures can be adversely affected by imbalanced data or a high number of clusters.
Therefore, we use AMI to evaluate synthetic convex cluster quality (see Fig. 5 ). We aim to assess the partitions by considering the CIVI performance relative to the clustering algorithm and penalizing an incorrect number of clusters evaluation. 2. The ''number of clusters score'' is a metric that measures how well the clustering results align with the ground truth labels in terms of the number of clusters. In our evaluation of both benchmarks and nonconvex datasets, we use this metric to determine the best partition, considering the shapes and capacity of CIVIs, regardless of the clustering algorithm used. Fig. 6  illustrates this approach. Once we have identified the optimal number of clusters, we evaluate the partition by looking at the number of cluster hits. 3. The F1 score is based on the harmonic mean of precision and recall  (Sokolova et al.
There are two recent approaches related to measuring uncertainty for partition evaluation RU  (Sirmen and Üstöndag, 2022) , and -Stable (Ozkan and Türkşen, 2012), both CIVIs have the limitation that   they require fuzzy membership degree hyperparameters. Therefore, we compare our proposal with the best-performance CIVIS in the literature for synthetic and real-world datasets. The CIVIs are the following: SI  (Jajuga et al. , 2020) , RTL  (Ratkowsky and Lance, 1978) , BH  (Ball and Hall, 1965) , SD  (Dudek, 2020) , DB  (Dudek, 2020) , XB  (Muranishi et al. , 2014) , CH  (Caliński and Harabasz, 1974) , Dnn  (Dunn, 1974) , MCR  (Zhang et al. , 2018) , PB  (Hands and Everitt, 2010) , RT  (Ray and Turi, 2000) , WG  (Wemmert et al. , 2000) , C  (Hubert and Schultz, 1976). We did not consider other recent CIVIs in the comparison due to their limitations concerning their underlying assumptions.
, 2021). (Ball and Hall, 1965)  0. 980 0. 965 0. 284 0. 647 0 0. 652 RTL  (Ratkowsky and Lance, 1978)  0. 944 0. 944 0. 275 0. 803 0 0. 566 SD  (Dudek, 2020)  0. 955 0. 954 0. 333 0. 640 0 0. 644 XB  (Muranishi et al. , 2014)  0. 955 0. 953 0. 287 0. 787 0 0. 557 MCR  (Zhang et al. , 2018)  0. 980 0. 945 0. 294 0. 800 4 0. 785 WG  (Wemmert et al. , 2000)  0. 956 0. 956 0. 277 0. 810 0 0. 557 PB  (Hands and Everitt, 2010)  0 We use Gaussian Mixture Models GMM (Expectation Maximization) to test the performance on real and synthetic datasets as it showed a proficiency for datasets with high uncertainty  (Rendon et al. , 2022b). To ensure a fair comparison of the CIVIs, we evaluate them using identical hyperparameters across all clustering algorithms and datasets. For the GMM, we used the following hyperparameters: covariance type: full, convergence threshold: 1e-3, and K-means initialization method to define means and covariance matrices.