dataesr/scientific-paragraphs-categorization huggingface dataset:
Results We designed a GUI Python application that calculates the mentioned CIVIs (including our proposal) to run the proposed tests. The code is available in: https://github. com/David9203/CVI-Frechet-Mahalanobis. 1  The link includes the real-world PAM dataset and the code to generate the synthetic data. The real-world data from benchmarks (Iris, Wine, Breast cancer, Digits, Haberman, Ionosphere, Liver, Swedish Leaf, Wafer, Arrowhead, Beet Fly, and Car) are available at UCI repository 2 and UCR repository. 3  The computing system used was a GenuineIntel CPU family 64-bit Byte, specifically an Intel(R) Core(TM) i7-6800K CPU running at a clock speed of 3. 40 GHz, 32 GB of RAM, 12 CPU(s) with two thread(s) per core. In the following subsections, we describe and analyze each one of the tests (see Table  7 ).
Convex clusters Fig. 8  shows normal convex data without noise. As the graph shows UF, SI, BH, WG, MR and XB obtain AMI performance higher than 0. 99. Fig. 9  shows best-performed indices in convex-noisy datasets. For normal, uniform, and triangular distributions with noise, each one with 900 datasets generated. We have evidence that there is an AMI higher than 0. 90 for UF, SI, BH, SD, XB WG, and MR. UF's performance obtained an AMI score of less than 0. 75 for gamma and logistic distributions. Regarding the noisy-convex distributions, the factors which reduce performance are the overlapping, the compaction factor, and the higher 1 All codes are available here https://github. com/David9203/CVI-Frechet-Mahalanobis. 2 UCI repository: https://archive. ics. uci. edu/ml/index. php. 3 UCR repository: https://www.
cs. ucr. edu/~eamonn/time_series_data/. UF performed well (AMI ≥ 0. 98) for Normal distribution. However, UF decreases the performance when the datasets have a high degree of compactness factor, as shown in Fig. 10. The degree of overlap is the most significant factor influencing the performance of CIVIS on noisy-convex distributions. Specifically, UF and PB are highly affected by the level of overlap, as illustrated  in Fig. 11. This behavior of UF can be attributed to the merging methodology. UF is prone to merge most closed clusters while not other indices. For example, Fig. 12. a shows a dataset with four clusters, in which SI recommends the same partitions as it is shown in Fig. 12. b, while UF merges the most closes indices recommending Fig. 12. c partition with two clusters. This relative behavior can be an advantage or disadvantage according to the criteria to decide what a cluster is.
Regarding the dimensions, Fig. 13  shows the performance of the CIVIs with different numbers of features. UF methodology exhibits superior performance ( > 0. 88) when applied to datasets characterized by high dimensions and following Gamma, Triangular, and Uniform distributions. Nevertheless, UF tends to decrease in performance in logistic noisy environments. We find that UF obtained the best performance for high dimensions ( = 0. 96), and even the performance decreases for smaller dimensions (more uncertainty). The PB CIVI performed poorly for all noisy convex distributions with high dimensions. On the other hand, XB under-performed (AMI ≤0. 80) in the case of noisy-normal datasets.
Non-convex datasets We show the performance for non-convex data in Fig. 15. Only UF and PB are the CIVIs that discovered non-convex shapes. Most frequently used CIVIs (C, DR, WG, DNN, XB, and DB) showed low performance for both of the distribution shapes used in the text: interleaving half circles (moon) and circles containing a smaller circle (circles) in the two shape compositions used, interleaving half circles (moon) and the circle surrounding a smaller circle (circles). The good results for UF are due to its ability to join small neighboring clusters based on the Fréchet distance proving the potential of uncertainty and merging methodologies used in non-convex data to select the correct number of clusters (see Fig. 14 ).
Real-world benchmark datasets Overall, Table  8  demonstrates that UF shows the potential to recommend the correct number of clusters for nearly all of the real-world benchmark datasets tested. The table provides detailed information about each dataset in the first four columns, followed by the number of clusters recommended by each CIVI in the subsequent columns. The table's last row summarizes the number of hits for each CIVI in the respective datasets. In these datasets, UF accurately predicted the number of clusters in 8 out of 13 datasets. Regarding the AMI performance, Fig. 15  presents the performance behavior that CIVIs have according to each real-world dataset. Fig. 15  indicates that the performance of clustering algorithms varies significantly across datasets and CIVIs. For example, the IRIs dataset exhibits higher average values (0.
71), compared to the Haberman dataset, in which the clustering algorithm did perform poorly despite the CIVIs recommending the correct number of clusters (see Table  8 ). Additionally, while CIVIs such as Silhouette yield impressive high performance for synthetic datasets, they show low performance for nearly all non-time-series datasets, except for the Wine dataset. Then, we have evidence that not necessarily the number of clusters equal to the ground truth corresponds to the real performance of the dataset. For example, UF recommends the correct number of clusters of ground truth for the Liver dataset but obtains a low performance compared to other CIVIs such as RTL, BH, XB, AND WG. However, UF is the best-performing CIVI in almost all cases of non-time series, except for the Liver dataset.
We highlight that UF is also the best AMI for the Digits dataset, recognizing the graphic patterns of this dataset better than other CIVIs. Regarding the number of clusters in the case of time series datasets, UF, WG, and Silhouette are the ones that behaved better in terms of predicting the number of partitions correctly (see Table  8 ). However, regarding AMI, the indices obtained a performance lower than 0. 70, as shown Fig. 16 , demonstrating the significant limitation of these indices suggesting the number of clusters for time series datasets.
PAM dataset As PAM seeks to understand the dynamics of ecosystems through sound, it is critical to partition interpretability in which the clusters represent different sound behaviors of anthropophony, geophony, and biophony. Table  9  shows the best-performed CIVIs with their F1 score performance and the number of clusters for the PAM application in each day period. The results show that it is possible to identify the ecological transformation of the tropical forest ecosystem through the CIVI UF. We found that UF, MR, BH, and SD have a performance greater than 0. 77 for each stage. However, UF recommends a low number of clusters (bold and italic values in Table  9 ) with high performance compared to N. Rendon, J. H. Giraldo, T. Bouwmans et al. Engineering Applications of Artificial Intelligence 124 (2023)  106635.
Dataset Nsamples Features Classes SI  (Jajuga et al. , 2020)  RTL  (Ratkowsky and Lance, 1978)  BH  (Ball and Hall, 1965)  SD  (Dudek, 2020)  XB  (Muranishi et al. , 2014)  MCR  (Zhang et al. , 2018)  PB  (Hands and Everitt, 2010)  WG  (Wemmert et al. , 2000)  UF  the other indices, which ensures better interpretability with the same score. On the other hand, other indices as XB, DB, BR, BH, MR, and G show monotonicity. UF obtain the best results considering both: the low number of clusters and the performance. The 17-5 period acquires the highest F1 score performance using almost all CIVIs (BH, C, DB, PB, SD, XB, UF, MR). This behavior could be related to the variability and distribution of sounds that occur at night and their intra-similarity. In PAM there are different distributions of data which are not necessarily normal since each recording varies according to the sounds of diverse sources.
Discussion UF demonstrates the capability to handle cases of noisy convex clusters for normal, uniform, triangular distributions, and nonconvex distributions as well as real-world applications. In the PAM application, there may be non-convex forms of the soundscape, not necessarily of biological species in which UF is liable to give an idea of these clusters. The performance of CIVIs such as Silhouette is satisfactory when dealing with convex synthetic datasets. These CIVIs tend to display unexpected clusters when faced with a lack of samples to define a distribution in real-world datasets or when dealing with data that has non-convex distributions. It is clear that there is no CIVI that is superior to others, as each has its advantages and limitations depending on the specific application.
Certain indices such as SI, MR, BH, SD, and WG are suitable for handling datasets with convex assumptions. Therefore, selecting the appropriate CIVI for a specific application should be based on understanding the underlying data assumptions. The silhouette CIVI may be a good option for some applications, while UF may be more suitable for others, as shown in Fig. 12. UF relies on the Frechet distance and the PFOU computation. The computational complexity of the Frechet distance,   (, Σ), repeated  times is ( 2  2 ) since we compute it between all clusters and the number of dimensions. On the other hand, the computational complexity of the PFOU relies on the Mahalanobis distance, which depends on the number of dimensions, , with the complexity of ( 2 ). Then, the overall complexity of UF is ( 2  2 ).
However, if the used clustering algorithms provide the covariance matrices the computational cost is reduced to ( 2 ). Although UF has shown to be an efficient methodology in most cases, our proposal has a limitation of reduced performance in the case of datasets with noisy distributions with a high overlap and logistic distributions. Probably, this is because of the method's normal distribution assumption and the merging methodology. Therefore, to improve the performance in datasets with noisy distributions and high overlap in logistic distributions, it would be beneficial to consider statistical assumptions for such data types in future work. The relativity of what a cluster is depends on the application and could be subjective, as well as the choice of the CIVI to use. Nevertheless, we emphasize the capability of UF to identify representative clusters even in the absence of distributional information.
Regarding the PAM application, we show the high potential to identify the health of transformed ecosystems through CIVIs. This approach helps with landscape monitoring, identifying sites with unique characteristics, and creating action plans to halt the ecological decline passively. In PAM and real benchmarks (Iris, Wine, Breast cancer, Digits, Haberman, Ionosphere, Liver, Swedish Leaf, Wafer, Arrowhead, Beet Fly, and Car datasets), UF is the one that behaved best, concerning performance and the number of clusters obtained when the merging is applied. Convex noisy-overlapped data could affect the performance of UF depending on what would be considered a cluster or not, as we showed in the example of Fig. 12. The importance of our application lies in the component that can aid in our comprehension of natural settings and which can support ecological research initiatives.
Conclusion In this study, we proposed a new CIVI, the Uncertainty Fréchet (UF), that can quantify uncertainty and assess the quality of cluster partitions in unsupervised learning scenarios. UF is a versatile metric that can accommodate both crisp and soft clustering approaches, making it a suitable option for Passive Acoustic Monitoring (PAM) of ecosystems. While other CIVIs such as SI, MR, BH, SD, and WG handled applications with assumptions of convex datasets, UF has shown competitive performance in these scenarios as well. More importantly, UF has demonstrated superior performance in non-convex and real-world datasets, showcasing the potential of uncertainty-based metrics that consider the underlying geometry of the dataset space. The results encourage further work on these types of CIVIs.
For example, an interesting future direction would be improving UF for compressing time series applications and datasets with overlapping noisy data. Choosing the most appropriate CIVI for an application requires careful consideration of the data distribution's characteristics and assumptions. Continuing to refine and develop CIVIs can lead to a better understanding of their strengths and limitations, resulting in improved accuracy and reliability of clustering results. We believe that UF and other uncertainty-based metrics may impact on unsupervised learning. Nonetheless, more research and testing on specific applications are needed to validate the effectiveness of these methods.
Variables and abbreviations. 2 , … ,   } composed of  standardized elements, where   is the th sample and  is the ground truth number of clusters. The clustering partition matrix () of size ×, is represented by  = [  ] × , where  is the number of clusters elected to make the partition,  = 1, … ,  and  = 1, … ,. is the membership of the sample   to the cluster . In crisp partition   = 1 if   ∈   , otherwise   = 0. In practice, two kinds of clustering exist as follows:• For crisp clustering, the purpose is to classify a dataset  such that:  ≠ ∅,   ∩   = ∅ for ,  = 1, … ,, and  ≠ , ⋃  =1   = . • For fuzzy clustering,  = [  ] × where   ∈ [0, 1] denotes the membership degree of  ℎ element to  ℎ cluster, with the next.
Acknowledgments This work was supported by  Universidad de Antioquia ,  Instituto Tecnologico Metropolitano de Medellín, Alexander von Humboldt Institute for Research on Biological Resources ,  Colombian National Fund for Science, Technology, and Innovation ,  Francisco Jose de Caldas, MINCIENCIAS (Colombia) :  Program No. 111585269779, and ECOS-Nord program :  MESRI (France)   C22M01  and  MINCIENCIAS (Colombia)  [Cod. 83477, 807404942021. Cto. 494-2021 ].
Distribution characteristics of fracture pore morphology The fracture pores of the specimen were primarily of millimeter-scale. Importantly, the pore morphology reflects the varying characteristics in pore scale and cemented particle arrangement in silt-like mudstone during damage, which was analyzed using 500x magnification SEM images under different working conditions. Subsequently, pore rate extraction provided quantitative Alterations in the pore microstructure can be discerned through the binarization of SEM images, as depicted in Fig. 7 -10. Image binarization was implemented using MATLAB to facilitate the analysis of microstructural characteristics. During the binarization process, SEM images were initially read into a grayscale matrix using the IMREAD function. A predefined grayscale threshold (128) was then applied.
Therefore, to accurately predict the number of material features by fractal dimension, it is necessary to obtain the accurate fractal dimension to reflect the irregularity and complexity  [48, 49]. There are many different definitions of fractal dimension according to different measurement methods, such as Hausdorff dimension, box dimension, similarity dimension, capacity dimension, information dimension, association dimension, etc. Box dimension, due to its ease of calculation and programming, is widely adopted in rock engineering research. Hausdorff dimension is difficult to determine for fractals that are statistically self-similar in large numbers. Furthermore, the box dimension method employs small squares with different side lengths to cover the set, which the box dimension can determine, and the process can be programmed by Matlab  [50, 51].
Based on this, this paper employs fractal theory to quantitatively characterize the fracture, pore, and tectonic laminae of irregular nonlinear silt-like mudstone specimens using SEM photographs under different initial conditions to analyze the variation of fractal dimension  [52]. To facilitate the programmatic design, this paper uses the box dimension method to find the fractal dimension of the above SEM photographs of the damaged specimens with the advantage of Image-J software in data processing and programmatic design methods. The box dimension method is implemented using Image-J software to obtain the fractal dimension of each image, and the fractal dimension D is obtained as in Eq. (  2 ): D = lim k→0 lg N(k) lg k (2) lg N(k) = D * lg k + h ( 3 ) where k is smaller the more accurate the obtained, the fractal dimension can be obtained by fitting a straight line; The Eq.
In Sections 2 and 3, we describe the data and a modified COSMOS2020 catalog made specific to this study. In Section 4, we describe the selection of a robust sample of massive galaxies at 3 < z < 5. In Section 5, we introduce the new color-selection method. In Section 6, we present this new selection applied to COSMOS2020 and the main results. Finally, we summarize our conclusions and outlook in Section 10. For all calculations, we use the WMAP9 flat Lambda cold dark matter cosmology  (Hinshaw et al. 2013 ) with H 0 = 69. 3 km s -1 Mpc -1 and Ω m = 0. 307. All magnitudes are in the AB system defined by  Oke & Gunn (1983)  as m AB = -2. 5 log f 10 3631Jy ( ) n.
2022; Moneti et al. 2022). COSMOS2020 contains four catalogs, combining two source-extraction methods and two photometric redshift codes. The CLASSIC catalog is produced using a classical aperture-based photometry method using SOURCE EXTRACTOR  (Bertin & Arnouts 1996) , while THE FARMER catalog is produced using a profile-fitting photometry method (J. Weaver at al. 2023, in preparation) , which is a wrapper written for the source profile-fitting code THE TRACTOR  (Lang et al. 2016). THE FARMER has a distinct advantage over classical photometry methods due to its ability to correctly model and deblend overlapping sources. This is particularly beneficial in deep fields where source crowding and overlapping is common. Both photometry catalogs are fit with two different photometric redshift codes, Le PHARE  (Arnouts & Ilbert 2011 ) and eazy-py  (Brammer et al.
2008; Brammer 2021). Weaver et al. (2022)  show that THE FARMER performs equivalently to SOURCE EXTRACTOR and excels at i < 24, independent of the redshift code used. For this analysis, we use THE FARMER photometric catalog combined with redshift and physical parameter estimation using eazy-py. Although THE FARMER photometry and its associated uncertainties are suitable for general use SED fitting,  Weaver et al. (2022)  noted that it is likely the photometric uncertainties are underestimated. To test this, we ran the custom code GOLFIR  (Kokorev et al. 2022 ) on a small subset of the COSMOS2020 IRAC images. GOLFIR uses a prior based on the highest-available-resolution imaging to model the flux in the IRAC photometry. Overall, the agreement of both photometric catalogs is high, however the IRAC errors derived with THE FARMER are smaller by a factor of ∼5.
3D-HST In Section 3, we will introduce the latest python implementation of eazy, eazy-py, and its newer features. To demonstrate their validity, in particular the computation of physical properties such as stellar mass and star formation rate (SFR), we use an observational catalog with similar properties as COSMOS2020 to benchmark the performance. We consider the PROSPECTOR version of the 3D-HST catalog from  Leja et al. (2019d). The 3D-HST survey  (Skelton et al. 2014 ) is a 248-orbit Hubble Treasury Program completed in 2015, providing Wide Field Camera 3 and Advanced Camera for Surveys (ACS) spectroscopy for galaxies in five extragalactic deep fields, including COSMOS, covering 900 square arcminutes (199 square arcminutes in COSMOS). The catalog includes photometry in up to 44 bands in COSMOS covering 0.
3-8 μm in the observed frame, with the inclusion of Spitzer Multi-Band Imaging Photometer 24 μm photometry from  Whitaker et al. (2014). The version that we considered contains a representative subsample of 58,461 galaxies from the 3D-HST survey (roughly 33%), which spans the observed SFR density and mass density at 0. 5 < z < 2. 5. These galaxies are fit with the Bayesian SED-fitting code PROSPECTOR  (Leja et al. 2017; Johnson et al. 2021 ). PROSPECTOR uses galaxy models generated using python-Flexible Stellar Population Synthesis (FSPS;  Conroy et al. 2009; Conroy & Gunn 2010)  code, nonparametric star formation histories, variable stellar metallicities, and a two-component dust-attenuation model, under the assumption of energy balance. For this paper, we cross-match our catalog and the 3D-HST PROSPECTOR catalog using a 0″6 matching radius, resulting in 8964 galaxies in common.
eazy-py In this study, we use photometric redshifts, stellar masses, SFRs, and rest-frame colors derived with eazy-py 13  (Brammer 2021). Here, we detail this process, including an updated description and presentation of the eazy-py code. eazy-py is a pythonic photometric redshift code adapted from the original eazy code written in C+  (Brammer et al. 2008). eazy-py estimates redshifts by fitting nonnegative linear combinations of galaxy templates to broadband photometry to produce a best-fit model. The flexibility of the code means that, in theory, any kind of template can be used, e. g. , quasar or AGN templates. The templates used in this paper are comprised of 13 stellar population synthesis templates from FSPS  (Conroy et al. 2009; Conroy & Gunn 2010)  spanning a wide range in age, dust attenuation, and log-normal star formation histories.
Summary and Conclusions In this work, we explore the massive QG population at 3 < z < 5 in COSMOS using the latest photometric catalog, COSMOS2020. We create a new catalog using the COS-MOS2020 photometry, with Spitzer/IRAC errors boosted, and derive redshifts and physical parameters with eazy-py. We motivate the need for a new rest-frame color diagram to select for QGs at z > 3 and present the GMM/NUVU -VJ method as a viable alternative. We use a GMM to fit the NUV -U, U -V, and V -J colors of massive galaxies at 2 < z < 3, and galaxies are assigned a probability of being quiescent based on their bootstrapped rest-frame colors. This GMM model is then applied to the colors of massive galaxies at 3 < z < 5. Both the GMM model and code to calculate quiescent probabilities from rest-frame flux densities are made available online.
The  Cosmic Dawn Center  (DAWN) is funded by the  Danish National Research Foundation  under grant No. 140. S. J. acknowledges financial support from the  European Union 's  Horizon research and innovation program  under the  Marie Skłodowska-Curie  grant agreement No. 101060888. Software: eazy-py (Brammer 2021), scipy (Virtanen et al. 2020), numpy (Harris et al. 2020), matplotlib (Hunter 2007), scikit learn (Pedregosa et al. 2011), astropy (Astropy Collaboration et al. 2013, 2018), python-FSPS (Conroy et al. 2009; Conroy & Gunn 2010), GMM-quiescent (Gould 2023).
INTRODUCTION As researchers in additive manufacturing (AM), we recognize the importance of equipping students with a comprehensive understanding of the technology and its potential applications. To achieve this, we have developed a course on "Design for Additive Manufacturing" (DfAM) that incorporates active pedagogical methods and immersive devices. The aim of this course is to enable students to design complex, multi-functional, and optimized products using AM by the end of the program. Students will be able to identify opportunities for additive manufacturing, apply DfAM principles  (Gibson et al, 2015) , and use optimization software to create innovative and high-performance products. To achieve successful DfAM, it is important to consider various factors such as part orientation, support structure, and material selection.