dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2021). Moreover, the presence of additional nodes in the radiation pattern diagrams suggests cable deployments with changes in the fiber orientation, to improve the resolution in the source parameters. Finally, the proposed approach, when integrated in a probabilistic formulation, can be fully automated, with the quality of the solutions based on the shape of the a-posteriori probability density functions  (Supino et al. , 2019). Also, when extending this approach to the Pwaves, this strategy could be applied in real-time, when few seconds of early P wave signal are available (e. g. ,  Caprio et al. , 2011). Validation of this approach on Chilean dataset (𝑀𝑀 𝐿𝐿 = 2. 6 -4. 3) shows a reliable estimation of source parameters, comparable with results from standard seismometers. We do not observe any dependence of parameters on the hypocentral distance, showing that attenuation correction is consistent throughout the whole cable, enabling DAS to characterize the source of manuscript submitted to Journal of Geophysical Research events in wide range of hypocentral distances.
Conclusions In this work we estimated source parameters from a spectral inversion of DAS data in their native representation, based on a novel formulation describing the far-field radiation in the strain domain. The theoretical modeling displays an enhanced sensitivity to the velocity structure beneath the cable and the radiation pattern. Including this model in a probabilistic framework for the inversion  (Supino et al. , 2019)  allowed us to estimate the moment magnitude and the corner frequency from two different datasets, showing consistent values when compared to authoritative catalogs. When analyzing data acquired from a 150𝑘𝑘𝑘𝑘 ocean-bottom dark fiber cable near the Chilean trench (𝑀𝑀 𝐿𝐿 = 2. 6 -4. 3), we found a self-similar behavior of the seismicity with an mean stress drop of 0.
Data Availability Statement The strain rates of the Chilean earthquakes and seismic traces from CSN used in this article are available at the link: https://doi. org/10. 5281/zenodo. 8340063  (Rivet et al. , 2023). DAS waveforms from the Southern Apennines dataset are available at: https://doi. org/10. 5281/zenodo. 8337580  (Strumia et al. , 2023). Seismic data from Chilean seismic station can be accessed through the from IRISDMC (http://ds. iris. edu/mda/), network code C1. Products from INFO network can be accessed through the Irpinia Seismic Network infrastructure (ISNet: https://isnet. unina. it). Seismic data can be accessed through EIDA portal (https://eida. ingv. it/it/, network code IX). Catalog of the analyzed events and codes used to produce the Figures in the paper are available on GitHub (https://github.
However, (1) the upper and lower bounds are generally not unique, (2) in practice, even for very small datasets, the number of partitions expected within the 95% credible ball is so large that an analyst cannot consider all of the them and (3) estimates are given among the MCMC draws. Considering only partitions explored in the MCMC draws is a big limitation of the method, as the most desirable partition is often outside the MCMC sample  (Hastie et al. , 2015; Jing et al. , 2022). In practice, the 'consensus' partitions are usually obtained by postprocessing the MCMC draws, for example applying partitioning around medoids on the dissimilarity matrix  (Liverani et al. , 2015). Finite mixture models are not subjected to all of these pitfalls, because first the space of partition is limited by the fixed number of clusters and second, constraints are generally added in application to make the different clusters identifiable across the MCMC draws.
In this matrix, each row of the matrix corresponds to an observation in the original dataset. Each column represents a cluster in the partition that has been identified by PAM as a consensus. The observations are ordered according first to their cluster allocation in the consensus partition, and then according to their probability of belonging to each cluster. This estimate is based on the posterior draws, readily available when MCMC inference is done. Its computation demands at each step, the evaluation of a small number of functions in about n points. If the integrals are in closed form, it is then possible to use the following estimate, with smaller variance (α + n) fl (D n+1 ) = αf 0 (D n+1 ) + n n l 1 T T ∑ t=1 ⎛ ⎝ ∑ c:n(Z t )>0 n lc f (D n+1 |{D i : Z t i = c}) ⎞ ⎠. (7) Finally, we estimate p l i as the posterior probability that data point i belongs to cluster l of the Z * partition as: pl i = n l fl (D i )/ ∑ k * j=1 n j fj (D i ) We propose to calculate these probabilities for each data of D n and for each cluster of Z * and to visualise them graphically.
Application to velocity galaxy data We consider the velocity galaxy dataset proposed by  Roeder (1990). See Appendix D for a detailed description of the dataset and our implementation. The predictive density and the densities fl (D n+1 ) are represented on the left hand side of Fig. 1. From the representation of the mixture of densities, the distinction between cluster 3 and 4 is unclear: some element of cluster 4 have a higher probability to belong to cluster 3. A clear representation of the proposed methodology is presented on the right hand side of Fig. 1 , where the pl i are displayed for a graphical analysis of the uncertainty of the selected partition. In this figure we note that cluster 1, 2 and 5 are well defined, because they are composed of elements that have a high probability to belong to the cluster that they are allocated to and low probability to belong to a different cluster.
From these rules, a solution that satisfies all constraints in Eqs. (B. 3) and (B. 4) follows. All the functions discussed in this paper are available in the R package PReMiuM, a package developed by  Liverani et al. (2015)  for profile regression, a method that has a wide range of applications, such as spatial modelling  (Liverani et al. , 2016; Lavigne et al. , 2020)  and epidemiology  (Hastie et al. , 2013; Molitor et al. , 2014; Pirani et al. , 2015; Mattei et al. , 2016; Coker et al. , 2016 Coker et al. , , 2018;; Liu et al. , 2020; Liverani et al. , 2021; Ricciardi et al. , 2022). The functions used to create the figures and plots in this paper are open source and available on Github at https://github. com/silvialiverani/partitionuncertainty.
Acknowledgments Hera is the ESA contribution to the AIDA collaboration. Juventas and JuRa are developed under  ESA  contract supported by national agencies. JuRa is built by  EmTroniX (Lux) ,  UGA/IPAG (Fr) ,  TUD (Gr) ,  Astronika (Pl)  and  BUT (Cz). Juventas is built by  Gomspace (Lux). This project has received funding from the  European Union 's  Horizon 2020 research and innovation program  under grant agreement No  870377  (project  NEO-MAPP ).
Crystallography The crystal structure of the phases was determined by both powder and single crystal X-ray diffraction. The powder patterns were collected by a PANanalytical X′Pert diffractometer with Cu Kα1 radiation (λ = 1. 54056 Å) [using Si as an internal standard (a = 5. 4308(1) Å)]. They were indexed by the help of Lazy Pulverix program  [18] ; accurate lattice parameters were calculated by means of least-square methods (handmade software). Single crystal investigation was performed on a small crystal selected from the sample DyCo 0. 6 Ni 0. 4. The reflection data were collected at 293 K by using a Bruker APEX CCD diffractomer (Mo Kα radiation, λ = 0. 71073 Å) in φ-and ω-scan modes using at least frames and exposure of 15 s per frame. The reflection intensities were integrated using SAINT program in the APEX software package  [19].
Physical properties measurements The magnetization data both as a function of temperature, M(T), and applied magnetic field, M(H), were collected using a Magnetic Properties Measurement System (SQUID, Quantum Design, Inc. , USA). Specific heat, C P , was measured for TbCo 0. 6 Ni 0. 4 by using an automated calorimeter  [23]  under zero and applied magnetic fields. For TbCo 0. 6 Ni 0. 4 and DyCo 0. 6 Ni 0. 4 the magnetization was measured between 2 and 300 K, both in zero-field-cooled (ZFC) and field-cooled (FC) modes. The data for TbCo 0. 6 Ni 0. 4 were collected under applied magnetic fields of 200 Oe, 2 kOe and 10 kOe, while those for DyCo 0. 6 Ni 0. 4 were measured under H = 200 Oe and 5 kOe. The magnetization of HoNi 0. 6 Ni 0. 4 and HoCo 0. 5 Ni 0. 5 was collected between 5 K and 300 K and under a field H = 10 kOe.
Further data were taken at K for the Ho-compounds and on HoCo 0. 6 Ni 0. 4 at 1. 5 K using the standard resolution. High intensity data were taken on D1B for TbCo 0. 5 Ni 0. 5 between 1. 5 K and 123 K using a temperature heating ramp of 0. 1 • /22 s and recording spectra of 10 min leading to a temperature resolution of ΔT = 2. 7 K between adjacent patterns. TbCo 0. 6 Ni 0. 4 was measured on D20 between 2 K and 150 K using a heating ramp of 0. 1 • /36 s and spectra of 12 min giving a ΔT = 2 K. The two Ho-compounds were measured as well on D20 between 1. 5 K and 80 K using a ramp speed of 0. 1 • /30 s and 15 min runs giving a ΔT = 3 K. All diffraction data were analysed using the Rietveld refinement program FULLPROF  [24] ; magnetic symmetry analysis was done using the program Basireps  [25, 26].
The refinement of the powder data included, as variables, the scale factor, the zero-shift and the lattice parameters, the free atom positions, isotropic temperature factors for the rare earth and the transition metal sites. The background was determined by selecting and refining background points at positions off the positions of the Bragg reflections; the peak shape was refined using a Pseudo-Voigt function and one asymmetry parameter. For the refinement of the TbCo 0. 6 Ni 0. 4 sample the angular regions of two small magnetic peaks of the impurity phase TbCo were excluded from the refinement.
Synchrotron diffraction Synchrotron X-ray powder diffraction data were recorded at the BL04-MSPD beamline  [27]  of the ALBA Synchrotron Light facility at Barcelona, Spain. Data were collected in transmission mode using the multi-analyser (MAD) setup using a wavelength of λ = 0. 3177 Å with samples placed in 0. 5 mm diameter borosilicate capillaries. Low temperatures were achieved using the liquid Helium flow cryostat Dynaflow  [28]. 11 data points were recorded between 20 K and 120 K for TbCo 0. 5 Ni 0. 5 while 5 data points were taken between 20 K and 100 K on TbCo 0. 6 Ni 0. 4. HoCo 0. 6 Ni 0. 4 was measured at 13 temperatures between 10 K and 120 K while HoCo 0. 5 Ni 0. 5 was measured at 20 K, 50 K and 80 K.
Physical properties of RCo 0. 6 Ni 0. 4 Heat capacity measurements were performed only on the Tb compound, TbCo 0. 6 Ni 0. 4. We purposely want to show the C P data first, and especially the zero-field ones, to give an overview of the orderings occurring in the low temperature range for a representative compound of this series. Fig. 1  shows heat capacity of TbCo 0. 6 Ni 0. 4 measured between 2 and 300 K and under zero and applied magnetic fields, H, of 10 and 20 kOe. The data reveal a single peak at about 84 K in the zero field data. This peak broadens under the effect of the magnetic field to a shoulder-like feature starting at slightly lower temperature and ending at higher temperature (Fig. 1 ). The magnetization as function of temperature and field of TbCo 0. 6 Ni 0. 4 is shown in Fig.
where the pure phase has T C ≈ 220 K  [33]. The temperature dependence of the most intense magnetic peak of both Tb-compounds is shown in Fig. 11  and is used to determine the magnetic transition temperatures to T C ≈ 82 K and 87 K. The magnetic transitions found for the 2 Ho-compounds which lead to the appearance of very similar magnetic reflections are significantly lower in temperature, T C ≈ 26 K for HoCo 0. 636 Ni 0. 364 and T C ≈ 24 K for HoCo 0. 552 Ni 0. 448. There is no sign for the presence of a second magnetic transition. "Using the program K-search, which is part of the FULLPROF suite of programs, the magnetic propagation" vector which indexes all new magnetic peaks can be determined to k = 0. Magnetic symmetry analysis performed for the 8e site of I4 1 /amd and k = 0 shows the existence of 6 allowed irreducible representations (IREP) having between 1 and 4 basis vectors (BV) listed in Table  3.
Acknowledgments Part of this work was performed at the  Ames Laboratory , which is operated for the  U. S. Department of Energy  by  Iowa State University of Science and Technology  under Contract  DEAC02-07CH11358. A. P. and P. M. thank the  University of Genova  and the  Institute SPIN-CNR  for supporting their stay abroad and the  Ames Laboratory (Iowa State University ) for the hospitality received as visiting scientists. A. P. and P. M. also thank the Project NEWS (New Windows on the  Universe and Technological Advancements ; trilateral  EU-US-Japan  collaboration) for the funds received to support their stay in the USA in 2017 and 2018; the collaboration enabled performance of the research reported here. A. -V. M. would like to thank  Energimyndigheten  for support through Grant No. 48699-1  and  DFF (Danmarks Frie Forskningsfond)  for support through grant no.
Magnetic measurements Magnetic measurements were performed using a vibrating sample magnetometer (VSM MicroSense EZ7) operating at 15 kOe of the applied magnetic field. The weighted powder samples (E 5-10 mg) were sealed in a tin capsule then glued onto a quartz fibre and placed in a nitrogen flux furnace between the magnets. The diamagnetic contribution of the quartz and the tin were subtracted from the data using a blank experiment. The procedure consisted of cycling the samples between 300 K and 420 K twenty times for each of them. The thermal cycles were performed at 5 K min À1 scan rate for all the measurements.
Starting material characterization The ). X-ray powder diffraction pattern of 1 reveals a well crystallized compound corresponding to the previously described polymorph I made of interacting [Fe(Htrz) 2 (trz)] + chains where Htrz and trz-act as bridging ligands. 62, 63  Rietveld refinement of 1 has been performed using JANA2006  64  and Fullprof softwares  65  using the previously described crystal structure as a starting point. 62  The calculated profile fits very well the experimental pattern (R wp = 0. 10, R p = 0. 07, R bragg = 0. 07), which confirms the crystal structure of 1 (Fig. 1 ). After subtraction of instrumental broadening, sample contribution to peak broadening could be estimated to a mean coherent domain size of ca. 50 nm and micro-deformations of ca. 20. 10 À4. Furthermore, the coherent domain sizes are anisotropic with a strong elongation along the b parameter corresponding to the chain direction (260 nm in the b direction and 34 nm in the ac direction).
Acknowledgements This work was supported by the  ANR-19-CE07-0026  (MEMORI). The authors acknowledge  Centre National de la Recherche Scientifique (CNRS) , the  University of Bordeaux and Bordeaux INP  for technical support and the  Lebanon State for part of PhD. grant of  Liza El-Khoury. Michae ¨l Josse  thanks  CNRS  and the  University of Bordeaux  for 6 months of sabbatical leave during 2017-2018 and 2019-2020, for the development of molecular ceramics and Cool-SPS. The X-ray diffraction facility of the ICMCB is thanked for the powder diffraction experiments and more particularly  Eric Lebraud  for his useful technical support. The authors also thank  U-Chan Chung  for his support for the SPS. The UAR 3626 PLACAMAT is acknowledged for the TEM facilities and more specifically  Marion Gayot  for her help.
The concentration profile is used as a year-long source in the GCM, 5) The GCM is run for a martian year with the ash profiles from ATHAM inserted at every timestep (switching ash sources depending on the season) as a passive tracer and allowed to advect, diffuse, and sediment. Each volcano location is run in a separate GCM simulation. 6) The deposited ash output is downloaded and analyzed. The result of this methodlogy is ash deposition maps that generally characterize the distribution of ash produced by individual volcanoes over many eruptions. For steps where output must move from one model to the other (steps 2 and 4), we use python scripts that are described in the following subsections.
Modifications to the generic PCM The Generic PCM was modified to provide a means of inputting a vertical one-dimensional profile of ash from a specific volcano location in the model as a passive tracer; the ash does not provide any feedbacks or affect any of the physical or dynamic parameterization present during the simulation. The Generic PCM takes an input of the volcano name, which the volcano module uses to find the latitude/longitude location in a lookup table. The code then finds which PCM grid point is closest to the volcano coordinates in question and which processor that grid point is on. Once the grid point is chosen, the delimited ash concentration file created earlier is read in for each season. As time progresses through the model, each season-specific concentration array is fed into the PCM at every timestep at the appropriate season (at L s = 0-90 for spring, L s = 90-180 for summer, L s = 180-270 for Fall, and L s = 270-360 for Winter).
Acknowledgments This work was supported by  NASA   MDAP  grant  80NSSC18K1375. The authors wish to thank  Dr. Michael Herzog  for the use of the ATHAM software and  Dr. Laura Kerber  for assistance in compiling and running the volcano submodule of the PCM. The authors also wish to thank  Dr. Ken Aho  and  Dr. Sarah Godsey  for helpful conversations regarding statistical methods. This research made use of the resources of the  High Performance Computing Center at Idaho National Laboratory , which is supported by the  Office of Nuclear Energy of the U. S. Department of Energy  and the  Nuclear Science User Facilities  under Contract No. DE-AC07-05ID14517.
Data availability GRS H 2 O data along with other chemical datasets are available at the LSU Digital Commons (https://digitalcommons. lsu. edu/geo_psl/1/;  Rani et al. , 2022). MOLA data used in background maps is available from the USGS Astropedia database (https://astrogeology. usgs. gov/search). The GIS version of the  Tanaka et al. (2014)  map is available at the USGS publication page (https://pubs. usgs. gov/sim/3292/). All code as well as input/output files are available at the following GitHub repository (https://github. com/palatyle/LMD_MATHAM_Utils). Links to the model output data are also available at the LMD_MATHA-M_Utils repository. The Generic PCM modified for this manuscript methodology is available at the following GitHub repository (https://github. com/palatyle/LMD_GCM_Paladino).
Thus our full position vs time dataset, for all beads and area fractions, should suffice for a complete and systematic study of changes in dynamics as jamming is approached. The MSD has long been used to characterize complex dynamics. In simple systems there is a single characteristic time scale given by the crossover from ballistic to diffusive regimes. In supercooled or glassy systems, the crossover is much more gradual and there are two characteristic time   The static structure factor S(Q) measured  [103]  in propylene glycol (PG), where T g = 160 K. A careful analysis of S(Q,T) for PG reveals that, upon cooling, the first peak decreases in height and moves to higher Q, while the second peak slightly increases in height and the structure of the third peak slightly developps. These subtle effects of cooling for PG come both from the liquid's increase in density, and from the ordering of molecular orientations, in which both the effects of hydrogen bonding and the constraints on molecular packing introduced by the change in density are involved  [103].
Acknowledgements The authors wish first to thank the hundreds of authors of the papers cited in this review for their contribution to our understanding of the glass transition. Besides, we wish to thank those with whom we have been fortunate to work with in the context our work which is cited here :  Christiane Alba-Simionesco ,  Samuel Albert ,  Paul Bartlett ,  Ludovic Berthier ,  Giulio Biroli ,  Jean-Philippe Bouchaud ,  Coralie Brun ,  Chiara Cammarota ,  Matteo Campo ,  Luca Cipeletti ,  Caroline Crauste-Thibierge ,  Pierre-Michel Déjardin ,  Paramesh Gadige ,  James Hallett ,  Nathan Israeloff ,  Walter Kob ,  Alois Loidl ,  Peter Lunkenheimer ,  Alex Malins ,  Levke Ortlieb ,  Erdal Oguz ,  Takehiro Ohtsuka ,  Rattachai Pinchipat ,  Ranko Richert ,  Camille Scaliett ,  Thomas Speck ,  Hajime Tanaka ,  Gilles Tarjus ,  Francesco Turci ,  Pierfrancesco Urbani ,  Ian Williams ,  Stephen Williams  for many insightful discussions over the years.
Acknowledgements The work of SC received funding under the  Framework Program for Research and "Horizon 2020" innovation  under the  Marie Skłodowska-Curie  grant agreement n°  945298. The work of AG and DK is supported in part by the  BSF  (grant number  2018068 ). The work of AG is supported in part by the  ISF  (grant number  256/22 ). The work of DK is supported in part by  DOE  grant  DE-SC0009924. This work was supported in part by the  FACCTS Program  at the  University of Chicago.
Dataset and Methods The active radar observations of Dione conducted by the Cassini Radar have been presented and analyzed by  [3] [4] [5]. Spatially resolved data were acquired during flyby DI163 in 2012, simultaneously in active (radar) and passive (radiometry) modes. The resulting images are shown in Fig. 1 ; the resolved radiometry data is deconvolved following the method described in  [6, 7]. A preliminary analysis of the resolved radiometry also points to a leading/trailing dichotomy. Indeed, the leading hemisphere, during late afternoon, should be radiometrically warmer than the trailing hemisphere, assuming uniform albedo, thermal inertia, and emissivity. The fact that the reverse is observed indicates variations in at least one of these properties. Distant radiometry scans have been acquired during four flybys.
The exact position of this boundary is subjective and depends on the whether it is drawn on the basis of a monochrome or colour image, and the contrast stretching used for display. Besse et al. (2020)  took a more objective approach to defining the edge of this facula (and several others) using spectroscopic data from MESSENGER's MASCS (Mercury Atmospheric and Surface Composition Spectrometer) instrument, a non-imaging instrument that recorded UV-visible-near IR spectral along the spacecraft ground-tracks. They defined spectral parameters that are extreme in the inner part of faculae and decline to the planetary background value at the edge of the facula: the UV downturn, the VIS slope and the NIR slope. Along a nearly north-south line across Nathair Facula they used these data from one track to determine a radius of 140 km.
Careful inspection of enhanced MESSENGER colour images, such as Figure  1 , and the map of  Wright et al. (2019; Figure 2)  shows that the facula is not actually centred on the vent, but is displaced northwards by about 20 km. Spectral analysis of MDIS data suggests the midpoint of the facula is in the NE of the vent, and reveals a slightly elliptical shape to the faculae edge (Figure  3 ). We interrogated data from five north-south MASCS crossings of Nathair Facula, distinguishing between data points north and south of the vent. One of these is illustrated in Figure  4 , showing that each spectral parameter falls to the background level at a greater distance north than south of the notional vent centre. Table  1  gathers data from a total of five tracks. While each spectral parameter records a slightly different radius, in all cases where a radius can be determined it is greater in the north than in the south.