dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction of Sub-Optimality Criteria in the Learning Step The above mentioned behavior of the learning MSE confirms that the space of optimal logic models returned by training procedures is very sensitive to the dataset under consideration. That is, it may constantly change when observations of new perturbations are being considered (see the toy example provided in Supplementary Material). Relaxing the tolerance of optimality in our learning procedure allows us in many cases (75% of artificial case studies and 40% of real case studies) to learn new perturbations that will decrease the testing MSE at each iteration (see Figure  5 ). On the contrary, in other cases, it heavily altered the space of learned logical models yielding a larger MSE. In these cases, however, the MSE of learned logical networks was always improved in a later step.
Whereas the cycle of learning and experimental design for artificial case studies follows homogeneous trajectories in all 100 cases (the number of iterations was on average 6. 45 with σ = 2. 3, the number of experiments selected was on average 11. 5 with σ = 3. 2), the cycle for real case studies shows more variability in the 30 considered cases (the number of iterations was on average 10. 4  with σ = 4. 5, the number of experiments selected was on average 18. 9 with σ = 8. 1). In Figure  5 , we show the trajectories of this cycle for three significative cases in both datasets: the case where a maximum testing MSE was found, where an average testing MSE was found, and when the minimal testing MSE was found.
The temperature of the water is thermostated by a precision chiller capable of removing up to 10 kW of heating power while maintaining the bath temperature between a 5 o C and 35 o C, stable to within ±25 mK. Temperature data is acquired via a digital data acquisition system capable of simultaneously sampling up to 32 thermistor channels, typically at a sampling rate of 10 Hz. In addition, 32 more channels are available to measure temperatures via K-type thermocouples, which we use to evaluate thermal losses and to monitor ambient temperature in the room. In laboratory convection systems, it is important to ascertain the thermal properties of the boundaries, in order to be comparable with theoretical models, cf. [21]. To evaluate the thermal boundary conditions, we determine the value of the Biot number, Bi, for the top and bottom thermal blocks.
Numerical Modeling Framework In close association with our laboratory experiments, we have carried out numerical simulations using a modified version of the SFEMaNS code, which has been used previously in studies of mechanically-forced magnetohydrodynamic flows in liquid metals  [24] [25] [26]. SFEMaNS is a hybrid code that makes use of Fourier series in the azimuthal direction. In meridian planes, it uses nodal quadratic Lagrange finite elements for the velocity field and nodal linear Lagrange finite elements for the pressure field. The discretization of time is made by means of a semi-implicit, second-order backward finite difference method (BDF2). This code is efficiently parallelized in Fourier space and on meridian sections (see  Appendix 1). The domain decomposition is made using METIS  [27] , and the parallelization is made using MPI and PETSC libraries  [28, 29].
The code's unstructured meridional mesh, shown in Figure  2c , allows SFEMaNS to be used to simulate MHD flows in any axisymmetric geometry. The key modification we have made to the code is the inclusion of a thermal field solver, allowing for thermally-driven MHD simulations of Boussinesq fluids in which the density is constant except in the buoyancy term  [30, 31]. This new version of the code, called SFEMaNS-T, has already been used successfully to simulate convection-driven, planetary dynamo action in a spherical shell geometry in the community benchmarking exercise of  [32]. In this study, we carry out numerical calculations in right cylindrical geometries (see Figure  2c, d ). The numerical tank geometries are nearly identical to our laboratory experimental cases, with numerical aspect ratio values of Γ = 2 and 4.
(The Γ 1 rotating convection laboratory data is from the study of  [20]. ) The three different suites of experiments, RBC, MC and RC, all show significant differences in their heat transfer behaviors. The lowest value of N u in the RBC data set is near two. Exceeding N u = 1, this implies that the Rayleigh numbers investigated in this set of experiments all exceed the critical Rayleigh number for RBC. In addition, the RBC data appears to display a single power law behavior, suggesting that we are interrogating a single behavioral regime of liquid metal convection. This scaling behavior is discussed in detail in Section 4. In contrast, the N u-Ra data shows that the zeroth order effect of either an imposed magnetic field or an imposed system rotation is to stabilize the layer of liquid metal against convective motions.
In the MC cases, the critical Rayleigh number is just below Ra = 3 × 10 4. In the RC cases, convection onsets closer to Ra = 1. 5 × 10 5. After convection onsets in the MC and RC systems, the heat transfer behaviors are more complex than in the RBC experiments. Just after the onset of convection, the MC N u data rises sharply with Ra and has a concave downward curvature until, at a sufficiently high Rayleigh number of about 10 6 , the MC data merges with the RBC data. In contrast, the RC data has a very shallow slope just after convection onsets. This gives way to a steeper trend at close to Ra = 10 6 , which then intersects with the RBC data in the vicinity of Ra = 10 7. The data in Figure  3  shows that the MC and RC return to the RBC trend at sufficiently high Ra. Qualitatively, this behavior is unsurprising: MC systems behave similarly to RBC systems when N c is sufficiently low and RC systems behave similarly to RBC systems when Ro c is sufficiently high.
Thus, the RBC heat transfer data provides an approximate upper bounding curve the MC and RC heat transfer data sets. This further implies that knowledge of RBC convective scaling behavior is necessary to understand the behaviors of the MC and RC systems. A similar result exists for rotating convective heat transfer in moderate P r fluids, such as water  [13]. Thus, the import of understanding RBC as the essential basis for more complicated convection systems holds broadly. In the following three sections, we will consider in greater detail the behaviors of Rayleigh-Bénard convection in liquid metal, magnetoconvection and then rotating convection.
Acknowledgments A. Ribeiro  and  J. Aurnou  gratefully acknowledge the support of the  US National Science Foundation (NSF) Geophysics Programs , ( EAR-1068019  and  EAR-1246861 ). G. Fabre is thankful for fundings from  ENS Lyon. J. -L. Guermond  acknowledges  NSF  support under grant  DMS-1015984. We thank the two anonymous referees for their constructive reviews as well as  M. Calkins ,  A. Grannan ,  K. Julien ,  G. Vasil  and  K. Zhang  for fruitful discussions, all of which greatly improved this work. Numerical calculations were carried out on Stampede at the  Texas Advanced Computing Center (TACC) at The University of Texas at Austin. Computational time on Stampede was kindly provided via  Computational Infrastructure for Geodynamics (NSF  award  ACI-1053575 ) as well as a  TACC computing award  ( TG-EAR140033 ).
2010; Conley et al. 2011; Riechers et al. 2011a; Bussmann et al. 2012; Wardlow et al. 2013; Bussmann et al. 2013). Sources discovered in SPT surveys have also been shown to have a high probability of being strongly lensed  (Vieira et al. 2013; Hezaveh et al. 2013). However, statistical models significantly over-predict the median magnification factor experienced by a Herschel DSFG of a given S 500  (Bussmann et al. 2013). This could herald new insights in our understanding of the bright end of the intrinsic DSFG number counts or in the nature of the deflectors. We here present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 0 imaging at 870 µm of a sample of 29 HerMES DSFGs. Three aspects of our dataset make it uniquely suited to improving our understanding of the bright end of the intrinsic DSFG number counts.
This result is not a surprise, given the typical angular separation of the ALMA sources ( 5 ) and the FWHM of the SPIRE beam at 250 µm (18. 1 ). We identify and catalog by-eye all sources with peak flux density greater than 5σ. 2. 3. Gemini-South Imaging Optical imaging observations using the Gemini Multi-Object Spectrograph-South (GMOS-S;  Hook et al. 2004)  were conducted in queue mode during the 2013B semester as part of program GS-2013B-Q-77 (PI: R. S. Bussmann). The goal of the program is to use shallow u, g, r, i, and z imaging to identify structure at redshifts below unity and determine which of the ALMA sources are affected by gravitational lensing. Nearly half of the ALMA sources lie in regions with existing deep optical imaging, thanks to the extensive multi-wavelength dataset available in the HerMES fields -these were excluded from our Gemini-S program.
2012 (Bussmann et al. , 2013)). When an intervening galaxy (or group of galaxies) is present along the line of sight, uvmcmcfit accounts for the deflection of light caused by this structure using a simple ray-tracing routine that is adopted from a Python routine written by A. Bolton 30. This represents a significant difference from  Bussmann et al. (2012)  and  Bussmann et al. (2013) , where we used the publicly available Gravlens software  (Keeton 2001)  to map emission from the source plane to the image plane for a given lensing mass distribution. Gravlens has a wide range of lens mass profiles as well as a sophisticated algorithm for mapping source plane emission to the image plane, but it also comes with a significant input/output penalty that 30 http://www. physics. utah. edu/∼bolton/python lens demo/ makes parallel computing prohibitively expensive.
For example, modeling a simple system comprising one lens and one source typically required 24-48 hours using the old software, whereas the same system can be modeled in less than one hour with the pure-Python code (tests of the Bolton ray-tracing routine indicate it produces results consistent with Gravlens). The use of pure-Python code for tracing the deflection of light rays is a critical component of making uvmcmcfit computationally feasible. In uvmcmcfit, lens mass profiles are represented by N lens singular isothermal ellipsoid (SIE) profiles, where N lens is the number of lensing galaxies found from the best available optical or near-IR imaging (a multitude of evidence supports the SIE as a reasonable choice; for a review, see  Treu 2010). Each SIE is fully described by the following five free parameters: the position of the lens on the sky relative to the arbitrarily chosen "image center" based on the ALMA 870 µm emission and any lensing galaxies seen in the optical or near-IR (∆α lens and ∆δ lens ; these can be compared with the position of the optical or near-IR counterpart relative to the "image center": ∆α NIR and ∆δ NIR ), the mass of the lens (parameterized in terms of the angular Einstein radius, θ E ), the axial ratio of the lens (q lens = b lens /a lens ), and the position angle of the lens (φ lens ; degrees east of north).
For the sources, our ellipticity limit is primarily designed to aid numerical stability in the lens modeling. No prior is placed on the position angle of the lens or source. The intrinsic flux density for any source is allowed to vary from 0. 1 mJy to the total flux density observed by ALMA (we ensure that the posterior PDF of the intrinsic flux density shows no signs of preferring a value lower than 0. 1 mJy). The source position is allowed to vary over any reasonable range necessary to fit the data (typically, this is ±1 -2 ). The effective radius is allowed to vary from 0. 01-1. 5. The surface brightness map generated as part of uvmcmcfit is then converted to a "simulated visibility" dataset (V model ) in much the same way as MIRIAD's uvmodel routine. Indeed, the code used in uvmcmcfit is a direct Python port of uvmodel (the use of uvmodel itself is not possible for the same reason as Gravlens: constant input/output makes parallel computing prohibitively expensive).
uvmcmcfit computes the Fourier transform of the surface brightness map and samples the resulting visibilities in a way that closely matches the sampling of the actual observed ALMA visibility dataset (V ALMA ). The goodness of fit for a given set of model parameters is determined from the maximum likelihood estimate L according to: L = u,v |V ALMA -V model | 2 σ 2 + log(2πσ 2 ) (1) where σ is the 1σ uncertainty level for each visibility and is determined from the scatter in the visibilities within a single spectral window (this is a natural weighting scheme). We use emcee (Foreman-Mackey et al. 2013) to sample the posterior probability density function (PDF) of our model parameters. emcee is a Markov chain Monte Carlo (MCMC) code that uses an affine-invariant ensemble sampler to obtain significant performance advantages over standard MCMC sampling methods  (Goodman & Weare 2010).
DSFG. This is different from the pairwise separation distance estimator used by  Hodge et al. (2013)  that becomes ill-defined when there are more than two ALMA counterparts (as is often the case in our Herschel-ALMA sample). Figure  7  shows dN/dA values for ALESS that have been re-computed using our method. We also show the median and 1σ range found from simulated datasets for both ALESS and our Herschel-ALMA sample. The simulated datasets consist of 200 runs of DSFGs with the same flux density and multiplicity as the observed datasets (both the ALESS sample and our ALMA sample), but placed randomly within the primary beam FWHM. We also show predictions from simulations by HB13 (see below for details). We recover the result from Hodge et al. (  2013 ) that the ALESS DSFGs are consistent with a uniformly distributed population.
2008 ) using the SMA  (Younger et al. 2007 (Younger et al. , 2009) )  and PdBI  (Miettinen et al. 2015). These interferometric observations have shown that all of the sources in their surveys are either unlensed or lensed by magnification factors < 2 (a similar result is found based on ALMA imaging of 52 DSFGs in the Ultra Deep Survey;  Simpson et al. 2015a). This is why the ALESS and COSMOS luminosity functions represent a plausible range of intrinsic number counts for DSFGs. These number counts are shown in the left panel of Figure  8. Interferometric follow-up data in COSMOS  (Smolčić et al. 2012 ) and GOODS-N  (Barger et al. 2012)  are published, but unknown completeness corrections in the single-dish surveys on which these follow-up datasets are based precludes their use here. In detail, we use a broken power-law of the form dn dS = N * S S * -β1 , for S < S * , dn dS = N * S S * -β2 (3) , for S > S *.
5 -2  (Rybak et al. 2015; Tamura et al. 2015; Dye et al. 2015). Therefore, it is plausible that both of the intrinsic luminosity functions tested here provide statistically consistent fits to the data. A related but distinct test of the intrinsic number counts for DSFGs comes from the probability of a given source experiencing a magnification above some threshold value, µ min. Unlike the case with the average magnification factor measurements, our ALMA and SMA data should provide a reliable estimate of this quantity. The results of this are shown in the right panel of Figure  8. For clarity of presentation, we show one choice of µ min : µ min = 2. 0. The shape of the curves varies with µ min , but the overall results are qualitatively the same. The models we consider are the same as those used in the left panel of Figure  8.
Instead of computing a running average of the data, we show a logistic regression fit to the data (obtained with the Scikit-learn package;  Pedregosa et al. 2011). Both models tested in this paper exhibit a sharp transition from low probability to high probability of being lensed, consistent with the data. However, there are sig-nificant differences in where this transition flux density, S trans , occurs -i. e. , where P (µ > µ 870 ) > 2. In the data, the logistic regression fit yields S trans = 24 ± 3 mJy (error accounts only for statistical uncertainty in S 870 and µ 870 ), whereas the models based on the ALESS and COSMOS number counts yield S trans = 37 mJy S trans = 69 mJy, respectively. This analysis highlights the difficulty encountered with the luminosity function based on the COSMOS data: unlensed sources with S 870 > 50 mJy are over-predicted and lensed sources with S 870 < 50 mJy are under-predicted.
The inability of numerical simulations to reproduce the small projected separations seen in the data might highlight a productive path forward to improve our theoretical understanding of the enhancement in star-formation by interactions and mergers of galaxies which are already forming stars at a very high rate. In the future, higher spatial resolution imaging is needed to investigate the morphologies of individual ALMA sources. Tidal tails, multiple nuclei, and other signs of mergers and interactions should become evident at 0. 1 resolution. In addition, molecular spectroscopy will be critical to determine distances to and dynamics of individual ALMA sources and hence characterize what fraction of Herschel sources are actually physically associated with each other (and not simply a result of projection effects along the line of sight).
This research has made use of data from the Her-MES project (http://hermes. sussex. ac. uk/). HerMES is a Herschel Key Programme utilizing Guaranteed Time from the SPIRE instrument team, ESAC scientists, and a mission scientist. HerMES is described in  Oliver et al. (2012). The HerMES data presented in this paper will be released through the Herschel Database in Marseille (HeDaM 31 ). SPIRE has been developed by a consortium of institutes led by Cardiff Univ. (UK) and including: Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA).
Karim et al. 2013)7Younger et al. , 2009;;Miettinen et al. 2015)es in COSMOS (black circles;Younger et al. 2007Younger et al. , 2009;;Miettinen et al. 2015)and from ALESS (pink diamonds;Karim et al. 2013). The magneta and blue lines represent the range of plausible intrinsic number counts for DSFGs given these two datasets. Middle: Magnification factors at 870 µm as a function of apparent S 870 for every source in our ALMA (green squares) and SMA (red circles) samples. The black line represents a running average of the magnification measurements when sources with µ 870 > 2. 0 are considered (grey shaded region highlights the 1σ uncertainty), and is truncated at the minimum flux density at which we have observed µ 870 > 2. 0. Colored lines show the average magnification factor, µ 870 , predicted by our models for the two intrinsic number counts shown on the left.
For dead animalsmostly roadkillwe supposed that the effort in a given region was proportional to the distance traveled by the officers. For living animals, we had no way to measure the sampling effort. We demonstrated that it was possible to use the whole dataset (dead and living animals) to estimate the following: (i) the relative densityi. e. , the density multiplied by an unknown constantof each species of interest across the different French agricultural regions, (ii) the sampling effort for living animals for each region, and (iii) the relative detection probability for various species of interest.
During the study period, each official car was equipped with a logbook in which information concerning each animal detected by the wildlife protection officers was recorded (i. e. , the species, the municipality, the date of detection, and whether the animal was dead or alive). The collected data could not be directly used to estimate relative density indices for the species of interest in the different French regions. Indeed, the number of detected animals in a given region partly depended on the time spent by the officers in this region. A large number of detected animals in a given region might have been the result of a high abundance of the species as well as the result of a strong observation effort (also called sampling effort in this paper) there. A model of the observation process was necessary to account for this source of variation in the abundance estimation  [18].
We also took into account the expected spatial regularity of species density, as well as the effect of the environment on these densities, using a ridge-type regularization. We provide an R package named scsl (see S1 Package). This package contains the data, the C code and the R functions used for the calculations carried out in this paper. We also provide a document written using the Knitr system  [19] , describing the model fit and evaluation with these functions, as well as additional analyses carried out to demonstrate the robustness of our findings.
Our aim was therefore to use the data collected under the SCSL program to estimate the density of the 6 Mustelidae species of interest in the 703 SARs of France. Let N ijk be the total number of animals of the species i (i = 1. I) in the SAR j (j = 1. J) with status k (k = 1 corresponding to dead animals and k = 2 corresponding to living animals) detected during the complete study period (i. e. , the sum, over the years of the study period, of the annual counts for this particular combination i,j,k). First of all, we supposed that N ijk could be described using a Poisson distribution: N ijk $ Pðl ijk Þ where λ ijk is the expectation of this distribution. Moreover, we supposed the following model for this expectation: l ijk ¼ S j A ij E jk P ik ð2Þ where S j is the known surface area of the j th SAR, A ij is the true density of the species i in the SAR j, E jk is the sampling effort in the SAR j for animals in the status k, and P ik is the detection probability of the species i in the status k.
Two possible measures of effort for the dead animals We did not know exactly the number of kilometers traveled by the officers in each SAR during the study period. However, the SCSL database contained enough information to estimate it. We compared two alternative ways to estimate the number of kilometers traveled by the officers in each SAR during the study period (see also section 2. 3 of S1 Appendix). A first measure V ð1Þ j could be derived from the total number of kilometers traveled in a department (calculated with Equation  1 ) by supposing that the effort was uniformly distributed in the department. Under this assumption, we could estimate the number of kilometers traveled in each SAR by redistributing this total number across SARs as a function of their area. Thus, S j being the area covered by the j th SAR, we approximated the number of kilometers V ð1Þ j traveled in each SAR with: V ð1Þ j ¼ T d Â S j P j 0 2D S j 0 where D is the set of SARs belonging to the department d.