dataesr/scientific-paragraphs-categorization huggingface dataset:
Reduction outline Our ANDROIDS/WIRCam reductions begin by unifying the World Coordinate System across the dataset with SCAMP  (Bertin 2006). Scamp matches stars in Source Extractor  (Bertin & Arnouts 1996)  catalogs of each WIRCam * p. fits frame both internally (to σ int = 0. 10), and against the 2MASS Point Source Catalog  (Skrutskie et al. 2006 ) to a precision of σ ref = 0. 15. By processing all 4286 frames in the ANDROIDS/WIRCam survey simultaneously, SCAMP allows an accurate and internally consistent coordinate frame for our mosaic. SCAMP handles this data volume gracefully provided we cull the input star catalogs for stars with S/N > 100, and by using the SAME_CRVAL astrometry assumption that the WIRCam focal plane geometry is stable. The next steps are flat fielding and median sky subtraction.
We also note systematic differences in spectral response of WIRCam detectors in the J and K s of order 5%. The flat itself is built by median combination. Median combination of a stack of hundreds of 2048 × 2048 pixel images, each with a weightmap masking astronomical sources, is computationally intensive. A convenient solution is to use Swarp (an image-mosaicing software package,  Bertin et al. 2002)  in a mode that combines images pixel-to-pixel.
Photometry of 2MASS stars in the uncrowded sky fields is obtained with Source Extractor  (Bertin & Arnouts 1996). We use the AUTO photometry mode to capture the full stellar light without using aperture corrections. Objects in the 2MASS PSC are matched to Source Extractor detections by position using J. Sick's Mo'Astro 5  Python package, that manages the full 2MASS PSC in a MongoDB database. The 2MASS PSC contains many galaxies, and many 2MASS sources are saturated in our deeper WIRCam images. Thus we select stars with m J < 14 or m Ks < 15 magnitudes, and stars with FWHM < 1. Additionally, we select sources with J -K s < 0. 8 (typical of foreground Milky Way stars) as we observe larger zeropoint residuals in redder stars. After filtering, typically 200 matched 2MASS sources remain in typical WIRCam images.
7. 1. Implementations The sky offset optimization summarized above is difficult to implement because it is over-constrained, requiring a nonlinear optimization. Any single image shares a network with others, and any error in the surface brightness shapes of fields will result in an imperfect match. In this work, we consider two implementations of sky offset optimization. First, we review the Montage software package in §7. 1. 1, and then introduce an alternative in §7. 1. 2.
Montage Montage is a FITS mosaicing package  (Berriman et al. 2008)  originally written for the 2MASS survey that includes sky offset estimation (background rectification, in their terminology) functionality. Images are rectified onto a mosaic pixel grid, and difference images are computed among overlapping images. Sky offsets are then chosen iteratively by looping through each image pair and choosing the offset needed to minimize the difference image of that pair, counting previous sky offset estimates. That is, at each step the sky levels of the two images are increased and decreased by half the total intensity difference. Sky offsets are refined over several loops through the entire set of overlapping image pairs until convergence is reached (that is, once incremental adjustments to sky offsets diminish below user-specified threshold).
Stack offsets, then, arise from uncertainties in the pipeline's measurement of the sky level from single frames in two stages: estimating detector-to-detector zeropoint offsets from frame sky levels ( §4. 2) and again when subtracting a median sky frame ( §5). Indeed, in §10 we show that median sky images have shape amplitudes of 0. 3% of the sky level and that individiual frames have surface brightness shapes that are uncertainty at a level of 0. 2%; ∆ S sky offsets are thus a consequence of the limited surface brightness flattness across a WIRCam frame. A comparison between the net sky offsets applied to the 2007B and 2009B data sets is provocative. Although the 2009B dataset employed rapid sky-target nodding to minimize temporal lags between disk and sky sampling, the magnitude of sky offsets in the 2007B and 2009B semesters is comparable.
RECONSTRUCTION Sky offsets produce a mosaic that is rigorously optimal only in the sense of field-to-field surface brightness continuity-  not absolute sky subtraction. In this section, we attempt to gauge the systematic surface brightness error inherent in the sky offset technique. 9. 1. Comparison to Montage-fitted images One means of testing for systematic errors in mosaic construction is to compare results from different methods. Besides the simplex method developed in §7. 1. 2- §7. 2 and analyzed in detail in Section 8, we also tested the Montage code that uses an iterative algorithm to solve either scalar or planar sky offsets (see §7. 1. 1). Figure  18  shows the surface brightness difference between our simplex solution and the iterative Montage mosaic solution assuming scalar sky offsets.
Despite an identical dataset, the two methods yield systematically differences of up to ∼ 0. 5 mag arcsec -2 at 20 kpc, though the solutions are consistent in their treatment of the inner disk. Although the simplex and Montage scalar-offset mosaics appear equivalently valid to the eye, a unique and optimal sky offset solution either does not exist, or is extremely difficult for our optimization algorithms to find. Montage is also capable of fitting planar sky offsets to images, which is a tempting solution to the field-to-field discontinuities that persist between scalar-offset blocks. The result of planar fitting is shown in Fig. 19. We see that planar sky offsets, in this case, do little to improve the mosaics, and indeed, have a dramatic effect on the systematic surface brightness of the mosaic (by more than 1 mag arcsec -2 in the K s band).
Distributions of frame shape residuals We now extend the previous analysis analysis across the entire dataset. In Fig. 28  we plot the distribution of frameblock residual shape amplitudes, measured at the 95% difference interval. In essence, this measures the consistency of imaging the shape of each M31 block. As in our test of median sky frame flatness ( §10. 2), we see that the consistency of frame shapes is ∼ 0. 3% of the sky level. This result is seen for both QRUN and FW100K sky flat pipelines and for 2007B and 2009B observing schemes, agreeing with our observation in §10. 3 that in background dominated regimes (as most of our blocks are) frame shape consistency is not correlated with flat field bias. Rather, we interpret Fig. 28  as measuring the amplitudes of additive stochastic background shapes originating either from the sky, or associated with the instrumentation itself.
CONCLUSIONS We have presented near-infrared (J and K s ) images of M31's entire bulge and disk with CFHT/WIRCam. These maps surpass the 2MASS  (Beaton et al. 2007 ) and Spitzer  (Barmby et al. 2006 ) mosaics with superior resolution that permits the identification of individual stars throughout M31's mid and outer disk. The dataset is also complementary to the HST/WF3 PHAT survey  (Dalcanton et al. 2012 ) by providing complete coverage of M31's disk within R = 22 kpc, and by offering a broader NIR colour baseline (J -K s ) than is offered by WF3 (approximately J -H). NIR mosaics of M31 have crucial applications for studies of the nearly attenuation-free stellar structure of our nearest spiral neighbour, and for tests of stellar population synthesis models in NIR regimes. Our focus in this paper has been the establishment of procedures for accurately recovering the NIR surface brightness across 3 sq.
This effect is predominantly influential in the signal-dominated regime of the M31 bulge; though it is also significant for resolved stellar photometry. We thus find that constructing real-time sky flats is essential for calibrating WIRCam images. In sky-dominated regimes, the 2D SB shapes of individual WIRCam frames (20 × 20 ) are uncertain by 0. 2% of the sky intensity, centreto-edge. These background fluctuations present a lower limit in the surface brightness uncertainty across a WIRCam frame since they appear to be caused by skyglow variations in target images that cannot be fully corrected with median sky sub-traction. We now summarize our analysis of the data taking and reduction methods developed in this work, and in doing so, formulate a set of best practices for similar wide-field NIR surveys employing sky-target nodding.
We thank  Loic Albert  and  Karun Thanjavur , previously from CFHT, for their help with WIRCam I'iwi data products and procedures and the  CFHT  staff for many informative discussions and their diligence in performing the queue service observations. We are grateful for the Spitzer 3. 6 µm mapping provided by  Pauline Barmby  ( University of Western Ontario ). J. S. and S. C. acknowledge support through respective  Graduate Scholarship and Discovery grants  from the  Natural Sciences and Engineering Research Council of Canada. M. M is supported by  NASA  through a  Hubble Fellowship  grant  HST-HF51308. 01-Aawarded by the  Space Telescope Science Institute , which is operated by the  Association of Universities for Research in Astronomy, Inc. , for  NASA , under contract  NAS 5-26555. This publication makes use of data products from the  Two Micron All Sky Survey , which is a joint project of the  University of Massachusetts  and the  Infrared Processing and Analysis Center/California Institute of Technology , funded by the  National Aeronautics and Space Administration  and the  National Science Foundation.
4 describes an algorithm for computing reflexive and transitive closures of the transition relations [[P ]] * ♯ (q init , q), and transition invariants [[P ]] T Inv ♯ (q), for every q ∈ Q. A version of this algorithm was implemented in the Flata tool  [22] , and is guaranteed to return the exact reflexive and transitive closures of the transition relations [[P ]] * (q init , q), and the strongest transition invariants of the program [[P ]] T Inv (q), for a specific class of programs, called flat (see Section 6. 5). A formal proof of correctness of Algorithm 4 is given in Section 6. 5.
Experiments We have validated the methods described in this paper by automatically finding preconditions for termination of all the octagonal running examples, and of several integer programs synthesized from (i) programs with lists obtained using the translation scheme from  [6]  which generates an integer program from a program manipulating dynamically allocated single-selector linked lists, (ii) VHDL designs such as hardware counter and synchronous LIFO  [39] , (iii) small C programs with challenging loops and (iv) small recursive Java programs from  [41]  translated to non-recursive programs using the procedure summarization method described in  [18]. We have computed the weakest non-termination preconditions reported in Table  1  using the methods from Section 4 and 6 which we implemented in the Flata tool  [22].
By computing octagonal abstractions of disjuncts of a transition invariant, we have verified universal termination of the ListCounter and ListReversal programs. Next, we have verified the Counter and SynLifo programs by computing the precise transition invariant and then the weakest non-termination precondition, which was empty in both cases. Thus, these models have infinite runs for any input values, which is to be expected as they encode the behavior of synchronous reactive circuits. Similarly, we have computed the weakest non-termination preconditions for numerical programs anubhav, cousot, leq, and plus. Second, we have compared (Table  2 ) our method for termination of polynomially bounded linear affine loops from Section 5 with the examples given in  [16] , and found the same termination preconditions as they do, with one exception, in which we can prove universal termination in integer input values (row 3 of Table  2 ).
Conclusion We have presented several methods for deciding conditional termination of several classes of program loops manipulating integer variables. The universal termination problem has been found to be decidable for octagonal relations and linear affine loops with the finite monoid property. For the class of polynomially bounded linear affine loops, we give sufficient termination conditions. Further, we extend the computation of weakest non-termination preconditions from simple loops to general programs, and define a class of programs, called flat, for which this computation yields precise results. Finally, we have implemented our method in the Flata tool  [22]  and performed a number of preliminary experiments.
Rankine Cycle The Rankine cycle model is a quasi-steady state model developed in Matlab. The model consists of three components including the pump, the evaporator and the expander. The condenser is not modeled in order to decrease the computational time. This hypothesis is valid since the condensation temperature will remain constant by adjusting the mass flow rate of the cooling fluid. The temperature at the entry of the pump is then set by the user. It corresponds to the saturation temperature at the condenser exhaust (which is the condensing temperature if no pressure losses are described) decreased by the subcooling. The pump is simply modeled by its efficiency and Equation (  1 ) is used to determine the outlet temperature: ϵ , ( 1 ) The evaporator is modeled as a counter flow evaporator, illustrated in Figure  4.
Since our modeling formalism is essentially based on the extension of Mealy automata with a monad T (i. e. thus allowing for capturing the most relevant computation structures including determinism, non-determinism and partiality  [35] ), it naturally follows that the language for stating system's requirements should allow one to express temporal properties of a system with the ability to express constraints that relate the production of output values from input ones. Being mainly interested in this paper by theoretical results of behavior and property preservation, we propose to extend a logic that subsumes most of modal and temporal logics: the µ-calculus  [5, 11, 27]. More precisely, following our work in  [3] , we propose a variant of first-order fixed point modal logic  [26, 45]. This extension to the first-order will allow us to export expected properties from components to systems, and thus allowing to study their preservation along integration operators.
Perspectives Both logic and associated results that have been presented here are devoted to discrete/computing complex systems. We are currently working to extend this work to heterogeneous complex systems (i. e. where components can be defined over discrete or continuous time scales). To do so, first we propose to introduce the notion of monad to components in  [2]  to take into account different computation situations, and then to study the results of properties preservation for the logic defined in  [3]. Thus, the defined formalism would be allowed to be used as a formal semantics for the system modelling language SysML. Moreover, the logic presented in the paper can be related to the language for the power set functor based on regular expressions defined in  [42] , though the approach followed in  [42]  differs from ours at least in the following two points: 1.
Fire is an important global ecological process that influences the distribution of biomes, with consequences for carbon, water, and energy budgets. Therefore it is impossible to appropriately model the history and future of the terrestrial ecosystems and the climate system without including fire. This study incorporates the process-based prognostic fire module SPITFIRE into the global vegetation model ORCHIDEE, which was then used to simulate burned area over the 20th century. Special attention was paid to the evaluation of other fire regime indicators such as seasonality, fire size and fire length, next to burned area. For 2001-2006, the simulated global spatial extent of fire agrees well with that given by satellite-derived burned area data sets (L3JRC, GLOBCARBON, GFED3. 1), and 76-92 % of the global burned area is simulated as collocated between the model and observation, depending on which data set is used for comparison.
The simulated global mean annual burned area is 346 Mha yr -1 , which falls within the range of 287-384 Mha yr -1 as given by the three observation data sets; and is close to the 344 Mha yr -1 by the GFED3. 1 data when crop fires are excluded. The simulated long-term trend and variation of burned area agree best with the observation data in regions where fire is mainly driven by climate variation, such as boreal Russia (1930Russia ( -2009)), along with Canada and US Alaska (1950Alaska ( -2009)). At the global scale, the simulated decadal fire variation over the 20th century is only in moderate agreement with the historical reconstruction, possibly because of the uncertainties of past estimates, and because land-use change fires and fire suppression are not explicitly included in the model.
Model description The processes and equations of the fire model SPITFIRE, as described by  Thonicke et al. (2010) , were implemented in the vegetation model ORCHIDEE  (Krinner et al. , 2005). The SPITFIRE model operates on a daily time step, consistent with the STOMATE sub-module in ORCHIDEE, which simulates vegetation carbon cycle processes (photosynthates allocation, litterfall, litter and soil carbon decomposition). The major processes within SPITFIRE are briefly described below with applicable minor modifications (see  Thonicke et al. , 2010  for more detailed description).
Input data set and the simulation protocol The 6-hourly climate fields used to drive the model were from the CRU-NCEP data set (http://dods. extra. cea. fr/store/ p529viov/cruncep/V4_1901_2012/readme. htm). Population density for the 20th century was retrieved from the His-tory Database of the Global Environment (HYDE) as compiled by the Netherlands Environmental Assessment Agency (http://themasites. pbl. nl/tridion/en/themasites/hyde/ download/index-2. html). From 1850 until 2005, the HYDE gridded data are available for the beginning of each decade and for 2005. Annual data were linearly interpolated within each decade, and further re-gridded to 0. 5 • resolution. For 2006-2009, population density was set as constant at the 2005 value. A three-step simulation protocol was used. For the first two steps, the atmospheric CO 2 was fixed at the preindustrial level (285 ppm) and climate forcing data of 1901-1930 were repeated in loop.
Before entering the transient simulation, the mineral soil carbon stock was verified to vary within 0. 1 % (with a slight global carbon sink of 0. 13 Pg C yr -1 and a negligible annual trend of 0. 003 Pg C yr -1 during the last 50 years of the fire-disturbed spin-up, excluding all crops, for which fires are not simulated). For the current simulation, the vegetation dynamics module of ORCHIDEE was turned off, i. e. the simulation used a static current-day vegetation distribution map (converted into the 13-PFT map in OR-CHIDEE based on the IGBP 1 km vegetation map, http: //webmap. ornl. gov/wcsdown/dataset. jsp?ds_id=930), and no land cover change was included. This static land cover could affect the model-observation agreement in terms of longterm trend and variation of burned area. Land cover change has double effects on burned area: fires used for land cover change contribute directly to burned area; and the indirect effect depends on fire frequencies of the land cover types before and after the land cover change.
Satellite-derived burned area data The GFED3. 1 data set provides monthly burned area data at 0. 5 • resolution for 1997-2009 with global coverage  (Giglio et al. , 2010). The GFED3. 1 burned area was mainly generated using MODIS imagery with additional images from TRMM VIRS and ERS ATSR. The fire carbon emissions were also provided which are model simulation results by applying a modified version of the CASA model  (van der Werf et al. , 2010). L3JRC data set provides daily global burned area data at 1 km resolution for April 2000 to March 2007; these data were generated from the 1 km SPOT VEGETATION satellite imagery  (Tansey et al. , 2008). This data set was assembled at 0. 5 • resolution at monthly time step for use in the present study. GLOBCARBON burned area data was produced from a combination of SPOT VEGETATION and ERS2-ATSR2/ENVISAT AATSR data as one of the four land products of the ESA GLOBCARBON initiative  (Plummer et al.
Historical burned area reconstruction for the 20th century To evaluate the simulated burned area for the 20th century, historical burned area data were used. These data, which cover the period 1900-2000, were compiled by  Mouillot and Field (2005)  at 1 • resolution and monthly time step (hereafter referred to as the Mouillot data). The data were generated by first synthesising the burned area information from published data at national or regional scale for the periods of the 1980s or 1990s, further interpolated spatially at the global scale at 1 • resolution using the available satellitederived active fire distribution. Then national fire statistics, historical land-use practices and other fire-relevant quantitative information (such as tree ring reconstruction) were used to build the historical fire temporal trend to interpolate historical burned area.
When comparing the burned area given by GFED3. 1 and the Mouillot data for their overlapping period of 1997-2000, the global total burned area given by  Mouillot and Field (2005)  is 52 % higher than GFED3. 1 with significant regional discrepancies. As the satellite-derived data is considered to be more reliable than the national or regional statistical data at a large spatial scale, a bias correction was performed on the Mouillot data. We calculated the ratio of burned area by the Mouillot data to GFED3. 1 for 1997-2009 for each region (Fig. 2b ) and also the globe. This ratio was then applied to correct for each decade of the burned area data in the Mouillot data set.
Fire patch data Alaskan and Canadian fire management agencies have maintained historical fire monitoring for a relatively long time (dating back to the 1950s). The historical fire information for the US Alaska was retrieved from the Alaska Interagency Coordination Center (AICC, http://afsmaps. blm. gov/ imf_firehistory/imf. jsp?site=firehistory). The fire information for Canada was from the Canadian Wildland Fire Information System (http://cwfis. cfs. nrcan. gc. ca/ha/nfdb). These data sets contain information on fire location, fire size (burned area), fire cause, and for some fires, the fire report and out date. Please note that in these two data sets fires with all sizes are included. Archibald et al. (2010)  classified the MCD45A1 500 m MODIS fire burned area data into individual fire patches for southern Africa (Africa south to the Equator).
Fire season length and the 95th quantile fire size The global fire season length and the 95th quantile fire size data are provided by  Archibald et al. (2013). The fire season length was quantified as the number of months required to reach 80 % of the annual burned area using GFED3. 1 data. The MCD45A1 burned area product at 500 m resolution was used to derive the individual fires by applying a flood-fill algorithm, and the 95th quantile fire size in each grid cell was extracted to represent the size of large fires.