dataesr/scientific-paragraphs-categorization huggingface dataset:
They also acknowledge generous financial support from La Région Haute-Normandie via the CPER  " THETE " project, and the  GRR Electronique, Energie et Matriaux , from the  "Fédération de Recherche Energie, Propulsion, Environnement ," and from the  LabEx EMC 3  , via the project  PicoLIBS  (No. ANR-10-LABX-09-01 ). ÅL acknowledges support from the  Swedish research council.
Acknowledgements This work was carried out under the HPC- EUROPA2  project (project number:  228398 ) with the support of the  European Commission Capacities Area -Research Infrastructures Initiative. This work made use of the facilities of  HECToR , the  UK 's national high-performance computing service, which is provided by  UoE HPCx Ltd  at the  University of Edinburgh, Cray Inc  and  NAG Ltd , and funded by the  Office of Science and Technology  through  EPSRC's High End Computing Programme. This work was also granted access to the HPC resources of IDRIS under the allocation 2013-i2011086670 made by  GENCI  ( Grand Equipement National de Calcul Intensif ). N. S. thanks the  Univ. Grenoble Alpes , the  CNRS  and the  ICMG FR 2607  for financial support, CIMENT for allocation of CPU time on the "ceciccluster" and "froggy" platforms (project "liqsim"), and  Chris Johnson  for technical support.
ACKNOWLEDGMENTS This work was supported by  NSF -DMR 1005293  and  1309146 , and the  NHMFL  is supported by  NSF  Cooperative Agreement No. DMR-1157490 , the  State of Florida  and the  US Department of Energy. Funding for the dilution refrigerator used for the  16 T experiment came from DOE NNSA SSAA DE-NA0001979. Collaboration within the  European Associated Laboratory Trans-Pyrénéen (LEA) (program : " de la Molécule aux Matériaux ") is appreciated. Work done at the  Laboratoire de Chimie de Coordination (LCC)  was supported by the  French Centre National de la Recherche Scientifique (CNRS). I. C. thanks the  French Ministére de l'Enseignement Supérieur et de la Recherche (MESR)  for a Ph. D. grant.
Discussion Summarising, in this paper we have addressed the problem of search on networks. To this end, we have preliminarily studied the trapping problem for a modified random walk that combines local hops along the links of the graph with non-local relocation jumps, i. e. not along the links contained in the adjacency matrix. We have shown, both for artificial and real datasets, that an optimal balance between local and non-local moves exists which minimizes the average time required to reach a trap. Furthermore, we have derived closed analytical expressions, that enable one to predict the optimal combination as a function of the network topology. In the second part of the paper we have focused on a random walker diffusing on a arbitrary number of interconnected networks, which share the same set of nodes but are characterized by different adjacency matrices.
Acknowledgments The authors would like to thank  Levon Chakhmakhchyan  and  Filippo Caruso  for inspiring discussions and  Alessio Cardillo  for his critical reading of the manuscript. This work has been partially supported by  Ente Cassa di Risparmio di Firenze  and program PRIN 2012 founded by the  Italian Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR).
ACKNOWLEDGMENTS We acknowledge stimulating discussions with  Oliver Ebenhöh ,  Riccardo Rao  and  Alexander Skupin. We would like to also acknowledge  P. Gaspard  for a critical reading of this work and for insightful comments. M. E. is supported by the  National Research Fund , Luxembourg in the frame of project  FNR/A11/02  and S. L. by the  Region Île-de-France  thanks to the  ISC-PIF.
We review the appropriateness of using SNIa observations to detect potential signatures of anisotropic expansion in the Universe. We focus on Union2 and SNLS3 SNIa datasets and use the hemispherical comparison method to detect possible anisotropic features. Unlike some previous works where nondiagonal elements of the covariance matrix were neglected, we use the full covariance matrix of the SNIa data, thus obtaining more realistic and not underestimated errors. As a matter of fact, the significance of previously claimed detections of a preferred direction in the Union2 dataset completely disappears once we include the effects of using the full covariance matrix. Moreover, we also find that such a preferred direction is aligned with the orthogonal direction of the SDSS observational plane and this suggests a clear indication that the SDSS subsample of the Union2 dataset introduces a significant bias, making the detected preferred direction unphysical.
SNIa data This section will be devoted to introducing the SNIa datasets that we will use later on for our analysis. We will discuss the χ 2 estimator to be used when using SNIa as well as some useful properties of our cosmological data sample which should be taken into account in order to obtain correct results. The most updated SNIa samples so far are SNLS3  [29]  provided by the SuperNova Legacy Survey team and Union2  [31]  provided by the SuperNova Cosmology Project team. A newer collection of SNIa from the Union team is available and called Union2. 1. It has 23 more SNIa with respect to its predecessor. However, we prefer to use the Union2 compilation in favor of making the comparison with older literature easier and more direct. Also, Union2. 1 only adds ≈ 23 SNIa, so we expect their statistical weight for our analysis to be not very significant.
There is also a recent compilation with 112 new SNIa provided by the Pan-STARRS1 Medium Deep Survey team  [32] , which we will not use because it has a nonhomogeneous angular distribution (see Table  1  from  [32] ), which makes it unsuitable for testing anisotropy. It is worth stressing here nevertheless that we aim to testing the suitability of current SNIa datasets to seek for anisotropic features and we do not intend to obtain the most updated constraints on them (since, as we will show, current datasets are actually unsuitable for that purpose).
Angular distribution Since the main aim of the present work is testing the isotropy of SNIa samples, it is important to perform a preliminary analysis of the angular distribution of the samples that we are going to use. This is important since one could encounter cases with a false detection of a preferred direction in the universe, whose actual underlying reason might be a non-homogeneous angular distribution of the sample. We also stress here that no tomographic analysis considering redshift distribution of SNIa will be performed in this work. Even if possible, it would reduce the number of SNIa data in each redshift bin, thus reducing the predictive power with too large errors on the cosmological parameters. We implicitly assume that the SNIa properties do not evolve throughout the expansion of the universe (at least for low redshifts where the SNIa are observed), but studying redshift-dependences of intrinsic SNIa properties is beyond the scope of the present work.
We also comment here in advance that the main problem (discussed in next sections) will be related to the angular distribution of SNIa in the Union2 and SNLS3 datasets (mainly due to the fact that the SDSS subsample only gives data along 4 specific directions in the sky). The SNLS3 sample is made out of four smaller sub-samples from four different surveys  [29] : Low-z, SDSS, SNLS and SNIa from the Hubble Telescope. In the left panel of Fig. 1  we show in galactic coordinates the position of each SNIa in the sky, the longitude l and the latitude b. SNIa from Low-z and Hubble samples are shown in light grey; SDSS SNIa are shown in black; SNLS SNIa are identified by numbers in brackets. SDSS SNIa are distributed in the region scanned by the SDSS survey and specifically chosen for the supernova survey project  [30].
Based on these considerations, and in order to develop our analysis, we will perform our statistical study considering two samples: the total Union2 data set; and the so-called cut Union2 one, which will correspond to the black points in Fig. 1. The cut sample is obtained considering only sub-samples which show a homogeneous distribution in space, so that, for example, SDSS, SNLS and others which have a peculiar angular distribution are not considered. The cut sample will be made of 226 SNIa, approximately the 40% of the total sample. The cut-criterium has not been arbitrarily chosen but it is well-motivated by the results we will show in next sections, essentially consisting in removing the highly inhomogeneous subsamples. Finally, we underline another important property of the SNIa distribution: the lack of observations in a narrow region about the galactic plane, clearly identified by the condition b = 0.
Despite the availability of more complex cosmological models involving a larger number of theoretical parameters, this choice seems a reasonably minimal extension and appropriate for our purposes. • The main difference from previous works (specially with  [22] ) will be the use of Monte Carlo Markov Chain (MCMC) methods for the statistical analysis. After having split the data into two hemispheres, we will not select a certain amount of random directions but, instead, we will use an MCMC method to explore the entire space parameter and to obtain an angular map of the χ 2 function. Then, we will be able to conclude which is the preferred direction of anisotropy of our SNIa sample, if any. We will minimize the χ 2 estimator using MCMC methods and testing their convergence with the power spectrum algorithm defined in  [34].
Moreover, present data sets comprise too few SNIa already for the simplest case, so even poorer constraints will be obtained if we allow for additional free parameters. It is worth to point out here that MCMC methods give us the possibility to easily implement priors on fitting parameters, if any physically well motivated reason is for them. In our analysis, we have left the cosmological parameters Ω N m and Ω S m free to span the range [0, 1] with no other requirement. On the other hand, the equatorial planes coordinates l a and b a can be constrained to a certain range due to evident symmetries considerations; we chose the ranges 0 • ≤ b a ≤ 90 • and 0 • ≤ l a < 360 •. This last point has to be investigated in detail, as long as we do not know the degree of suitability of MCMCs for such a test.
The main parameters to be fit here will be the two cosmological values of Ω m , namely Ω N m and Ω S m , and the two equatorial plane coordinates, i. e. l a and b a. While it is well known the way Ω N m and Ω S m are related to observations and theory, this is not the same for the equatorial plane coordinates. Ω N m and Ω S m are smoothly varying quantities, in the sense that χ 2 varies smoothly when they are changed; on the other hand, a change in l a and b a might not be related to a change in χ 2 for a given dataset. Depending on the spatial distribution of SNIa, there are voids in the SNIa distribution because of the few number of SNIa available for the whole sky, so that any value of l a and b a in that range would give the same result. In other words, for changes in (l a , b a ) such that the number of supernovae on each hemisphere remains the same, χ 2 will not vary.
Analysis: preliminary tests Prior to the application of the method to real data, we will first study and assess the following relevant aspects: • Suitability of MCMCs for anisotropy detection. • Degradation in the anisotropy signal due to the use of the full covariance matrix error. • Degradation in the anisotropy signal due to galactic plane. The first point to be addressed is whether the use of MCMC is effectively suitable to look for a certain level of anisotropy in the SNIa distribution. For that, before using real SNIa data sets, we will apply our algorithm to a set of simulated data with a homogeneous distribution in the sky data set of supernovae. We will endorse this simulated data with a known anisotropic signal as follows: We will demand a preferred direction determined by r and given by the equatorial plane galactic coordinates l a = 136.
84 • and b a = 27. 07 •. This plane came out as the preferential plane when the MCMC analysis was applied to the cut Union2 sample when the full covariance matrix error is used (see following sections). Then, we generate a homogeneous set of random vectors ri that will give the distribution of the SNIa in the sky. With this distribution, we confer each SNIa a distance modulus following the CDM model given in Eq. (  8 ), where we chose Ω N m = 0. 5 and Ω S m = 0. 1, and assuming that the Hubble constant is H 0 = 72 km s -1 Mpc -1. All the other quantities needed, namely, redshifts and covariance matrix errors, are assumed to be exactly equal to those of the real Union2 dataset. Another issue that we want to study is the following. Given that our galaxy prevents us from having observations of SNIa near the galactic plane (or, equivalently, a lack of data points around that plane with respect to the rest of the sky) we want to explore also whether the absence of SNIa data in the region near the galactic equator can introduce a potential bias or not.
Cut sample cases There seems to be a clear evidence that the statistical analysis using the full Union2 sample is dominated by the SDSS subset, aligned with SDSS scanning direction, and that such a subset is introducing a strong bias in the best fits. This is the reason for defining the cut sample, where SDSS and SNLS SNeIa are removed in order to have a more homogeneous distribution of supernovae. This might help to assess more clearly for a detected anisotropy, even though the cut in the number of data will inevitably degrade the signal (if any), as we have shown in the preliminary analysis with mock data. Effectively, working with the cut sample and the full covariance matrix gives much more interesting hints (see last row of Table  1 ). In that case we found an anisotropic signal in terms of both amount and direction.
SNLS3 fits Finally, we also consider the SNLS3 SNIa for our analysis. As we have discussed, their angular distribution can be seen as a paradigmatic badly suited sample for testing isotropy on full-sky ranges. But their interesting feature of being aligned along four directions makes them a specially suitable dataset to look for deviations with respect to isotropy in a scanning mode, in a way as the one suggested in  [14]  to be the optimal manner. However, we have to keep in mind that the number of SNIa in each beam is still quite low and a large error should be expected. In any case, this is a very interesting pattern that could be very useful for isotropy tests like the one performed here if a higher number of supernovae is detected along each direction in future observations. We have applied a line-of-sight approach to this compilation of SNIa by independently fitting the supernovae of each beam search- The likelihoods of two of the beams  (3, 4)  peak at Ω m values which are very similar to each other, but the peak values for the other two are quite dissimilar: one is rather higher (1) and the other rather lower (2).
Our result is in agreement with those in  [28] , where no significant indication of hemispherical anisotropy was found. Moreover, we have shown that the particular alignment of the SDSS SNIa seems to introduce a strong bias when searching for anisotropic features. On the other hand, we have used the SNLS3 data and have taken advantage of its very special distribution with the SNIa lying along four different directions. We have then fitted each direction to an independent CDM model and have obtained the corresponding matter density parameters. Although the four directions yield likelihoods overlapping at the 1σ level, we have found that two of the directions give likelihoods that peak at quite different values of Ω m. However, the low number of SNIa in each direction does not allow to draw any significant conclusion.
Acknowledgements J. B. J. is supported by the  Wallonia-Brussels Federation  grant  ARC No. 11/15-040  and also thanks support from the  Spanish MICINN  Consolider- Ingenio 2010 Programme  under grant  Multi-Dark   CSD2009-00064  and project number  FIS2011-23000. J. B. J. also wishes to acknowledges the  Department of Theoretical Physics of the University of the Basque Country  for their warm hospitality. V. S. and R. L. are supported by the  Spanish Ministry of Economy and Competitiveness  through research projects  FIS2010-15492  and  Consolider EPI   CSD2010-00064 , and also by the  Basque Government  through research project  GIC12/66 , and by the  University of the Basque Country UPV/EHU  under program  UFI 11/55.
Acknowledgements Our original interest in difference equations on elliptic curves arose from discussions with  Jean-Pierre Ramis  some years ago. We thank  Jean-Pierre Ramis  and  Michael Singer  for interesting discussions. We thank the referees for their careful reading and useful suggestions. The first author is founded by the labex  CIMI. The second author is partially funded by the  French ANR  project  QDIFF  ( ANR-2010-JCJC-010501 ).
Number of binaries and their luminosity As all the works from which we construct our sample give the data of individual sources in the galaxy, we took directly the observed number of sources N and their individual X-ray luminosities from the aforementioned works (the complete data of our sample is given in Table  1 ). The luminosity threshold L th above which sources are detected was also recorded. Although we cannot ensure that all the sources listed are indeed HMXBs, the selection criteria imposed minimize the contamination by other types of sources. In the case of the data taken from  Mineo et al. (2012) , we only used objects with location flag equal to 1 in their Table  A1 , which are those sources lying in the HMXB-dominated regions of the galaxies. For the data of low-metallicity galaxies, the association of the few X-ray sources found with star-forming regions makes highly improbable of them being other kind of sources.
The luminosity L G,38 X was determined in the same way as L G,36 X , but using L th,2 instead of L th,1 in Eqn. 1. The corrections in this case are lower than 7%, except for NGC 4194 (15%). The corrections made by Eqns. 1 and 2 allow us to obtain a uniform sample of the numbers of sources and luminosities of the galaxies. It is important to note that most of these corrections are small, and that they do not affect our final results, as N 38 , L G,38 X , and L G,36 X are used only to visualize and derive preliminary trends. The full Bayesian analysis of the data, from which our final results are obtained and our conclusions are drawn, relies on the original data (N, L G X , and L th ).
Conclusions We compiled from the literature a large sample of 49 galaxies with measured star-formation rates, oxygen abundances and HMXB population properties (observed number of sources and luminosities above some threshold luminosity). This sample enhances those previously compiled by  Mineo et al. (2012)  and Brorby et al. (  2014 ) by giving the oxygen abundances of the galaxies, and by including both the number of sources in each galaxy together with its integrated luminosity. As the low-and high-metallicity galaxies were taken from different works, with different uncertainties and selection effects, the data were homogenized to make statistical comparisons and draw meaningful conclusions. The SFRs in our sample were corrected to a common estimator. For the oxygen abundances, we used a single estimator in the largest possible subsample and the rest of the sample was shown to be unbiased with respect to this homogeneous set.
Acknowledgements. We would like to thank the referee for useful comments that helped to clarify the manuscript. This work was partially supported by  Argentine  grants  PICT 2011-0959  ( ANPCyT ),  PIP 2009-0305  and  PIP 2012-0396  (CONICET). Our MC models were run in the Fenix cluster of the  Numerical Astrophysics Group at the Institute for Astronomy and Space Physics (CON-ICET/UBA ).
Acknowledgments We gratefully acknowledge support from  NSF ,  DOE ,  SNF ,  UZH ,  FCT ,  Region des Pays de la Loire ,  STCSM ,  BMBF ,  MPG ,  FOM , the  Weizmann Institute of Science, EMG, INFN , and the  ITN Invisibles  ( Marie Curie Actions ,  PITN-GA-2011-289442 ). We thank the technical and engineering personnel of  Hamamatsu Photonics Co. for the fruitful cooperation in producing the ultra-pure photomultiplier tube. We are grateful to LNGS for hosting and supporting the  XENON  project.
Acknowledgements We thank  J. W. Fleischer ,  G. Molina-Terriza ,  A. Poddubny ,  P. Voisin  and  M. Wouters  for fruitful discussions. This work was supported by the  French RENATECH , the  ANR-11-BS10-001  contract "QUANDYDE", the  ANR-11-LABX-0014  Ganex, the  RTRA Triangle de la Physique  (contract " Boseflow1D "), the  FP7 ITN "Clermont4 " ( 235114 ), the  FP7 IRSES "Polaphen" (246912) , the  POLATOM ESF Network , the  Nanosaclay Labex  and the  ERC grants Honeypol and QGBE.
Acknowledgments This work was partially supported by the  VEGA Grant Agency , Project  2/0003/13 , as well as by the  Austrian Science Fund (Fonds zur Förderung der Wissenschaftlichen Forschung (FWF)) ,  Research  Project  M1564-N27. We would like to express our sincere gratitude to  Hans Havlicek  ( Vienna University of Technology ) for a number of critical remarks on the first draft of the paper. Our special thanks go to  Jörg Arndt  who computed for us multiplication tables of octonions, sedenions, 32-nions and 64-nions. We are also very grateful to  Boris Odehnal  ( University of Applied Arts, Vienna ) for creating nice computer versions of several figures.
A note on the fitting strategy Our choice of separating the analysis in two steps (Secc. 4. 1 and 4. 2) is motivated by the fact that the structural parameters pM‹, R‹q physically describe the mass distribution of stellar discs and hence, in principle, they are best measured on the basis of available data for Σ‹ alone, irrespective of the distribution of newly born stars. Also, once such a measurement has been achieved, the fact that the SFRD profiles can be reproduced without a further tuning of pM‹, R‹q provides a valuable test for the validity of our theory. However, we also investigated whether our results would change if our 4 parameters pM‹, R‹, νM, νRq were allowed to vary simultaneously to reproduce both the stellar mass and the SFRD radial profiles. To this purpose, we ran, for each galaxy, a Monte Carlo Markov Chain based on the combined likelihood of both our datasets (Secc.
ACKNOWLEDGMENTS G. P. is grateful to  L. Posti  and  E. M. Di Teodoro  for useful discussion. G. P. and F. F. acknowledge financial support from  PRIN MIUR 2010-2011 , project ' The Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies ', prot. 2010LY5N2T. In this work we made use of the Groningen Image Processing System.
Acknowledgments The authors thank  C. Genes ,  P. S. Julienne  and  J. Moran  for discussions and acknowledge support from the  ERC  (Grants  227557  and  307688 ), the  International Center for Frontier Research in Chemistry (icFRC, Strasbourg) , the  ANR Equipex " Union " ( ANR-10-EQPX-52-01 ) and the  Labex NIE  projects ( ANR-11-LABX-0058_NIE ) within the  Investissement d'Avenir program   ANR-10-IDEX-0002-02 , and  EOARD.
Numerical optimal control-state of the art If the set of control equations, resulting from the maximum principle, cannot be solved analytically, numerical optimal control theory provides a viable alternative. Algorithms comprise (i) gradient ascent algorithms  [210]  (which can be extended to second-order quasi-Newton and Newton methods  [79, 98, 264] ) and (ii) Krotov-type methods  [226, 266, 332] , also permitting this extension  [118]. The main difference between these two approaches is that the control is updated (or replaced) for all times simultaneously in case (i) and sequentially in case (ii) which implies different convergence properties. The algorithms are comparatively easy to use and several program packages include optimal control modules, i. e. , SIMPSON  [415] , SPINACH  [169] , DYNAMO  [264] , and QuTiP  [184].