dataesr/scientific-paragraphs-categorization huggingface dataset:
Effective Hamiltonian methods As we shall see in the experimental part, the spectrum of 3-pentyn-1-ol is analyzed using two different programs treating internal rotation, the xiam  [15]  and the belgi-C 1 code  [16]. Both programs can be accessed at the PROSPE website  [17]. The program xiam uses the combined axis method, which is a combination of the principal axis method and the rho axis method. The Hamilton matrix of each internal rotor is set up in its own rho axis system. After diagonalization, the eigenvalues and torsional integrals are used to set up the Hamilton matrix in the principal axis system. Matrix elements of each internal rotor are added to the Hamilton matrix, which also contains the matrix elements of the overall rotation. Finally, the matrix is diagonalized to obtain the rotorsional eigenvalues.
In the second step, we used a basis set consisting of products of the torsional eigenfunctions obtained from the first step diagonalization and the symmetric top wavefunctions |JK to diagonalize the rest of the terms of the Hamiltonian, i. e. H R , H cd , and H int allowed for the C 1 symmetry  [16]. The nine lowest torsional states v t are taken to create a matrix of the size (2J + 1) • 9 × (2J + 1) • 9 associated with the second step. This truncation has been tested so that it does not affect the energy calculation of the ground torsional state v t. For comparable results, the same k max = 10 is used in the program xiam. Unlike belgi, xiam normally uses only the lowest torsional state, leading to a (2J + 1) × (2J + 1) matrix, which significantly increases the speed of the calculation. The program belgi-C 1 is referred to as a global approach  [19] , because it takes into account explicitly the interaction between the nine lowest torsional states, unlike the xiam code which fits each v t state separately.
Additionally, compared to the xiam code, a number of higher order terms can be fitted in the belgi-C 1 code. It has been shown in a number of studies that the xiam code and the belgi codes are complementary  [20, 21]. The xiam code is widely used for many internal rotor problems mainly because of its ease of use and speed. However, in cases with rather low barriers, E species transitions are not always satisfactorily predicted due to the fact that the interactions between torsional states can be large. An example is allyl acetate (V 3 = 98. 1 cm -1 ). For this molecule the A species could be fitted with a standard deviation of 2. 7 kHz within the measurement accuracy of 3 kHz, but for the E species a standard deviation of 54. 0 kHz was obtained with xiam  [22]. Using the belgi-C 1 code, both species were fitted to a rms deviation of 2.
Spectral analysis and fits As mentioned in section 2. 1, we only attempted to assign the spectrum of conformer I. At the beginning, we neglected internal rotation and treated 3-pentyn-1-ol as an effective rigid rotor, i. e. only the A species lines were considered. Using the rotational constants calculated at the MP2/6-311++G(d,p) level of theory, we predicted a theoretical spectrum in the same frequency range as that of the broadband scan. Seven lines belonging to the a-type R branch with J = 4 ← 3 and K a ≤ 3 were first assigned and fitted with the program xiam, yielding accurate B and C rotational constants. In agreement with the largest calculated dipole moment component in a direction, these lines were the most intense in the spectrum. Thereafter, some b-type Q branch transitions were also assigned which fixed the A rotational constant.
A total of 52 A species lines could be fitted using only the rotational constants and quartic centrifugal distortion constants to a root-meansquare (rms) deviation of 2. 1 kHz, which is almost the measurement accuracy. The fitted parameters are given as Fit A in Tab. 2. A list of all measured lines is available in Tab. S-4. As a next step, we took the methyl internal rotation into account and predicted the E species frequencies with the program xiam. The initial barrier was assumed to be 7 cm -1 , which is the value calculated at the MP2/6-311++G(d,p) level of theory (see section 2. 1). The angles between the internal rotor axis and the principal axes of inertia were also taken from the optimized geometry at the same level. It was surprising that the assignment of the E species was straightforward, whereas we expected it to be difficult because of the low barrier height.
We searched first for a-type R branch transitions in the scan, whose A-E splittings were expected to be small. Indeed, the E components were close to the A components with splittings from 0. 2 to 0. 5 GHz. The smallest splitting of 3. 3 MHz was found for the 6 15 ← 5 14 transition at 19. 523 GHz. Afterwards, b-type R branch, Q branch, and P branch E species transitions with much larger A-E splittings from 2 to 2. 5 GHz, from 1 to 4 GHz, and from 1 to 5 GHz, respectively, were also assigned. Finally, we identified c-type Q branch and P branch lines with splittings from 1. 5 to 3. 5 GHz and 2 to 3 GHz, respectively. A global fit with 52 A and 40 E species transitions was performed using the program xiam to a rms deviation of 20. 7 kHz, which is much larger than the experimental accuracy of 2 kHz.
The fitted parameters are given as Fit A/E in Tab. 2. A list of all measured lines is available in Tab. S-5. As an alternative, the same data set was fitted using the belgi-C 1 code. The starting values of the rotational constants A, B, and C were derived by a transformation of the values obtained from Fit A/E in Tab. 2 into the rho axis system. The initial values of the internal rotation parameters V 3 , ρ, and F were taken directly from Fit A/E. The off-diagonal element D ab (multiplying the off-diagonal P a P b + P b P a term) of the moment of inertia tensor was estimated from quantum chemical calculations. At first, we floated only the rotational constants A, B, and C and fixed V 3 , ρ, F , and D ab to the initial values. A reasonable rms deviation was obtained readily. Subsequently V 3 , ρ, F , D ab , and D bc (multiplying the off-diagonal P b P c + P c P b term) were floated.
We also took the centrifugal distortion constants Table  2. Molecular parameters in the principal axis system obtained using the xiamcode (Fit A and Fit A/E) and the belgi-C1 code (Fit belgi). For the belgi-C1 code, the molecular parameters in the rho axis system have been transformed into the principal axis system. Details on the conversion are given in Ref. 24. The calculated values were obtained at the MP2/6-311++G(d,p) level of theory. Watson's S reduction and the I r representation were used.
Discussion Using the programs xiam and belgi-C 1 , 92 torsional components of 3-pentyn-1-ol were fitted to a rms deviation of 20. 7 and 1. 5 kHz, respectively. As mentioned in section 2. 2, both programs have their individual advantages and disadvantages. belgi-C 1 takes the interaction between different torsional states into account and includes more higher order terms. Therefore, the belgi-C 1 fit provides a much lower rms deviation and has higher predictive power, especially for the E species. The program xiam on the other hand is well-suited for the assignment step, because it is fast, user-friendly, and yields parameters with physical meaning and small correlations. The rotational constants A, B, C deduced from the xiam and belgi-C 1 fits are quite consistent and in good agreement with the values calculated at the MP2/6-311++G(d,p) level of theory.
Calculations at different levels of theory yield quite good B and C rotational constants, but the calculated A rotational constant is much worse. Fit A in Tab. 2 indicates that for the A species, a semi-rigid rotor fit with centrifugal distortion correction is quite satisfactory even for a molecule with a barrier as low as 10 cm -1 like 3-pentyn-1-ol. The rms deviation of 2. 1 kHz is essentially the measurement accuracy. Of course the rotational constants from this fit do not represent the molecular structure, as can be seen by comparison of the quite different A rotational constants from Fit A and Fit A/E in Tab. 2. The barrier to internal rotation of the propynyl methyl group was fitted by the program xiam to 9. 4552(94) cm -1 , which is close to the barrier of 9. 099(68) cm -1 given by belgi-C 1.
7 kHz of the xiam fit were approximately 10 times the measurement accuracy, which is surprisingly good considering the very low propynyl methyl barrier of 3-pentyn-1-ol. Larger deviations have been found in other internal rotation problems with higher barriers treated by the program xiam, i. a. ethyl acetate (101. 606(23) cm -1 , 85. 3 kHz)  [24] , allyl acetate (98. 093(12) cm -1 , 54. 0 kHz)  [22]  and vinyl acetate (151. 492(34) cm -1 , 92. 3 kHz)  [25]. xiam appears to work quite well in this case, and we conclude that the deviation that is much larger than the measurement accuracy could be due to the limited amount of fit parameters rather than to an inadequacy of this program for low barriers. In comparison to the values found for other molecules containing the propynyl methyl group mentioned in the introduction (R = CD 3 , SiH 3 , CH 2 Cl, CH 2 OH, COF, COOH), the barrier in 3-pentyn-1-ol is closest to that of 1-chloro-2-butyne (10.
Acknowledgment We thank the  Land Nordrhein-Westfalen  for funds and the  IT Center of the RWTH Aachen University  for free computer time. K. E. thanks the  Université Paris-Est Créteil  for travel funding, which enabled him to work at  Paris  for two months. R. K. thanks the Graduate fund of the  RWTH Aachen University  for a Ph. D. fellowship.
Acknowledgments XB acknowledges  Asia Pacific Center for Theoretical Physics (APCTP)  in Pohang, Korea, for hospitality where part of this work was done during the program, "Duality and Novel Geometry in M-theory". JHP is grateful to the members of the  Laboratoire de Mathématiques et Physique Théorique (LMPT)  at the  Université Francois Rabelais de Tours, France , the  Mainz Institute for Theoretical Physics (MITP) ,  Germany , and  Tohoku University, Japan , for their warm hospitalities while writing this manuscript. We wish to thank the anonymous referee of JHEP for constructive suggestions, especially pointing out the absence of (2. 57) in the first submission. We also thank  S. Didenko  for pointing this out independently while the first version of the paper had been already submitted to JHEP.
III. EXPERIMENTAL DATA TAKING CONDITIONS The experimental data used for the analysis in this paper were obtained at three different collision energies and colliding particle configurations. Data taking conditions are explained in the subsections below, ordered according to the dates of the operation periods with the earliest first. A. p + p collisions at √ s = 7 TeV The data in p + p collisions at √ s = 7 TeV with a zerodegree beam crossing angle were obtained from May 15 to 22, 2010 (LHC Fills 1104, 1107, 1112, and 1117). The events that were recorded during a luminosity optimization scan and a calibration run were removed from the data sets for this analysis. The integrated luminosities for the data analysis reported in this paper were derived from the counting rate of the Front Counters  [27]  and were 2.
67 nb -1 (Arm1) and 2. 10 nb -1 (Arm2) after taking the live time efficiencies into account. Pileup interactions in the same bunch crossing may increase the multi-hit events that have more than one shower event in a single calorimeter, leading to a potential bias in the momentum distributions of π 0 s. The contamination of multi-hit events due to pileup interactions is estimated to be only 0. 2 % and therefore produces a negligible effect  [18]. Detailed discussions of background events from collisions between the beam and residual gas molecules in the beam tube can be found in a previous report  [25]. (= 1/2 × log((A p Z Pb )/(Z p A Pb )) where A and Z are the mass and atomic numbers, respectively  [28] ). Data used in this analysis were taken in two different fills; during LHC Fill 3478 on January 21, 2013 and during LHC Fill 3481 on January 21 and 22.
The integrated luminosity of the data was 0. 63 nb -1 after correcting for the live time efficiencies of the data acquisition systems  [29]. The trigger scheme was essentially identical to that used in p + p collisions at √ s = 7 TeV. The bunch spacing in p + Pb collisions (200 ns), which was smaller than the gate width for analog to digital conversion in the LHCf data acquisition system (500 ns) created the possibility of integrating two or at most three signal pulses from the pileup of successive p + Pb collisions. The probability for this to occur was estimated from the timing distribution for shower triggers and was less than 5 %. Contamination by successive collisions is not corrected for in this study, while it is considered in the beam-related systematic uncertainty. The contamination of multi-hit events due to pileup interactions is negligible (0.
4 %). It should be remarked that beam divergence causes a smeared beam spot at the TAN, leading to a bias in the measured momentum distributions. The effect of a non-zero beam spot size at the TAN was evaluated with MC simulations (see Ref. [19] ). This effect is taken into account in the final results reported for the p T and p z distributions. C. p + p collisions at √ s = 2. 76 TeV The data in p + p collisions at √ s = 2. 76 TeV were obtained with a 145 µrad beam crossing half angle and beam energy 1. 38 TeV for each proton. Data used in this analysis were taken during LHC Fill 3563 on February 13, 2013. The integrated luminosity for this data was 2. 36 nb -1 after correcting for the live time efficiencies of the data acquisition system  [30]. The trigger scheme, trigger efficiency, and contamination of multi-hit events were mostly the same as the p + Pb collision data at √ s NN = 5.
Energy reconstruction The photon energy is reconstructed using the measured energy deposited in the LHCf calorimeters. The charge information in each scintillation layer is first converted to a deposited energy by using the calibration coefficients obtained from the SPS electron test beam data taken below 200 GeV  [26]. The sum of the energy deposited in the 2nd to 13th scintillation layers is then converted to the primary photon energy using an empirical function. The coefficients of the function are determined from the response of the calorimeters to single photons using MC simulations. Corrections for shower leakage effects and the light-yield collection efficiency of the scintillation layers are carried out during the energy reconstruction process  [20]. In the case of multi-hit events, the reconstructed energy based on the measured energy deposited is split into two energies, primary and secondary.
V B, the phase spaces covered by Type-I and Type-II events are complementary. In particular, the inclusion of Type-II events extends the p T upper limit for analysis from 0. 6 GeV in the previous analyses to 1. 0 GeV. Figure  2  shows the reconstructed two-photon invariant mass (M γγ ) distributions of LHCf data in the rapidity range 8. 8 < y < 10. 8. The left and right panels of Fig. 2  show the distributions for Type-II events in the Arm2 small calorimeter and Arm2 large calorimeter respectively. The sharp peaks around 135 MeV are due to π 0 events. The distributions in Fig. 2  are based only on data from p + p collisions at √ s = 7 TeV during LHC Fill 1104. Similar invariant mass distributions are obtained from other fills and from Arm1. Kinematic quantities of the π 0 s (four-momenta, p T , p z and rapidity) are reconstructed by using the photon energies and incident positions measured by the LHCf calorimeters, and are used for producing the p T and p z distributions.
VIII. CONCLUSIONS The inclusive production of π 0 s was measured with the LHCf detector in p + p collisions at √ s = 2. 76 and 7 TeV and in p + Pb collisions at √ s NN = 5. 02 TeV. In p + p collisions at √ s = 7 TeV, differential cross sections as a function of p T and p z for the π 0 s were measured by two independent LHCf detectors, Arm1 and Arm2, with consistent results. Conversely, only the LHCf Arm2 detector was used in p + p collisions at √ s = 2. 76 TeV and in p + Pb collisions. In p + p collisions, qgsjet II-04 shows an overall agreement with LHCf data, while epos lhc distributions have a slightly harder behavior than LHCf data for p T > 0. 5 GeV. dpmjet 3. 06 and pythia 8. 185 have in general shown a harder momentum distributions and a poor agreement with LHCf data. In p + Pb collisions, dpmjet 3.
06 showed good agreement with LHCf data for -8. 8 > y lab > -10. 0 and p T < 0. 3 GeV, while qgsjet II-04 and epos lhc did better reproducing the LHCf data for p T > 0. 4 GeV than dpmjet 3. 06. The average values of p T , denoted p T , at y > 8. 8 in p + p collisions and at y lab > 8. 8 in p + Pb collisions were calculated using the LHCf p T distributions. The p T values obtained have been shown to be independent of the center-of-mass energy at the 10 % level. Tests of limiting fragmentation and Feynman scaling hypotheses using LHCf data in p + p collisions show that both hypotheses hold in the forward region at the 15 %-20 % level. The leading exponent α and the nuclear modification factor R pPb derived from LHCf data indicate a strong suppression of π 0 production from the nuclear target relative to that from the nucleon target.
ACKNOWLEDGMENTS The LHCf Collaboration acknowledges  CERN  staff and the  ATLAS Collaboration  for their essential contributions to the successful operation of LHCf. We thank  S. Ostapchenko  and  T. Pierog  for numerous discussions and for confirming the results of the MC simulations. We are grateful to  C. Baus ,  T. Pierog  and  R. Ulrich  for providing the crmc program codes and useful comments. This work has been partly supported by a  Grant-in-Aid for Scientific research  by  MEXT of Japan , a  Grant-in-Aid for a JSPS Postdoctoral Fellowship for Research Abroad , a  Grant-in-Aid for Nagoya University GCOE "QFPU"  from  MEXT , and  Istituto Nazionale di Fisica Nucleare (INFN)  in Italy. Part of this work was performed using the computer resources provided by the  Institute for the Cosmic-Ray Research (University of Tokyo ),  CERN , and  CNAF (INFN).
The Paris declination series Early declination data can be found in published catalogues or time series. For French catalogues, we can quote the Guillaume de Nautonier one  (Mandea and Mayaud, 2004)  and the one published by Guillaume Delisle around 1705 (with more than 10 000 measurements, which can be found in the Archives Nationales de Paris). Large efforts have been made to improve the existing database of historical observations, including the navigation measurements  (Jackson et al. , 2000; Jonkers et al. , 2003). Another category of sources is made of time series at a given location; for a mere handful of sites, series with more or less regular observations, spanning a few centuries, do exist. We can quote the time series of declination and sometimes inclination which have been compiled by  (Malin and Bullard, 1981) ,  Cafarella et al.
Hence, understanding its behaviour is crucial, even if long-term accurate predictions are not presently possible. It is inevitable that the geomagnetic field will continue to exhibit secular variation at all timescales, and its strength continues to change, producing changes in the structure and dynamics of the magnetosphere. One can expect a corresponding change in the geometry of the magnetosphere, which is controlled to first order by a balance between static pressure generated by the geomagnetic field and the dynamic pressure of the solar wind. The possible consequences for our planet are not yet completely acknowledged. Understanding how the future geomagnetic field varies is strongly dependent on how well we know the past magnetic field. And for this, geomagnetic data, represented by the declination curve, remain a unique dataset.
Charge asymmetry measurements are largely limited by the size of the available data sample, and therefore the larger dataset recorded by the ATLAS detector at √ s = 8 TeV allows for an improvement on the precision of the measurement from the √ s= 7 TeV dataset. At hadron colliders, t t production is predicted to be symmetric under the exchange of top quark and antiquark at leading order (LO). At NLO, the process q q → t tg develops an asymmetry in the top-quark rapidity distributions, due to interference between processes with initial-and final-state gluon emission. The interference between the Born and the NLO diagrams of the q q → t t process also produces an asymmetry. The qg → t tg production process is also asymmetric, but its contribution is much smaller than that from q q. In q q scattering processes in p p collisions at the Tevatron, the direction of the incoming quark almost always coincides with that of the proton, and this knowledge of the direction of the incoming quarks allows one to define a direct measurement of the forward-backward asymmetry, A FB  [8] [9] [10] [11].
Signal and background modelling Monte Carlo simulated samples are used to model the t t signal and all backgrounds except for those from multijet events, which are estimated from data. All simulated samples utilise Photos (version 2. 15)  [49]  to simulate photon radiation and Tauola (version 1. 20)  [50]  to simulate τ decays. They also include simultaneous pp interactions (pile-up), generated using Pythia 8. 1  [51] , and reweighted to the number of interactions per bunch crossing in data (on average 21 in 2012). Most of them are processed through a full Geant4  [52]  simulation of the detector response  [53] , and only the alternative t t samples described in Sect. 5. 1 are produced using the ATLAS fast simulation that employs parameterised showers in the calorimeters  [54]. Finally, the simulated events are reconstructed using the same software as the data.
4, the matrix-element prediction is used, otherwise the parton-shower prediction is used. The Z+jets background is normalised to its inclusive NNLO theoretical cross section  [74] , while data is used to normalise W+jets (see below for details). Further corrections are applied to Z+jets simulated events in order to better describe data in the preselected sample. A correction to the heavy-flavour fraction was derived to reproduce the relative rates of Z+2-jets events with zero and one b-tagged jets observed in data. In addition, the Z boson p T spectrum was compared between data and the simulation in Z+2jets events, and a reweighting function was derived in order to improve the modelling as described in Ref. [75]. The procedure to estimate the normalisation of the W+jets background in data exploits the difference in production cross section at the LHC between W + and W -, where the W + production cross section is higher than W -  [76].
This is due to the higher density of u quarks in protons with respect to d quarks, which causes more u d → W + to be produced than d ū → W -. The W boson charge asymmetry is then defined as the difference between the numbers of events with a single positive or negative lepton divided by the sum. The prediction for the W boson charge asymmetry in W+jets production is little affected by theoretical uncertainties and can be exploited, in combination with constraints from W + and W -data samples, to derive the correct overall normalisation for the MC sample prediction. The W boson charge asymmetry depends on the flavour composition of the sample, as the size and sign of the asymmetry varies for Wb b+jets, Wcc+jets, Wc+jets, and W+light-jets production. The in situ calibration procedure embedded in the unfolding and described in Sect.