dataesr/scientific-paragraphs-categorization huggingface dataset:
Data reduction We have PSF images on the target direction (i. e. the central star) taken using the IR camera. In parallel to the IR images, the realtime slopes of all WFSs (off-axis and TS) plus DM voltage data are saved to determine the atmospheric parameters and evaluate the error budget. We record two types of synchronous data for all the WFSs: engaged slopes recorded while the MOAO loop is engaged. It stands for the open loop sensing on the 3 off-axis WFS (used to compute the correction on-axis) and residual slopes seen by the TS. disengaged slopes recorded while the MOAO loop is NOT running. DM is flattened allowing measurements of the turbulence in open loop on each of the 4 NGS WFS directions. We now present the procedure used to reconstruct different terms in the error budget of CANARY from these data.
BW The bandwidth error is computed using a set of recorded engaged-loop WFS data using the off-axis WFS with the highest signal-to-noise ratio (in open loop). The principle is to numerically filter this real data set in order to reproduce frame-by-frame the loop behaviour in engaged mode, then derive the error from the simulated residuals. The method ensures the computation of a bandwidth error term that corresponds to the precise recorded turbulence conditions. A first step computes the open loop controller filtering (see Sect. 3. 4) of the slope measurements: S t = (1 -g) S t-1 + g S t. (24) Then a second step simulates the application of the DM command, which acts as a zero-order hold, and that occurs partly during the integration of the subsequent frame t + 1, and partly during the frame after that at t + 2.
Figures  8, 9  and 10 present the C 2 n (h) measured during the on-sky observations (left) and post-processed (right) using these sets of disengaged slopes. The turbulence profiles have not been rescaled by the airmass to maintain the profile as it was observed in the line of sight of CANARY. At 23 h 59 m (Fig. 8 ), we measured more than 95% of the turbulence below 1 340 m (best resolution achievable on asterism  A#47, see also Table  2 ) during the on-sky operations. A weak layer of 5% was also detected at ≈ 3 000 m. After post processing the data with a higher vertical resolution sampling, we measured the ground layer contribution at 91% and one high layer at  ≈13 500 m of 9% (right). On the 3 h 14 m dataset (Fig. 9 ), we measured during the observations a ground layer contribution at 77% (74% post processed), a 14% layer contribution at 1 080 m (11% post processed) and 1 layer at 10% at ≈4 000 m (spread into 3 layers of 10% contribution with the new 15 layer profile).
We superimpose the expected (D/r 0 ) 5/6 law showing the overall behavior of this error term. This trend is globally verified by our estimates of this error. One can see the improvement of the L&A tomographic reconstruction versus the GLAO mode. The large scatter of the MOAO results is due to the large number of con- figurations tested during the night. Many MOAO datasets were taken when system parameters were not optimal and the observing conditions were also evolving. Figures 13 represent the statistics of Zernike expansion coefficients on the data set of disengaged slopes at 03h14. We compute the Zernike expansion of the uncorrected turbulence (black/diamonds), the GLAO reconstruction (black/square) MOAO correction with 3 reconstructed layers (black/circle) and 15 reconstructed layers (empty/cross), The uncorrected wavefront error is measured at a level of 1 139 nm rms.
One clearly sees the improvement for all modes using the MOAO reconstructor with 3 layers (tomographic error reduced by 215nm rms). Similarly Fig. 14  illustrates the quadratic difference between the MOAO reconstruction with 3 layers (black/circles) and MOAO reconstruction with 15 layers (black/triangles). For this dataset the total improvement by reconstructing 15 layers instead of 3 could be reduced by 84nm rms. Table  3  summarizes all the numbers for 3 data sets of disengaged slopes respectively at 23h59, 3h14, and 6h02 and highlights the quadratic differences between error terms. It shows that the 15 layer profile increases the performance of the tomographic reconstruction compared to the 3 layer reconstruction by an amount ranging between 80 and 60 nm rms. This comparison reveals the impact of the model error in the tomography error term, even in our observing conditions with a dominant ground layer.
Simulation parameters We used the end to end adaptive optics simulation program called Yorick Adaptive Optics (YAO) written by  (Rigaut 2011)  to produce series of engaged and disengaged data sets of slopes for each of the 4 WFS (including TS). These data sets mimic the data that were acquired on-sky with CANARY. The YAO code was modified to perform a simulated MOAO correction, in particular using the tomographic estimator M ct (see  Sect. 3. 3 ) and the open loop integrator scheme as described in Sect. 3. 4. Finally, the 2 sets of data (engaged and disengaged slopes) produced by YAO are used as inputs to our on-sky data reduction software. We emphasize that we used the same data pipeline software to compute both the on-sky error budget and the simulated error budget in order to avoid any bias in the data reduction.
The variance of the noise on the simulation dataset is therefore identical to the real noise encountered on-sky, with both measured as described in 4. 3. 4. The sampling frequency is simulated at 150 Hz. In order to simulate a loop latency of 1. 5 frames, we ran two numerical simulations to compute the bandwidth error at 1 and 2 frames delay (YAO only simulates latencies of an integer number of frames) and linearly interpolated the bandwidth error at 1. 5 frames. We simulated 7 000 iterations (≈ 45 seconds at 150 Hz) to produce typical data sets on all the WFS. The estimation of the average wind speed was deduced from the on-sky datasets by measuring the FWHM of the temporal autocorrelation of disengaged slopes data, and we reproduced the same in the simulation by tuning the speed. The simulated wind speeds were set respectively to 6, 6 and 8 m s -1 as measured from the datasets at 0 h 10 m , 3 h 24 m and 6 h 07 m.
4. 3. 1). Finally, the estimated total error budget for the IR camera (σ ErrIR ) gives 297, 419 and 357 nm rms. Converting these to Strehl ratio using the approximate formula SR ≈ exp(-(2πσ ErrIR /λ) 2 ) ( 36 ) at λ = 1 530 nm, we find the estimated SR: 22. 6%, 5. 2% and 11. 7%. Real IR images were recorded a few tens of seconds from the dataset of slopes. We measure on these images SR of 20. 1%, 10. 3% and 16. 4% (±2%) respectively. The observed discrepancy is mainly due to the pessimistic estimation of the SR using the exponential formula from the error budget. This formula gives much better estimation when SR is higher, typically larger than 30%. We will come back to this point after the presentation of the simulated error budget.
Conclusion CANARY is a single channel MOAO demonstrator installed at the William Herschel Telescope. It obtained the first on-sky MOAO compensated images in September 2010. In this paper, we detail the calibration procedures used in CANARY, in particular to compute the optimized tomographic estimator required in MOAO and its software implementation. We present a method to process the slope data recorded on-sky and apply this to data taken during the night of the 27th of September 2010. The presence of the Truth Sensor allowed us to build a full error budget for the instrument. We evaluate 9 error terms including the tomographic and the open loop error, which are new terms introduced by the MOAO control scheme. The tomographic error is estimated from synchronous disengaged slopes while the open loop error also requires data taken when the MOAO loop is engaged.
We have also computed other classical AO error terms like noise, aliasing, bandwidth, fitting and NCPA. For the error budget, we distinguish two terms in the aliasing due to both the ground and the high altitude layer contributions. We check and successfully compare the measured on-sky error budget with numerical simulations for 3 datasets differing in guide star configuration, magnitudes and atmospheric conditions. The conclusion is encouraging, with the open-loop term, although larger than expected, being small compared to the other terms, and the to-mographic term behaving as expected from simulation. But we identify on-sky an additional term linked to the residual quasistatic field aberrations found to be of the order of the open-loop term. The turbulence profile derived from the instrument data is presented and used in the tomographic optimization.
Acknowledgments This work was supported by  Agence Nationale de la Recherche  ( ANR ) program  06-BLAN-0191 ,  CNRS / INSU, Observatoire de Paris , and  Université Paris Diderot Paris 7 in France ,  Science and Technology Facilities Council, University of Durham  and the  Isaac Newton Group of telescopes in UK  and  European Commission   Framework Programme 7 (E-ELT Preparation Infrastructure  Grant  211257  and  OPTICON Research Infrastructures Grant 226604 ).
Many research topics in the fields of condensed matter and the life sciences are based on small-angle X-ray and neutron scattering techniques. With the current rapid progress in source brilliance and detector technology, high data fluxes of ever-increasing quality are produced. In order to exploit such a huge quantity of data and richness of information, wider and more sophisticated approaches to data analysis are needed. Presented here is GENFIT, a new software tool able to fit small-angle scattering data of randomly oriented macromolecular or nanosized systems according to a wide list of models, including form and structure factors. Batches of curves can be analysed simultaneously in terms of common fitting parameters or by expressing the model parameters via physical or phenomenological link functions.
(2012). For model fitting and in-depth analysis, a large range of software packages designed to analyse both SAXS and small-angle neutron scattering (SANS) data are available to the scientific community at present. A non-exhaustive list of them can be found at the SAS Portal (http://smallangle. org), where the respective application areas are identified. Among the main references in the area of SAS data from biological macromolecules there is ATSAS, which is a very extensive and sophisticated set of programs offering the user a rich choice of different shape determination methods as well as various modelling capabilities  (Petoukhov et al. , 2012; Graewert & Svergun, 2013). Besides a number of programs that have been designed for specific aims, there are also multi-purpose program tools, which in general encompass a wide list of models in direct space that can be applied to analyse SAS curves.
In the light of this and of the user's quest for accurate and reliable modelling abilities, we have developed the program GENFIT, targeting the following list of requirements: (a) Fitting large experimental data sets by the selection of one or more models that can be suitably combined from a repository of over 30 models, ranging from simple asymptotic behaviours (e. g. Guinier and Porod laws) up to complex geometric architectures or entirely atomic structures. (b) Providing form-and structure-factor based models that take into account interactions between particles in solution. (c) Supplying a model-fitting approach which intrinsically allows for polydisperse distributions of particles of arbitrary form having an internal structure. (d) Featuring the ability to relate the parameters of the theoretical models to experimental chemical-physical conditions (temperature, pressure, concentration, pH, ionic strength etc.
), e. g. by means of userdefined link-functions. (e) Generating theoretical SAS curves based on model assumptions or on knowledge of the species in solution, with the aim of predicting the optimum experimental conditions to be explored in a prospective SAS experiment. ( f ) Offering an open-source distribution mechanism which enables end users to contribute their own models to the GENFIT scope via a simple plug-in architecture. Today, more than ever, the visibility and testability of the internal structure of a software package is required by the scientific community in a common effort towards transparency of process with the public bodies representing tax payers across different countries.
Features of GENFIT GENFIT is written in Fortran and a simple-to-use and modular graphical user interface (GUI) has been added. The GENFIT GUI has been designed so as to evolve at the same pace as the related code and to enable the efficient use of the program, even online during a campaign of measurements with generally little time availability. In the following sections we provide an overview of the main features of GENFIT, making use of sample data recorded mainly at European large-scale facilities.
Input SAS curves and the GENFIT GUI The input data for GENFIT are experimental one-dimensional SAS curves, usually taken to be the macroscopic differential scattering cross section, indicated here as I exp (q), as a function of the modulus of the momentum transfer, q = (4/)sin , where is half the scattering angle and is the wavelength of the incident radiation. If the SAS experiment has been correctly calibrated, I exp (q) is given in absolute units, usually cm À1. However, data in arbitrary units are also treated by GENFIT. An experimental SAS curve is normally written in a three-column ASCII file, with q, I exp (q) and its standard deviation (q) in the first, second and third column, respectively. Numbers can be expressed in any format. If standard deviations are not provided in the data file, they can be generated using a simple power-law expression, (q) = k[I exp  (q) ].
Global fit One of the distinctive features of GENFIT is the ability to analyse more than one experimental SAS curve at a time, a way of proceeding indicated by the term 'global fit'. This task is accomplished by minimizing the standard reduced 2 function, defined for a set of N c experimental SAS curves I exp,c (q) as 2 ¼ 1 N c X N c c¼1 1 N q;c X N q;c i¼1 I exp;c ðq i Þ À Î I c ðq i Þ c ðq i Þ " # 2 ; ð1Þ where N q,c is the number of q points on curve c and Î I c ðqÞ is the fitted SAS curve as determined by GENFIT. In order to make allowance for data in arbitrary units and/or the possible presence of a flat scattering signal (for example the incoherent background of a neutron scattering experiment), the fitted SAS curve is written as Î I c ðqÞ = c I c (q) + B c , where I c (q) is the model SAS curve expressed in absolute units.
The scaling factor c and the background B c can be fixed by the user or are easily calculated using standard linear leastsquares minimization  (Press et al. , 1994). The main window of the GENFIT GUI. The top, middle and bottom sections display information on the scattering curves, the models applied to analyse the scattering curves and their respective parameters. Detailed information regarding each section is supplied by the user by activating the buttons on the right-hand side. Commands in the menu bar allow opening a GENFIT (File) input file, selecting the 2 minimization methods (Edit), executing the calculation and exploring the results (Run), and managing the settings parameters of the software (Settings).
Model scattering curve The general object of GENFIT is to depict the SAS curve, I c (q), intended to fit the experimental curve c, as a linear combination of M c models: I c ðqÞ ¼ P M c m¼1 w c;m I c;m ðqÞ; ð2Þ where w c,m is the weight of the mth model curve, I c,m (q), that contributes to the best fit. This model depends typically on a set of P m unknown parameters, here indicated as X c,m,1 , X c,m,2 ,. , X c,m,P m and called 'model parameters'. They are, in general, structural parameters, such as thickness, scattering length density, electric charge and so on. Each model parameter can be associated with a flag which determines whether the parameter is fixed or fitted. Moreover, the flag indicates whether the model parameter is linked to one or more experimental SAS curves, or is rather involved in a physical or phenomenological function.
The various flag utilities are described in xx2. 6-2. 8. Weights and model parameters are estimated by minimizing the 2 distribution [equation (  1 )]. The GUI assists the user in associating with each of the experimental curves the M c models, which can be selected from a list including more than 30 items and which is continuously upgraded. Notice that in equation (  2 ) the index m is a counter for the number of models used to analyse curve c. This number is different from the number that GENFIT uses to label a model within the list of all the models that the program can handle (see xS1 in the supporting information 1  ).
PDB-based models Several models included in GENFIT are able to calculate the form factors of atomic structures on the basis of Protein Data Bank (PDB) files  (Berman et al. , 2000) , taking into account the contribution of the solvation shell around the macromolecule. Some models make use of a Monte Carlo approach  (Mariani et al. , 2000; Spinozzi et al. , 2000 Spinozzi et al. , , 2002)) , whereas others are based on the recently developed SASMOL method  (Ortore et al. , 2009 (Ortore et al. , , 2011)) , which uses the spherical harmonic expansion of the scattering amplitudes, similar to the widely known CRYSOL software  (Svergun et al. , 1995). The main idea of SASMOL is to embed the macromolecule in a 'tetrahedrical close-packed' lattice and assign the lattice positions in contact with the atoms of the macromolecule to hydration molecules.
Basic calculation of parameters GENFIT prompts the user to specify how to handle both the weights, w c,m , and the model parameters, X c,m,k. The way this is done in GENFIT is by setting a starting value of a parameter together with its lower and upper values, hence three fields, called Starting, Lower and Upper, are correspondingly filled (Fig. 2 ). It may be that some of the parameters are known from a priori information on the system. In order to make provision for such cases, each parameter within GENFIT is associated with a Flag: if Flag = 0 the parameter is considered fixed to the value indicated in the Starting field, whereas if Flag = 1 the parameter is optimized in the range between Lower and Upper values. If the same model is used to fit more than one curve within the set of N c SAS curves, some of its parameters can be defined by the user as 'common parameters', the values of which should be shared by all the curves I c,m (q) adopting model.
Calculation of parameters through link functions The user might see good reasons to apply some constraints to the weights or model parameters. As an example, in the case of a mixture of different oligomers, the weights of the models describing each oligomer should be linked to the nominal concentration of the sample, which the user probably knows. Another example could be the case of curves recorded at different temperatures: the user could try to check whether the fitting parameters are linear or exponential functions of temperature. On the other hand, one would possibly like to combine structural models able to fit the SAS curves with chemical-physical models suitable for describing, for example, the dependence of some species on concentration, temperature, pressure and so on. In order to encompass such complex and interesting cases, GENFIT allows the user to define a parameter (w c,m or X c,m,k ) through a 'link function'.
This option is activated by entering Flag = 4 and writing in the field named Link Function the expression that GENFIT will use to calculate the parameter. In general, expressions are written as functions of coefficients that are classified into two groups within GENFIT. Coefficients that characterize each experimental SAS curve (such as temperature, pressure, concentration etc. ) are referred to as 'p-coefficients' and are not adjustable. All other coefficients can in principle be adjusted and are called 'f-coefficients'. A link function can contain both p-and f-coefficients. For instance, if the user has defined among the p-coefficients the temperature as temp and wishes to impose linear behaviour on a model parameter X c,m,k versus temperature, the Link Function associated with X c,m,k can be written as a+b*temp.
GENFIT recognizes that a and b are fcoefficients associated with the c curve to be fitted. Through Flag = 5 a more general case can be introduced: all the f-coefficients (a and b in the example above) that GENFIT finds in the link function are considered 'common parameters' of the set of N c curves. The parameters of the polydispersity models introduced in x2. 7 can also be expressed using link functions, which can include either p-or f-coefficients or both. The polydispersity option is selected either by Flag = 8, indicating that all the f-coefficients that appear in the link function pertain to curve c, or by Flag = 9, allowing the whole set of f-coefficients to be common to all the N c SAS curves.
, 1999; Spinozzi et al. , 2003; Ortore et al. , 2005). Using GENFIT, such relations may be transformed to link functions that can be used during the SAS curve-fitting procedures to converge to a stable and well defined result. As the understanding of protein aggregation is a central issue in different fields, from heterologous protein production in biotechnology to amyloid aggregation in many neurodegenerative and systemic diseases, we focus on an example concerning protein oligomerization and present the case of -lactoglobulin (BLG), an 18 400 Da protein belonging to the lipocaline family. This protein can be found in solution in both monomeric and dimeric states and it is known that the association behaviour can be influenced by protein concentration, ionic strength  (Schaink & Smit, 2000; Baldini et al.
, 1999; Spinozzi et al. , 2002) , temperature and pressure  (Valente-Mesquita et al. , 1998; Ortore et al. , 2005). This BLG example shows how GENFIT can be exploited to derive thermodynamic parameters from a batch of SAS curves. To this end, a number of SAXS curves were generated for increasing BLG concentrations from 2 to 10 g l À1. As the BLG dissociation free energy at ambient pressure and temperature, pH 2. 3 and an ionic strength of 100 mM is known (ÁG dis = 8 k B T, k B being the Boltzmann constant and T the temperature;  Baldini et al. , 1999) , SAXS curves were simulated considering the actual fraction of monomers and dimers of BLG in solution and their form factors, as derived by applying to the corresponding PDB coordinate files the spherical harmonics approach of the SASMOL tool, described in x2.
Unfolding processes Protein unfolding is another scientific issue widely investigated by SAXS/SANS techniques. In fact, even the radius of gyration obtained by Guinier analysis  (Guinier & Fournet, 1955)  of a SAS experimental curve readily provides an initial and meaningful indication of protein compactness, and hence of its folding/unfolding state. However, a deeper analysis of the unfolding process, which proceeds under the control of denaturing agents such as temperature, pressure, pH or concentration of cosolvents, should take into account the equilibrium between folded and unfolded species present in solution. As in the previous case, the application of GENFIT link functions and the extended use of common fitting parameters allows the determination of crucial factors. (Left) SAXS simulated curves obtained at increasing BLG concentration in solution (from bottom to top, open squares, circles, up-triangles, down-triangles and diamonds correspond to 2, 4, 6, 8 and 10 g l À1 , respectively) and their best fits obtained with GENFIT (solid red lines).