dataesr/scientific-paragraphs-categorization huggingface dataset:
The red dashed lines show the best-fit model obtained from the cross-correlations of all tomographic bins with each frequency map separately. The best-fit model obtained from the coadded map marginally under-estimates the correlation although, as described in Section 4. 3 , the resulting model constraints are compatible within the statistical uncertainties. Similar results are found for the KiDS data, which we do not show here for brevity. of cosmic history. This reinforces the interpretation of the CIB as being sourced primarily by the re-emission of UV light absorbed by dust in star-forming galaxies. The solid black line in the same figure shows the best-fit star formation model found by  Maniyar et al. ( 2021 )  from the analysis of the CIB auto-correlation. Although our measurements are broadly compatible with this preferred model, the combination of C γ, CIB and b ρ SFR data predicts a higher SFRD at redshift ∼2.
Robustness tests We have quantified the robustness of the results presented in the previous sections to various choices made in our analysis, as well as various potential sources of systematic uncertainty. First, in order to test for the potential impact of systematics in the cosmic shear measurements, which would affect the DES and KiDS data sets differently, we have re-run MCMC chains using only one of the two data sets. The resulting constraints are shown in the left panel of Fig. 10  in red and blue for DES and KiDS, respectively, together with our fiducial combined constraints as black solid lines. We show results for the three parameters that our data are able to constrain: { m 0 , m z , η 0. 4 } , and the corresponding 1 σ bounds are listed in Table  2. The constraints found with either data set are compatible within ∼1 σ.
Ho we ver, we find that the KiDS data set has a preference for lower peak efficiency mass values. This is in line with the results from the cosmological analysis of the KiDS collaboration  (Asgari et al. 2021 ; Heymans et al. 2021 ) , where the weak lensing amplitude, parametrized by S 8 ≡ σ 8 √ m / 0. 3 , was found to be lower than the preferred Planck value at the ∼3 σ level. Since we use the best-fit Planck cosmology as fiducial in our analysis, a lower halo mass value (and hence a lower halo bias) is required in order to match the KiDS data. Cosmological constraints from weak lensing data are sensitive to systematics in the calibrated redshift distributions used to interpret them. Although we have made use of the official redshift distributions, and marginalized o v er systematic uncertainty Downloaded from https://academic.
AC K N OW L E D G E M E N T S The authors would like to thank  Martin Rey ,  Aprajita Verma , and  Ziang Yan  for useful discussions. BJ is supported by the  ENS Paris-Saclay. DA is supported by the  Science and Technology Facilities Council  through an  Ernest Rutherford Fellowship , grant reference  ST/P004474. CGG is supported by  European Research Council  Grant No:  693024  and the  Beecroft Trust. JRZ is supported by an  STFC doctoral  studentship. The authors made e xtensiv e use of computational resources at the  University of Oxford Department of Physics , funded by the  John Fell Oxford University Press Research Fund. The authors made e xtensiv e use of the numpy (Oliphant 2006 ; Van Der Walt, Colbert & Varoquaux 2011 ), scipy (Virtanen et al. 2020 ), astropy (Astropy Collaboration et al.
), B éthermin et al. ( 2015 ), B éthermin et al. ( 2017 ) for the Planck channels, made available in https: //github. com/abhimaniyar/halomodel cib tsz cibxtsz. Downloaded from https://academic. oup. com/mnras/article/520/1/583/6993092 by Oxford University user on 16 February 2023.
We show how the conic hull method, recently developed for the analytic and noniterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the ϵ-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in ϵ of MB representations. We upgrade the Mathematica package MBConicHulls. wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals.
MB integrals have not been an exception to this rule and powerful softwares are now available to ease their use  [9]. Although MB integrals have been widely studied, the problem of their analytic and numerical evaluation is still an active field of research, in particular when these integrals are multifold. In  [10] , an important progress has been achieved in this context, where the first systematic method of computing multifold Mellin-Barnes (MB) integrals analytically, in a noniterative way, has been presented, along with the powerful and user-friendly Mathematica package MBConicHulls. wl allowing applications of this technique in an automatic way. From this approach, one obtains series representations of multiple MB integrals by computing the latter using multidimensional residue theory.
MB integrals with straight contours generally have the sets of poles of some or all gamma functions of the numerator of their integrand split in subsets by the contours. This prevents from directly applying the method of  [10]  to the computation of such integrals: it is first necessary to perform some transformations of the MB integrand, as we show in the next section. Therefore, in order to deal with these cases, we have adapted the MBConicHulls. wl package (which can be downloaded from  [20] ) by adding an option in the code allowing the user to define straight contours of integration. Once the straight contours are specified by the user, the package performs the corresponding necessary transformations automatically and the results of the computation of the multifold MB integral can then be derived in an automatic way, as done with the original version of the package presented in  [10].
An alternative computational approach of multifold MB integrals with straight contours has been developed in  [21]  and automatized in the MBsums. m Mathematica package. It is based on an iterative approach: the MB integrals are evaluated sequentially. In contrast, our MBConicHulls. wl package computes multifold MB integrals in a noniterative way. As one will see, the pentagon example of Sec. III gives us the opportunity to compare these two different approaches and packages. The conclusions of our paper then follow.
One can see this fact by looking at Fig. 1  (left) where the red point ðc 1 ; c 2 Þ ¼ ð-1 7 ; -1 9 Þ is surrounded by the singular lines of the five gamma functions of the numerator of the MB integrand in a particular way, whose visualization we have tried to ease by giving an identical color to all the singular lines of a given gamma function. Indeed, it is clear from the picture that the point ð-1 7 ; -1 9 Þ is not located between two singular lines of the same color. This is what is meant when we say that, for each of the gamma functions in the numerator of the MB integrand, the corresponding set of poles is not split in subsets by the contours. Therefore, the result of Eq. (  3 ) can be directly checked using the original version of our MBConicHulls. wl Mathematica package (i. e. without explicitly fixing the contours), as the package is based on this assumption.
Doing this exercise, one obtains from the package that there are 8 different conic hulls associated to this MB integral and that these lead to 5 different series representations. The simplest of the latter is the first one, obtained using the MBResolve[,1] and EvaluateSeries[,1] commands of the package. It gives the well-known double series representation of F 1 and its overall factor written in Eq. (3) above. We now want to compute the MB integral of Eq. (  2 ) in the less trivial situation where c 1 ¼ 7  3 and c 2 ¼ -3 2. In this case, the first and fifth gamma functions of the numerator of the MB integrand in Eq. (  2 ) have arguments with negative real parts. Therefore, their sets of poles are now split by the contours, as can be seen in Fig. 1 (left) (the point ðc 1 ; c 2 Þ ¼ ð 7 3 ; -3 2 Þ is located between singular lines having the same color: two are yellow and two are green).
This allows us to write Eq. (  2 ) in the following equivalent way Iðx 1 ; x 2 Þ ¼ Z c 1 þi∞ c 1 -i∞ dz 1 2πi Z c 2 þi∞ c 2 -i∞ dz 2 2πi ð-x 1 Þ z 1 ð-x 2 Þ z 2 Γð3 -z 1 ÞΓð-2 þ z 1 Þ Γð1 þ z 1 Þ Γð-z 2 Þ Γð 3 7 þ z 1 þ z 2 ÞΓð 2 3 þ z 1 Þ Γð 1 2 þ z 1 þ z 2 Þ Γð-3 5 -z 2 ÞΓð 8 5 þ z 2 Þ Γð 2 5 -z 2 Þ ð7Þ where now all the gamma functions in the numerator have arguments with positive real parts for the chosen contours c 1 ¼ 7 3 and c 2 ¼ -3 2. As, for c 1 ¼ 7  3 and c 2 ¼ -3 2 , this MB integral is now satisfying the main constraint for the use of the original version of our MBConicHulls. wl package (see Fig. 1  (right) where the point ðc 1 ; c 2 Þ ¼ ð 7 3 ; -3 2 Þ is not anymore located between singular lines having the same color), it can be computed with the latter (i. e. without specifying the contours of integrations).
I 1 matches with the first term of Eq. (  8 ) once Eq. (  4 ) is used in the latter. The second set is ðz 1 ; z 2 Þ ¼ ð3 þ n 1 ; -3 5 Þ, whose associated residues give I 2 ¼ ð-x 1 Þ 3 ð-x 2 Þ -3 5 Γ 3 5 Γð which is equal to the second term of Eq. (  8 ). We have seen above, as a motivating example, how to treat a simple case of multifold MB integral with arbitrary straight contours, by hand. We now show how the same calculations can be performed in an automatic way using the new version of our MBConicHulls. wl package that we have implemented and which now allows the user to choose, if needed, arbitrary straight contours of integration for multifold MB integrals (details about some of the commands that are used in this calculations can be found in  [10] ). For this, we first load in a Mathematica notebook the package as follows: In  [1] :SetDirectory[NotebookDirectory[]]; In  [2] :=<<MBConicHulls.
wl; where we assume that the MBConicHulls. wl package is kept in the same directory as the notebook. The MultivariateResidues. m package  [28]  also has to be put in this directory since it will be called internally by MBConicHulls. wl. Then we input our MB integral with the above chosen contours, using the MBRep[] command, as follows: In ½3∶ MBRepOut ¼ MBRep½1; fz 1 → 7 3 ; z 2 → -3 2 g; f-z 1 ; -z 2 ; 3 7 þ z 1 þ z 2 ; 2 3 þ z 1 ; 3 5 þ z 2 gf 1 2 þ z 1 þ z 2 g; which gives as an output Straight contours∶ fReðz 1 Þ → 7 3 ; Reðz 2 Þ → -3 2 g.
III. THE ONE-LOOP MASSLESS PENTAGON IN D = 4 -2ϵ In this section, we apply our method to the computation of the dimensionally regularized massless one-loop pentagon integral in general kinematics and D ¼ 4 -2ϵ space-time dimensions. Indeed, in the MB representation approach, the ϵ-expansion of this object obtained from the Mathematica packages MBresolve. m [19]  or MB. m  [29]  requires the computation of a combination of eleven MB integrals (up to 4-fold) with straight contours, which gives us the opportunity to test the new features of our MBConicHulls. wl package in a nontrivial physical case. The results will be checked by direct numerical integration of the involved multifold MB integrals, as well as by computing the pentagon using FIESTA  [30]. We will also compare our results with those obtained from the package MBsums.
m. While the results discussed above for general ϵ are interesting (in particular because, to our knowledge, our MBConicHulls. wl package is the only available tool for such analytic calculations with nonstraight contours), in the rest of this section we will focus on first performing the ϵ-expansion of the MB integral using MBresolve. m (or MB. m). Indeed, this leads to the evaluation of several MB integrals with straight contours on which we can apply the techniques discussed earlier in this paper and demonstrate the efficiency of our approach in deriving analytic solutions. As shown in the Pentagon. nb notebook, the result of the ϵ-expansion given by the package MBresolve. m is a sum of a constant term, five 1-fold, three 2-fold, two 3-fold and one 4-fold MB integrals with straight contours, all of them not satisfying the constraint of positivity of the real part of the arguments of their gamma functions for the contours given by this package.
As a final (side) remark, we note that the first version of MBConicHulls. wl could not evaluate 1-fold MB integrals, therefore we upgraded our package so that the new version can now also evaluate this class of integrals (with straight or nonstraight contours). Hence, the checks mentioned above have been performed by including, in the automatic evaluation, the 1-fold MB integrals of the pentagon given in Eqs. (A3)-(A7).
IV. CONCLUSIONS In this work, we have shown how the computational method of  [10] , dedicated to the evaluation of multifold MB integrals, can be adapted to deal with the case of arbitrary straight contours of integration. We have detailed, on a 2-fold example, how this can be achieved by using simple transformations of the MB integrand and we have automated this procedure in a new version of the MBConicHulls. wl package (see  [20] ). This package has been tested on several examples, including the nontrivial computation of the ϵexpansion of the (resonant) one-loop massless pentagon in D ¼ 4 -2ϵ with unit propagator powers, which involves a combination of eleven MB integrals with straight contours (and up to 4-fold). An excellent agreement has been obtained when comparing the evaluation of the pentagon from the analytic computation of these integrals, derived with MBConicHulls.
wl, with the direct numerical evaluation of this Feynman integral with the help of FIESTA  [30]  (as well as with the numerical evaluation of each of the eleven MB integrals separately using MB. m  [29] ). We have also compared our results with those derived from MBsums. m  [21] , an alternative Mathematica package available for the analytic computation of MB integrals with straight contours. Although we got complete numerical agreement with the expressions derived from the latter, our approach gives more compact results, confirming the concluding remarks of  [10]. This is probably due to the fact that MBsums. m computes the multifold MB with straight contours iteratively, one integral after the other, whereas our package is based on a noniterative technique based on multidimensional residue theory.
A deeper analysis is needed to better understand the difference between the results obtained from these two methods, which is left for future investigations. We conclude this work by mentioning that, although our MBConicHulls. wl package is, to our knowledge, the unique tool that can treat the automatic analytic calculations of multifold MB integrals with both straight and nonstraight contours, 1 which is of considerable interest in the theory of MB integrals, as well as for the study of multivariable hypergeometric functions, their transformation theory, and for other domains where these integrals appear, there is still one progress that has to be achieved in order that our computational technique and package can be more widely used for phenomenological applications in particle physics. Indeed, in its present version MBConicHulls.
Acknowledgments The author is very grateful to  Chris Smeenk ,  Barry Madore  and  Wendy Freedman  for their helpful feedback. They would also like to thank the  Bonn History and Philosophy of Physics Seminar , the  APC colloquium (Paris 7) , and the audience of the "What can Astrophysics teach us about Reblicability?" workshop organized by the  CSH center (Bern)  for insightful discussions. Finally, the author would like to thank the two anonymous referees for their helpful feedback. This paper is based on work done while funded under the  John Templeton Foundation  grant: " New Directions in Philosophy of Cosmology " (grant number  61048 ).
YSO studies with these instruments will critically inform planet formation models and reveal temporal phenomena responsible for shadowing variability seen in stellar disks on large scales. Figure  2  shows the population of YSO targets in the nearby Taurus star-forming region and the Fig. 1  A sample uv-plane track available in a single night for the Herbig Ae/Be star AB Aurigae. (Note that this figure does not include overheads for collecting calibration data; realistically, this uv-coverage is attainable over the course of two nights. ) Utilizing all six CHARA telescopes, MIRC-X and MYSTIC can collect more simultaneous data at higher angular resolutions than any other currently available near-infrared interferometer facility. Fig. 2  Required instrumental sensitivity to observe YSO targets in the Taurus-Auriga molecular cloud region,  9  which drove the design specification of MYSTIC.
MYSTIC is fully motorized so that observers can operate the instrument entirely remotely. MIRC-X and MYSTIC use a shared software architecture and MYSTIC adopts nearly the same GUIs as those already familiar to users of MIRC-X; even subsystems with different hardware implementations between the two instruments, such as the fiber injection strategy, provide a uniform interface for the observer. Both instruments use a single, common GUI for data collection and high-level observing tasks. A continually running server logs the vacuum status, temperature, vibration, hard drive usage, and camera status of both instruments, and an automatic system health summary is generated every 12 hours and posted to an internal Slack channel. The real-time software allows either MIRC-X or MYSTIC to act as the "primary" instrument, controlling the CHARA delay line carts and maintaining phase delay tracking for itself, with the "secondary" instrument managing its own group delay via dedicated linear actuators within its optical train.
Tip/Tilt Correction Beam guidance for the CHARA Array is conducted at visible wavelengths, several reflections upstream of the instrument benches. Atmospheric differential refraction causes the beams to drift in the infrared over timescales of several minutes and over angular scales as high as 1 arcsec. 17  To maximize flux injection into the cold optic system, this tip/tilt error must be corrected as often as possible while minimizing operational overhead. MYSTIC employs a magnetic coil-driven faststeering mirror (Optics in Motion) for each beam, with a AE3 deg angular range and 0. 25 arcsec resolution, corresponding to a tip/tilt correction of ∼10 mas on-sky. This provides ample steering resolution compared to the ∼0. 5 arc sec diffraction limit of a 1-m telescope at K band. The fast-steering mirror (FSM) modules themselves are 1.
81 to 2. 51 μm. Figure  13  reports the measured throughput of this filter. The remaining two filters were provided by First Light and prevent photons with wavelengths exceeding 2. 45 μm from reaching the detector. The instrument operational software was designed from its conception to provide the same interface for controlling MIRC-X and MYSTIC. Both instruments operate on a client/server model, allowing any number of GUIs, either on-site or remotely, to connect to servers running at CHARA. Although the MYSTIC camera interface and data acquisition is handled by a separate computer to that of MIRC-X, many other servers of the MIRC-X instrument are extended to now include MYSTIC subsystems in a single GUI. For example, the stepper motor server communicates with all DC stepper motors on the entire MIRC-X/MYSTIC table and the vacuum server now monitors the internal temperatures and pressures for both C-RED One cameras and the MYSTIC dewar.
3. 5-52. The data were separated into 5 min epochs and fit to a geometric model composed of two uniform disks with variable diameters, fluxes, and separation. Figure  15  shows a sample of these data points and the subsequent model fits. We find excellent agreement between the model and data closure phases. We find that the data reduction pipeline does not well calibrate the square visibility data at the shortest baseline, which is set to the lowest spatial frequency in the MYSTIC AIO combiner and includes crosstalk from the DC spike. These discrepancies will be improved in the near future with on-going developments to the data reduction pipeline. Fig. 14  Simplified overview of the various software servers in MIRC-X/MYSTIC and their integration with other servers at CHARA. We note that while many servers related to the operation of hardware components unique to MIRC-X and MYSTIC run on their respective instrument computer, some additional servers related to shared hardware or the system as a whole operate on the MIRC-X computer (see left side of red box).
The beams are then tracked with a C-RED 2 camera from First Light, operating at 600 Hz, and the beam drift is corrected for by the CHARA lab-AO tip/tilt system. A pupil viewing lens is also made available via a small filter wheel prior to the camera. We are currently working to optimize the beam tracking software, though we optimistically anticipate a factorof-two improvement in total photon coupling into the MYSTIC fibers once this system is operational. Pending additional sources of funding for the instrument, we could replace the C-RED One camera for a newer version with a lower overall background. 23  MIRC-X and MYSTIC feature the first two commercially produced SAPHIRA detector-based cameras, and newer units resolve some early electronic tuning and isolation issues present in our cameras.
Acknowledgments MYSTIC is funded by the  USA National Science Foundation Advanced Technologies and Instrumentation Program  (PI: Monnier, Grant No. NSF-ATI 1506540 ). MIRC-X received funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 Research and Innovation Program  (Grant No. 639889 ). Additional funding for  MIRC -X and MYSTIC was received through the following grants:  NASA -XRP  (Grant No. NNX16AD43G ),  NSF-AST  (Grant No. 1909165 ), and  NASA-MSGC  (Grant No. NNX15AJ20H ). B. R. S. and J. D. M. would like to acknowledge support by  FINESST  ( NASA  Grant No. 80NSSC19K1530 ). S. K. would also like to acknowledge support from an  ERC Starting Grant  (Grant No. 639889 ),  ERC Consolidator Grant  (Grant No. 101003096 ), and  STFC   Consolidated Grant  (Grant No.
Now, we note below the compelling reasons for applying a DD-based solver for COVID modelling. • Like their ODE-based counterparts, PDE-based compartmental models can be very fine grained, accounting for accurate dynamics among populations (see Appendix C). This can be further extended to consider different age groups, socio-economic status, vaccination status, and comorbidity (e. g. ,  [1] ). We note that corresponding spatial and temporal data for these stratifications could be obtained from private healthcare databases (e. g. ,  [21] ). These highly complex coupled models can be solved efficiently by using an iterative solver equipped with parallel preconditioners offered by DD methods. • The application of the above mentioned five-compartment model with finer spatial and temporal discretizations covering large geographical areas (including many public health units) involves system sizes above millions as well as the associated computational cost.