dataesr/scientific-paragraphs-categorization huggingface dataset:
This has been shown to be a good assumption in simulations of galaxy-sized halos  [54, 86]. Given the selfsimilar nature of collapse of ΛCDM halos, we extrapolate this conclusion to halos from our CSIBORG ensemble. We assume that the distribution of masses is a power law dP M dM ∝ M -α M ; ð22Þ in the range M ∈ ½10 -6 M ⊙ ; 10 -2 M h for a halo of mass M h , where α M ¼ 1. 9 (see Sec. 2. 3 of  [87]  and references therein). Again, the values are motivated by numerical simulations of Milky Way sized halos, which we extrapolate to bigger halos present in our forward model. Besides modeling the uncertainty due to the spatial and mass distribution of substructure, the CLUMPY package also allows us to include the uncertainty in the mass-concentration relation. For the substructure component, we consider two cases for the concentration distribution.
We use the EMCEE sampler  [93]  and terminate the chain when the estimate of the autocorrelation length changes by less than 1 percent per iteration and the chain is at least 100 autocorrelation lengths long in all of the parameters. We apply a Monte Carlo estimate to the likelihood of the CSIBORG samples, such that the one-dimensional posterior for the amplitude A X i (X being J or D) is LðA X i jD i Þ ¼ 1 N sim X j Z dfA t i gdA Y i LðA J i ; A D i ; fA t i g; jjD i Þ; ð48Þ where Y ¼ J if X ¼ D and vice versa. In practice, we compute the average over CSIBORG realizations by first fitting the one-dimensional posteriors LðA X i jD i ; jÞ with a spline using the GETDIST package  [94]  and then computing the mean of the resulting functions. This is equivalent to concatenating the Markov chains if each chain had the same length.
Constraining DM parameters We now have a posterior, LðA J i jD i Þ, describing the gamma-ray spectrum from sources that have the same spatial distribution as the J factor. We wish to fit this spectrum to a model, f i ðθÞ, for these sources and infer the model parameters θ. We assume that our model is deterministic, such that LðA J i jθÞ ¼ δðA J i -f i ðθÞÞ; ð49Þ and therefore we obtain the likelihood for the observed gamma-ray sky by incorporating Eq. (  48 ), LðD i jθÞ ¼ Z dA J i LðD i jA J i ÞLðA J i jθÞ ¼ Z dA J i LðA J i jD i ÞZðD i Þ PðA J i Þ δðA J i -f i ðθÞÞ: ð50Þ We assume that all energy bins are independent such that the likelihood of θ given the full dataset D is LðDjθÞ ¼ Y i LðD i jθÞ; ð51Þ and so with a final application of Bayes' identity we obtain the posterior for our model parameters LðθjDÞ ¼ LðDjθÞPðθÞ ZðDÞ : ð52Þ If f i ðθÞ comprises exclusively DM annihilation, then, at fixed DM mass and annihilation channel, the transformation from the posterior distribution of A J i to that of <σv> is trivial.
Another source of systematics due to substructure modeling might be driven by the breakdown of our assumption that the uncertainty in the J factor is Gaussian. Namely, as the considered mass of the clump grows, the total number of such clumps within the host halo decreases. Therefore, it is expected that at some point we transition from the Gaussian into a Poisson regime  [107]. Furthermore, it is not obvious that the contribution to the J factor from these more massive clumps will not outshine the cumulative contribution of the lower-mass clumps. To check for this, we use the -H5 module of the CLUMPY package to explicitly draw substructure realizations for a typical halo (M h ≈ 5 × 10 13 M ⊙ ) from the CSIBORG simulations. We modify Eq. (  35 ) such that hJ p i ¼ hJ cont;p ðM th Þi þ hJ drawn;p ðM th Þi ð56Þ and hJ cont;p ðM th Þi ¼ J sm;p þ hJ subs;p ðM th Þi þ hJ cross;p ðM th Þi; ð57Þ where we introduce hJ drawn;p ðM th Þi ¼ 1 N ds X N ds i J drawn;pi ðM th Þ; ð58Þ with N ds being the total number of explicit realizations of the clumps with a mass above a given mass threshold, M th.
VII. CONCLUSIONS Indirect detection of DM annihilation or decay through gamma-ray emission has previously typically involved inference from a small number of nearby, DM rich objects (the Milky Way, dwarf spheroidals in the Local Group or local groups and clusters) or by cross-correlating the gamma-ray background with other catalogs. Instead, in this work we utilize the CSIBORG suite of constrained simulations of the local 155h -1 Mpc to forward model the predicted gamma-ray sky for s-wave DM annihilation or decay due to the large-scale structure. We marginalize over uncertainties in the density field reconstruction, unresolved substructure, and non-DM contributions to the signal, and compare to data from Fermi-LAT via a MCMC algorithm. We rule out the thermal relic cross section at 95% confidence for DM particles of mass m χ ≲ 7 GeV=c 2 whose annihilation produces gluons or quarks less massive than the bottom quark.
As with analyses on smaller scales, there is some sensitivity to how one parametrizes the halo density profiles, and thus future analysis should include procedures to (probabilistically) model baryonic effects on the DM density profile. Data availability This Letter required modifications to the CLUMPY package in order to model substructure in extragalactic halos and process all the halos from CSIBORG at once. These modifications will be included in the next CLUMPY release. Our J and D factor maps may be useful for other indirect detection analyses of current or future data, so we will make these maps available upon publication  [152].
ACKNOWLEDGMENTS We thank  David Alonso ,  Eric Baxter ,  Céline Combet ,  Sten Delos ,  Julien Devriendt ,  Seth Digel ,  Scott Dodelson ,  Pedro Ferreira ,  Moritz Hütten ,  Harley Katz ,  Eiichiro Komatsu ,  David Maurin ,  Samuel McDermott , Lance.
As a result, by design, multivariate nonlinear CIMs (e. g. , PCMCI-CMI) would seem best suited to retrieving effective hydrological connections: they account for nonlinear dependencies and deal with confounding effects, e. g. , seasonality or the forcing of precipitation and evapotranspiration, through a multivariate framework. Following a theoretical introduction of the different CIMs, we test this assertion and get hands-on the CIMs using a toy model to conduct a virtual experiment reproducing a simple case of two parallel hydrological reservoirs forced by the same effective precipitation. In a real case study, we apply the CIMs to data acquired at the Lorette cave (Rochefort, southern Belgium). This dataset includes rainfall and potential evapotranspiration data, electrical resistivity time series patterns from the subsurface obtained from a geophysical monitoring experiment using timelapse electrical resistivity tomography (ERT)  (Watlet et al.
PCMCI: the ParCorr and CMI tests PCMCI is based on a stochastic framework testing conditional independence  (Spirtes et al. , 2000; Pearl, 2009) , adapted to account for highly time-dependent time series and implemented in the Tigramite Python package  (Runge et al. , 2019b). It follows a two-step procedure: PC and MCI. The PC abbreviation refers to its authors Peter Spirtes and D. Delforge et al. :  Detecting hydrological connectivity using causal inference from time series Clark Glymour (1991). PCMCI's grounding lies in a multivariate definition of the Wiener-Granger causality  (Wiener, 1956; Granger, 1969) , here referred to as MCI  (Runge et al. , 2019b, a) : a lagged variable X t-d is said to be a cause of Y t if X t-d has a significant dependence or predictive power over Y t while removing the effect of all other potential variables influencing X t-d or Y t , except X t-d.
These potential variables are called parents and are symbolized by P(X t-d ) and P(Y t ) {X t-d }. Conditioning the analysis on the parents allows one to deal with confounding variables. Parents are subset variables found in the dataset that includes delayed variables up to 2d max , as P(X t-d ) has to be estimated beyond the maximum causal lag d max. Parents are estimated during the conditions' selection step performed with PC. The resulting estimates are noted as P(X t-d ) and P(Y t ) {X t-d }. PC removes irrelevant conditions from the full set of variables and delays by iterative independence testing until there is no more condition to drop out (see  Runge et al. , 2019b). The resulting sizes of the parents' set are controlled by α PC , a liberal parameter varying between 0 and 1, with the latter being the less restrictive case that includes all possible variables.
P1, P2, and P3 (Fig. 1c ) are daily means of the percolation rate. An ERT profile was installed to investigate the hydrology of the subsurface and potential connections above the cave  (Watlet et al. , 2018b). ERT is a geophysical monitoring tool to study various types of hydrological processes (see  Slater and Binley, 2021, and references therein). The ERT profile is not flat and starts from the depression of a sinkhole where the entrance to the cave is located (ERT, Fig. 1a ). The ERT experiment allowed collection of ERT data daily between 2014 and 2017, which represents the longest high-resolution ERT monitoring experiment conducted in a karst environment to our knowledge (see  Watlet et al. , 2018b, for details). This dataset consists of processed ERT data, defined over 1558 spatial cells and 465 daily time steps.
As a necessary prior step to causal inference, the 1558 time series were dimensionally reduced to six time series clusters (R0 to R5, Fig. 1b  and c ). We used hierarchical agglomerative clustering with the Ward linkage method to minimize the squared distance between time series within clusters. This algorithm is similar to k means. As clustering was applied to the standardized ERT dataset, clusters represent groups of linearly correlated resistivity dynamics. The optimal number of clusters of six was selected using the optimal silhouette index as a clustering evaluation metric  (Rousseeuw, 1987). The methodologi-cal aspects associated with clustering are extensively covered in another issue  (Delforge et al. , 2020c). R0 is associated with a dense limestone area in the model's center (Fig.
96 (ε lvl = 0. 05) and 0. 24 (ε lvl = 0. 7). With the four combinations of Table  2  and the 14 noise levels, 56 datasets were generated from 4 years of effective precipitation data P eff (2014-2018) and initial storages S A and S B equal to 30 mm. Only the last years of the three variables P eff , Q A , and Q B were considered for the causal inference experiment, the first three being considered a warming-up period. The data generation is repeated to produce 56 additional datasets with an effective connection. Q A and Q B are causally related by overwriting Q B such that Q B = Q B +(H AB * Q A ) , where H AB = [0. 1, 0. 8, 0. 1] is a linear transfer function convolved forwardly on Q A. Finally, the whole synthesis process is repeated to generate first-order differenced datasets (i. e. , Y t -Y t-1 ), that is, a total of 224 datasets with 4 model combinations and 14 noise levels, connected or not and differenced or not.
Results Figure  3  depicts the average and interquartile range of Q A - Q B time dependencies, or Q A -Q B if connected, obtained with the four CIMs (panels a-d) on the synthetic datasets for a maximum delay d max = 5 d. The multivariate analysis includes P eff. We distinguish between cases where the reservoirs are connected or not and where the data are differenced or not. Regarding the bivariate methods (panels a and b), CCF and CCM both exhibit sustained time dependencies for non-differenced data due to the auto-correlation and seasonal patterns left in the series. For differenced data, the results better screen the expected peak at lag 1 d, including disconnected reservoirs. This illustrates that bivariate CIMs cannot deal with the confounding effect related to the common forcing of reservoirs.
Multivariate methods For multivariate methods, we chose to report causal graphs for the raw (non-differenced) data since differencing is theoretically unnecessary and reduced the precision of CMI in the virtual experiment (Table  3 ). Hence, Fig. 5  shows linear conditional dependencies (ParCorr) obtained from the raw time series for the full dataset (all data, Fig. 5a ) and considering the discharge series one by one (P1, P2, and P3, Fig. 5b to d ). The P1, P2, and P3 datasets allow the analysis to be performed over larger time domains (Fig. 1c ). Except for R4, the dominant relationships between resistivity and meteorological variables are maintained between the graphs, Regarding PCMCI-CMI, we found unstable results on all datasets: all data, P1, P2, and P3 (see Sect. S2. 3). The causal graphs varied substantially when we repeated the analysis with the same parameters due to the stochastic nature of the independence test  (Runge, 2018b).
PCMCI: ParCorr ParCorr is linearly interpretable and computationally efficient. As with CCM, the ParCorr results for the real experiment (Fig. 5 ) seem promising because they generally favor the expected preferential flow and effective connection between the surface and P1  (Poulain et al. , 2018, and Fig. 1). ParCorr did not experience any stability problem, first, because ParCorr always provides the same results for the same dataset. Secondly, we deemed the most significant connections to remain between the results from the dataset variations that we tested (Fig. 5a-d ). Although there are a few differences between the links that are evaluated in the four variations, these are often related to relationships of lesser significance or magnitude. Some of them are alarming, such as R5 → RF at lag d = 1 in Fig.
In the real case study, PCMCI-CMI was found to be unstable, providing different results across consecutive runs (see  Figs. S5 and S6). Two main reasons might explain this instability. First, PCMCI conditions dependencies on the parents (Eq. 2) and, therefore, builds a dataset containing the initial variables and their delayed versions up to 2d max. The overlapping time domain over which all variables and delays are defined is small (see Fig. 1 ). It covers only 48 up to 218 time stamps (P3). Ruddell and Kumar (2009)  reported that 500 to 1000 samples are generally sufficient to obtain a qualitatively robust estimate of the TE, estimated using a binning approach. The nearest-neighbor approach that we used  (Runge, 2018b ) is more suited for short datasets. However, we found that our final sample sizes, accounting for missing data, are lower and the dimensionality is potentially higher, though variable and depending on the size of the parents' sets (Eq.
2), than those tested in the evaluation of the CMI estimator  (Runge, 2018b). This could be the main reason for the instability. In addition, we applied our analysis to highly correlated data from a smooth inverted electrical resistivity model (Fig. 4a ). PCMCI-CMI encountered highly interdependent anomalies regarding resistivity (reported in Figs. S5  and S6 ). We suspect that these anomalies may be related to a violation of the faithfulness hypothesis  (Runge, 2018a). PCMCI-CMI may fail because the resistivity series (R1 to R6) are overly deterministically related while accounting for nonlinear dependencies, i. e. , without a sufficient stochastic variability. This complementary reason for the instability is further illustrated and detailed in the Supplement (Sect. S2. 3). For short datasets, or with unevenly distributed missing values, we consider that building a consensual graph from multiple runs is a good strategy as our results suggested a fast preferential flow in the case of P1 only (Fig.
Besides, the selected CIMs operate on the time domain, limiting us to studying close temporal connections. However, hydrological connections and processes can be spread over much longer timescales. This further questions our tacit assumption of causal sufficiency. Accordingly, studying methods that operate on the frequency domain or that couple the frequency domain with the time domain may deserve particular interest (e. g. ,  Granger, 1969; Molini et al. , 2010; Rinderer et al. , 2018). The PCMCI algorithm is still being actively developed. A more recent implementation of PCMCI is now available in the new version of the Tigramite Python package (v4. 2), with refined default parameters and improved computational performance. In particular, a new algorithm, PCMCI+, deals with contemporaneous links and strong auto-correlation in series, with the promises of stronger recall and a wellcontrolled false-positive rate  (Runge, 2020).
Acknowledgements. We are thankful to  Michel Van Ruymbeke , who designed and constructed drip discharge sensors utilized in this study, and to  Olivier Kaufmann , who also constructed drip discharge sensors, maintained the underground monitoring system, and conceptualized the time-lapse ERT experiment. The authors would like to thank the four anonymous reviewers whose insightful comments significantly improved the quality of the manuscript. Arnaud Watlet  publishes with the permission of the Executive Director,  British Geological Survey (UKRI-NERC ). Financial support. This research has been supported by the  "Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture" (FRIA). Damien Delforge  is FRIA grantee of the " Fonds de la Recherche Scientifique " (FNRS). The publication in an open access journal has been supported by the sector of science and technology of UCLouvain.
Code and data availability. CCF and the Student's t test are computed using the Scipy Python package (Virtanen  et al. , 2020;  https://doi. org/10. 1038/s41592-019-0686-2). The CCM Python implementation is available from Delforge et al. (2020a; https://doi. org/10. 1029/2019WR025771). The official R implementation is available from the CRAN repository: https://CRAN. R-project. org/package=rEDM (last access: 22 April 2022; Park et al. , 2022). PCMCI and independence tests are implemented within the Tigramite (v. 4. 1 in this case) Python package: https://jakobrunge. github. io/tigramite/ (last access: 22 April 2022; Runge et al. , 2019b, https://doi. org/10. 1126/sciadv. aau4996). Evapotranspiration data were obtained from the agrometeorological PAMESEB network for the station of Jemelle: https://agromet.
be (last access: 22 April 2022; CRA-W, 2022). All other environmental time series can be obtained from Watlet et al. (2018b; https://doi. org/10. 5194/hess-22-1563-2018) and the related repository: https://zenodo. org/record/1158631 (Watlet et al. , 2018a). Resistivity-clustered time series can be reconstructed following Delforge et al. (2020c)   (https://doi. org/10. 1016/j. jappgeo. 2020. 104203) and the example available from the repository: http://dx. doi. org/10. 17632/ zh5b88vn78. 2 (Delforge et al. , 2020b). Supplement. The supplement related to this article is available online at: https://doi. org/10. 5194/hess-26-2181-2022-supplement.
We estimated these limits as a function of the number of data points in a light curve from 100,000 simulated time series. The advantage of these metrics is that they are very sensitive to systematic noise and to outliers. 3. The fitted transit time should not have an uncertainty greater than 10 minutes and it should be in agreement with other observations on the same day or a few days apart (if such observations exist). The total number of approved light curves for this data release is ∼1600, spanning the period from 2008 to 2020. For 48 exoclock. space 49 github. com/ExoWorldsSpies/hops 50 github. com/ucl-exoplanets/pylightcurve 51 https://github. com/ucl-exoplanets/ExoTETHyS 52 github. com/kbarbary/nestle the majority (∼60%) of the planets, the number of observations is lower than or equal to 10, indicating that more observations in the future are necessary.
Literature Data Approximately 2350 transit midtime values were collected from the literature for the 180 planets in our sample. While collecting the literature midtimes we: 1. included individual transit-time measurements and not ephemerides, with the exception of the discovery paper, 2. included transit-time measurements with uncertainties less than 10 minutes (similarly to the restriction for the ExoClock data), 3. did not include measurements that came from the Exoplanet Transit Database (ETD, Poddaný et al. 2010) to avoid duplications, as we have started sharing data directly with the ETD collaboration (see Section 3. 3) and these data will be directly linked to ExoClock, and 4. converted the reported time formats to BJD TDB. We need to note here that 35% of the planets in our sample have only one data point from the literature, related to the discovery of the planet.
ETD Data In an effort to make the best use of all available resources, we would like to collaborate with other ground networks which have current or past observations of the Ariel candidate targets. At the moment the largest database of such observations is the Exoplanet Transit Database (ETD, Poddaný et al. 2010) run by the Czech Astronomical Society since 2009, which provides more than 10,000 transit light curves for more than 350 exoplanet systems. In this study, we included 18 observations for three planets provided by the ETD network and midtimes from these were integrated with the ExoClock and the literature data. In order to maintain homogeneity and reliability in our analysis, we only considered observations with a data quality index lower than three which were then processed on the ExoClock website using the same methodology and validation criteria as for the ExoClock data (Section 3.
Without scaling, the uncertainties on the final ephemerides would have been largely underestimated, leading to reduced chi-squared values larger than 1. Table  2  in Appendix B provides all the new ephemerides and references to the literature values used. Figure  4  shows the uncertainties in the 2028 predictions before and after the updates presented in this work (σ p and s ¢ p , respectively). We note that all the new predictions have uncertainties lower than 10 minutes and an improvement has been achieved for 162 (90%) of them. There is a small number of planets (6) for which the prediction uncertainty has increased from ∼0. 1 minute to ∼1-4 minutes. These planets were observed by Kepler/K2 but the individual midtime data were not reported in the literature, hence only the initial ephemerides were used.
Catalog of ExoClock Observations The new catalog of ExoClock observations contains ∼1600 light curves analyzed in this work, which refer to 180 planets from the ExoClock target list. These observations were   conducted between 2008 and 2020, submitted to the ExoClock platform before the end of 2020, and validated according to the criteria described in Section 3. 1. From the ∼1600 observations in this data set, 66% were obtained by amateur astronomers and the remaining 34% by professionals. In the online repository, each observation is accompanied by: 1. metadata regarding the observer(s), the planet observed (link to ECC), the equipment used (telescope-camerafilter), the exposure time and the time and flux formats; 2. the raw light curve filtered for outliers, converted to BJD TDB , and flux formats and enhanced with the estimation for the uncertainties, the target altitude, and the airmass; 3.
Catalog of ExoClock Ephemerides The new catalog of ExoClock ephemerides contains the updated ephemerides for 180 planets from the ExoClock target list (see also Table  2  in Appendix B). In the online repository, each observation is accompanied by: 1. the midtime values used to calculate the ephemeris, 2. references for the literature data used, 3. links to the ExoClock and ETD data used, and 4. flags concerning the detection of nonlinear ephemerides or high-frequency noise in the O -C diagrams.