dataesr/scientific-paragraphs-categorization huggingface dataset:
Consistency of HSJointExp on constant data 0 +α -α -1 1 -α/4 α/4 X(n/2) X(0) X(1) X(n-1) X(n) × × × × ×. δ JE (1, X, x) ≤ n/4 ≥ n/4 points ≥ n/4 points 1 [-α,α] (w) 2α dw, and HSJointExp returns the output of ExponentialQuantile/JointExp with m = 1 on the noisy data X: M := E (2/ ) u JE ( X). The true median of the dataset is 0, and we study the quadratic risk E(M 2 ) of our mechanism. Note that the classical way of analyzing exponential mechanisms is to use the utility bounds found in  [30]. However, here we do not have the required level of control on the normalization factor. We hence go for a more direct way of controlling the output distribution. Denoting by N (x, y) = n i=1 1 [x,y) (0 + w i ) the number of noisy points falling in the interval [x, y), we define the event G := N (-α, -α/4) ≥ n/4 ∩ N (α/4, α) ≥ n/4.
For a given dataset X, we define eff := sup X∼Y sup q log (L(X, Y, q)) the effective difficulty of distinguishing X from any of its neighbors. We always have that eff ≤ but we would like to measure the difference between the two and its dependence on the noise level. The theoretical study of such is out of the scope of this article and is left for future work, but we conduct a numerical analysis in Section 6.
Distributions We claimed that HSJointExp has a huge advantage over regular JointExp in the case of distributions with isolated atoms. In order to test it numerically, we propose to do so with synthetic data in the first place. Indeed, in allows us to tune various interesting quantities. For real world distributions, it is harder to identify which ones satisfy the condition of having isolated atoms. We propose to evaluate the performance of the algorithms by identifying a real-wold distribution with the empirical distribution of a real-world dataset. The concentration of this dataset (i. e. how peaked its histogram is) is then the decisive criterion: The more concentrated it is, the more suboptimal JointExp/IS is expected to be compared to the smoothed variants.
The distributions that we call Pages and Ratings correspond to the empirical distributions of a collection of ratings and of number of pages of books from the Goodreads-Books dataset  [36]. Gillenwater et al. [22]  used the same datasets as numerical evidences of the performance of JointExp for estimating empirical quantiles. Again, sampled histograms are represented in Figure  2. The distributions look relatively smooth (i. e. not too peaked and with a relatively small support), and as a result, we can expect the gap between JointExp/IS and HSJointExp to be negligible. We can notice that contrary to the previous two real-world distributions, these two are much more concentrated. For Earnings, the concentration is due to the existence of categories of extremely high revenues. As a consequence, the support of the distribution is necessary big, and the algorithms that seek for privately estimating the quantiles have little information about the localization of the data points.
Privacy Amplification In Figure  5  we numerically estimate eff in the following setup: For each of the datasets (noted X), we estimate the median using HSJointExp with Laplace noise tuned with = 1. We estimate L(X, Y, q) for any Y ∼ X by discretizing the search space of Y and by Monte Carlo averaging to integrate with respect to the noise. The variance of the resulting eff is high, but we can see two regimes: For low values of the noise, the privacy of the mechanism is unchanged. For high values of noise, on the other hand, eff < and differentiating the datasets from their neighbors is harder. By crossing the results with Figure  4  however, it seems that the privacy amplification only occurs for values of the noise for which the utility of HSJointExp is already degraded compared to regular JointExp.
Very recently, a new approach was proposed by  Kaplan et al. in [26] : they present an algorithm that experimentally beats JointExp when the number of empirical quantiles of a dataset is high. Determining under what conditions and in what circumstances this empirical gap reflects in terms of statistical utility is left as future work. B Inverse sensitivity smoothing  [5]  B. 1 General principle When the output space O is a subset of a Euclidean space, the theory of Inverse Sensitivity comes with a smoothing operation with some parameter ρ > 0. The utility function u IS can be replaced with u ρ IS (X, o) = sup o ∈O: o-o 2 ≤ρ u IS (X, o ). It is easy to see that this new utility function has sensitivity ∆u ρ IS = 1. Contrary to the nonsmoothed inverse sensitivity mechanism which only comes with guarantees for finite output spaces O, this smoothed version gives more general results that only rely on a few mathematical tools.
(B. 4) Hence, when the dataset X has many points close to its empirical quantiles, the modulus of continuity ω Q (X, k) should not grow too fast in k. Convergence with high probability : The concentration bound (i. e. , Equation (B. 1)) along with the upper bound on the modulus of continuity (i. e. , Equation (B. 4)) gives that, with high probability E (2/ ) u 1/n r IS (X) -O(X) 2 ≤ O   m i=1 X np i +δ -X np i -δ 2 + 1 n r   , where δ = (4rm log n)/. Hence, whenever the dataset has many points in the neighborhood of the empirical quantiles, we can expect the smoothed inverse sensitivity mechanism for multiquantile (i. e. , E (2/ ) u 1/n r IS (X)) to perform well. This will typically be the case when the data distribution has a Dirac on a quantile whose mass accounts for more than 4rm log n n or when the data distribution has a density that is strictly positive on a neighborhood of its quantiles and δ is not too large.
C. 1 Proof of Theorem 1 If Y ∈ Q -1 (q) then: • Each "bin" has the right number of points: δ(i, Y, q) = 0, i ∈ {2. m + 1}, and δ closed (1, Y, q) = 0. • Every point of q appears in Y: q ⊆ Y. Then we can understand the modifications that have to be made to X in order to obtain a Y ∈ Q -1 (q). For the first condition, some points have to be moved from bins in excess to bins in deficit. This procedure accounts for m+1 i=2 δ(i, X, q) + + δ closed (1, X, q) + operations which can be reformulated as 1 2 m+1 i=2 |δ(i, X, q)| + 1 2 |δ closed (1, X, q)|. For the second condition, we have to make sure that for all i, q i belongs to the dataset. For a bin in strict deficit, at least a point has to be added to it due to the first condition. Hence, we can make sure to add the associated quantile at no extra cost.
Acknowledgments Aurélien Garivier  acknowledges the support of the  Project IDEXLYON of the University of Lyon , in the framework of the  Programme Investissements d'Avenir  ( ANR-16-IDEX-0005 ), and  Chaire SeqALO  ( ANR-20-CHIA-0020-01 ). This project was supported in part by the  AllegroAssai ANR  project  ANR-19-CHIA-0009.
To use interrupted time series analyses of routine monitoring data as a responsive feedback mechanism, the intervention activity needs to have a clearly defined starting point. Many family planning programs implement social or mass media campaigns (e. g. to encourage contraceptive use) that fit this requirement. Because several pre-and post-intervention data points are needed for the analysis, routine monitoring data (e. g. , the monthly number of family planning clients or the number of contraceptives distributed) that are collected at fixed intervals are an ideal data source. Our study uses monitoring data on the monthly number of calls received during the pre-campaign period (January to November 2021) to calculate 1) the linear trend in the number of calls, and 2) the logarithmic trend.
Data source The data source for this responsive feedback study consists of public records on the number of incoming calls received by the Honey & Banana Connect call center, as published by DKT International Nigeria  (Olutola et al. , 2023). The database excludes calls that were not related to family planning (e. g. , wrong number, crank calls, or calls not related to family planning). DKT generated the database based on customer records about all incoming calls received by the call center, which are entered using Customer Relations Management (CRM) software. The number of family planning related calls was extracted from the CRM customer records and aggregated by calendar month for inclusion in the database. Our outcome indicator is the monthly number of incoming calls that were related to family planning.
This study used analyzed routine data on the number of calls received by the Honey&Banana Connect call center in Nigeria to get regular feedback about the effectiveness of a radio jingle campaign for increasing the demand for family planning information. Effectiveness of the campaign was measured using a simple interrupted time series design, without a control group. The first phase of the ITS analysis consists of a simple review of the graphed results  (Jandoc et al. , 2015; Penfold & Zhang, 2013; Wagner et al. , 2002) , which Honey&Banana was already doing as part of their program monitoring activities. Because the graphed results are easy to interpret, this already made it clear that the radio program triggered an increase in the number of calls received. The second phase of the ITS analysis consists of the creation of an artificial control group by projecting the pre-campaign trends in the number of calls received, which then enables quantification of the estimated number of calls that were added each month due to the radio campaign.
Basic ITS analyses-as illustrated here-can be conducted using only Excel spreadsheet software, and do not require extensive in-house research capacity. There are a number of simple ways to replicate the proposed approach to get more detailed programmatic information. Although our illustrative example only used one outcome measure (the number of calls received), it would be recommended to apply the same approach to all available outcome measures. For example, had the radio campaign resulted a drastic increase in the number of incoming calls, then the next step would be to use similar ITS analyses to access whether it also increased the number of callers who requested a referral to a family planning provider. Similarly, subject to data availability, it could be used to assess whether the radio intervention resulted in an increase in the number of clients who visited a network provider.
Reply: The reviewer is correct that there may be instances in which the proposed technique will not be suitable. In any study that detects outliers, it will be important to try and identify the cause of those outliers. If the pre-intervention data pattern is poorly understood, then it will be hard to make the case this pattern would have continued without the intervention. We have emphasized this in the "study design" section. (The option to run the analysis with the outliers removed, as is done by some other authors is also discussed in paragraph 1 of the results, and in footnote 1). d. Reporting accuracy of prediction models is usually done using metrics such as RMSE. It is difficult to bench mark the accuracy using such tables. Moreover, how are program implementers expected to use such predictions? Reply: As the reviewer probably suspected, the only goodness of fit metric that Excel provides is the R 2.
Data availability Harvard Dataverse: Monthly number of phone calls received by the Honey&Banana Connect family planning call center in Nigeria (January 2021 -December 2022). https://doi. org/10. 7910/DVN/OMVLLB  (Olutola et al. , 2023). Data are available under the terms of the Creative Commons Zero "No rights reserved" data waiver (CC0 1. 0 Public domain dedication).
We describe first the method and its implementation. Then, we use the implemented algorithm to conclude on optimal orientations of PV panels and schedules. This program is made publicly available using a GitLab repository: https://gitlab. com/3it-cpv-public/panel-orientation. The program can be used as an effective tool to optimize the orientation of PV arrays for existing or future photovoltaic plants. This research work makes a significant contribution to enhancing the efficiency of photovoltaic installations. It presents a robust and flexible methodology for determining the optimal panel orientation that maximizes energy production. Additionally, our study contributes to advancing scientific knowledge by investigating the benefits of biannual orientation and its impact on energy yield.
Daily Energy Production We first used the Python library PVLib  [12, 13]  and its integrated photovoltaic simulation model to create the daily energy production library. PVLib uses meteorological samples, the sun position and an electrical model of PV panels to predict the energy production of a photovoltaic array at any location and any days of the year. For this paper, the objective was to set the PVLib model in a standard configuration, thus only a minimal set of parameters has been used. P dc0 = 240W and γ P dc = -0. 0004C -  has been set to characterize PV Panel performances. The temperature model has been arbitrarily defined with the open rack glass-glass model provided by Kratochvil et al. [14]. The azimuth angle of the panel is set at South or North depending on the hemisphere. For the meteorological model, an hourly typical meteorological year (TMY) for each location has been used.
Brute Force Method The implementation of the brute force method consists of finding all the possible vectors D k. The D vector of all the possible D k set of dates is the size of M = ( 365 N ) = 365! N!(365-N)!. This number M illustrates the limitation of the brute force method as its maximum obtained for N = 182 is equal to M = 3. 1 × 10 108. To strike a balance between computational burden and capturing key temporal dynamics, a weekly resolution was chosen. By transitioning to a weekly frequency, the size of the list D is reduced to ( 52 N ) , alleviating the computational demand. Utilizing the daily energy production database with this reduced weekly D vector allows us to identify the maximum energy production for each configuration D k. Consequently, the calculated optimal dates provide accurate results at a weekly resolution.
The vector D is created using the Python libraries itertools and more itertools and by considering that the calculation time must not exceed seven days for one reorientation scenario using our laptop (Intel 11 th Gen i7-1165G7, 2. 8 GHz clock frequency, 16 Go of RAM), it is possible to execute the second layer of the algorithm with N going up to 6. In the future, the code could be optimized using multiprocessing Python feature.
The second layer optimizes the dates of schedules and finds optimal tilts for each period. By considering 2 to 4 orientations at four different locations, we concluded that 2 orientations improve the energy produced up to 4. 8 % in Brasília. Considering more reorientations has a limited energy gain and in the case of a daily orientation scenario, the energy gain is up to 5. 9 %. Using the solar seasons to determine the scheduled dates of reorientation is a fast and simplified method. However, up to 0. 14 % and 1. 26 % more energy can be produced by optimizing the dates for 2 and 4 orientations, respectively. We implemented the method in an open-source software. It can be applied for short term installations as well as for permanent installations for any locations. The PV Model can be adapted for a specific study (customized horizon profile, proper PV Panel data sheets, shading on the panels) and thus the accuracy of the algorithm will be improved and the absolute energy production gain obtained with a multi-tilt orientation can be analyzed and compared to the induced costs of this method.
Acknowledgements LN2 is a joint  International Research Laboratory (IRL 3463 ) funded and co-operated in Canada by  Université de Sherbrooke (UdeS)  and in France by  CNRS  as well as ECL,  INSA Lyon , and  Université Grenoble Alpes (UGA). It is also supported by the  Fonds de Recherche du Québec Nature et Technologie (FRQNT). We also acknowledge  Joris Placette  for its advice in the building of the calculation method.
A database of field measurements of air concentrations of pesticide active ingredients has previously been compiled by CropLife Europe with an aim to revise the default air concentration values and assumptions applied in assessing vapour exposure in the risk assessment of bystanders and residents. The BROWSE model, released in 2014, which is a regulatory risk assessment model that includes the exposure of residents and bystanders has a component relating to post-application vapour inhalation. Predictions of concentration deduced from exposures obtained using the BROWSE model were compared with field measurements of 24-h and 7-day average concentrations. The methodology for obtaining concentration estimates from the BROWSE model is described, and the criteria for including field studies in the comparison are given.
, 2017b)  was reported, no comparison between BROWSE predictions and field data has been undertaken to date. Furthermore, as recommended by  EFSA et al. , 2022, additional data  and/or models for bystander and resident exposure to substances during and after application, which consider relevant daily air concentrations, are still necessary to produce more realistic exposure assessments. Hence, the CropLife Europe member companies have collected data from regulatory field studies previously used for PPP registrations. The objective of this study was therefore to use data collated by CropLife Europe (CLE) member companies into a database of measured vapour concentrations of pesticides to compare with BROWSE predictions, aiming to determine whether BROWSE would provide a more reliable method of predicting exposures to vapour compared with the current EFSA approach.
BROWSE exposure scenario Full details of the BROWSE model are available in the user guidelines  (Butler Ellis, 2013). The BROWSE model itself is available at https:// www. fera. co. uk/the-browse-software. The main features of the exposure scenario are: • PPP applied as a spray (applications of solids such as granules, and liquid injection into the soil are not included); • A field size of either 200 × 200 m, 500 × 500 m or 2000 × 2000 m; • The PPP applied to either soil only or crop only. For tall crops such as orchards and vines, BROWSE assumes the application is distributed evenly on the ground which is probably a worst-case scenario for bystander vapour exposure; • Residents and bystanders at a distance of 10 m from the edge of the treated field; • Residents and bystanders on four sides of a square field, with the highest value of exposure selected at each time period; • Hourly meteorological data for a five-year period.
At least one dataset is available for each of the regulatory zones (i. e. , southern, central and northern Europe) as a default, plus some additional countries in the central and southern zone. Default countries for southern, central and northern Europe are Spain, Hungary and Denmark, respectively. All data are from a location representing the 90th percentile for temperature in that zone; • Adult breathing zone height of 1. 5 m; child breathing zone height of 0. 7 m; • An application made every seven days, with any remaining AI in the treated area being set to zero before the next application. The predicted rolling 24-h average concentration was calculated for every bystander location and every hour following application. If an individual concentration measurement is denoted C i then the 24-h averages are calculated as 1 24 ∑ i+24 i C i.
Field data A database was compiled by  Felkers et al. (2022b)  which contains all available data generated by member companies of CropLife Europe relating to vapour concentrations measured in a range of experimental field conditions. This database contains studies which were conducted to refine product-specific risk assessments for PPP registration purposes and were not designed for comparison with the BROWSE model. Studies that were consistent with the BROWSE scenario were selected for comparison, thus inclusion criteria were: • Spray applications; • Outdoor applications; • Measurements of concentrations of primary  AI (i. e. , parent compound). In addition, the size of the treated area for many studies was much smaller than the smallest available in BROWSE, which was 40,000 m 2. In order to have sufficient data available for comparison, we made a decision to include much smaller treated areas (down to 7200 m 2 ) and then adjust the data accordingly, as described in section 2.
3. The full database was made available for the purposes of this study and then filtered according to the above inclusion criteria (see Supplementary Table  1 ). The list of trials from 23 GLP (Good Laboratory Practice) compliant studies is given in Table  1. These produced 24 sets of data as one study measured two AIs. These studies were conducted under representative conditions of use in various locations across Europe (France, Germany, Ireland, Italy, Spain, Lithuania, Poland, UK) and included low crops (wheat, barley) and high crops (pome fruit, vineyards). Field sizes ranged from 0. 72 to 8. 8 ha. Vapour pressures covered in the trials range from 4. 00 × 10 -7 to 9. 00 × 10 -3 Pa at 20 • C. Concentrations in air were measured with static sampling pumps with sorbent tubes placed at 4 points around the treatment area.
Each study in the database contains an analytical phase report, where GLP-compliant analytical methods are described for each AI. Analytical methods have been validated for determination of residues of each AI in relevant matrices. The LODs and LOQs for each AI are stated in Supplementary Table  1. None of the experiments used a scenario identical to that for BROWSE but all of them had some elements in common: • Sampling heights were similar to the height of adult and child breathing zones in BROWSE; • Distances downwind were 10 m and less; • Sampling durations enabled rolling 24-h averages and longer-term averages to be obtained in the same way as in the BROWSE model as described above, but generally with longer measurement durations than 1 h (8 h was typical); • Samples were taken around the field to reduce the effect of wind direction.
The data in 7 out of 23 studies were also collected at a closer distance than the 10 m used in the BROWSE scenario, which could lead to an over-estimate of the exposures at 10 m. Again, exploration of the effect of distance was undertaken to establish if adjustment to the data was necessary. Since LODs and LOQs vary between studies, a simple approach was applied to assure comparability between trials. In estimating the average air concentrations, values < LOD were assumed to be zero. Values between LOD and LOQ were treated as ½ LOQ, and values > LOQ have been used as measured  (Felkers et al. , 2022a; 2022b). It is important when comparing data with model predictions that values that are less than LOD are not set to the LOD, as often happens when data is used as the basis of an exposure assessment, as this would artificially increase the underprediction by the model where predictions are less than the LOD.
Modelling the effect of field size and distance The components of the BROWSE model, OPS and Consensus-Pearl, were not available separately to undertake a sensitivity analysis for field size and bystander or resident distance from the treated area. Therefore, in order to evaluate the effect of field size and bystander distance from the treated area, we used a commercially-available plumedispersion model (ADMS v 4. 1, Cambridge Environmental Research Consultants, Cambridge, UK). This model was used in the BREAM project to explore sensitivities for vapour exposure  (Butler Ellis et al. , 2010b). This sensitivity analysis was undertaken using generic meteorological data, provided with ADMS, to explore the range of possible sensitivities, because the full meteorological data needed to be able to directly model each of the trials were not accessible.