dataesr/scientific-paragraphs-categorization huggingface dataset:
2015). In the large majority of cases, however, the noise in RV residuals is not white, but colored and with an unknown power spectral density (PSD). Providing reliable FAP estimates in this situation remains, to our knowledge, an open problem. The assumption that the noise PSD is flat leads logically to increased false alarms in the PSD bumps, and to a loss of detection power in the PSD valleys (e. g. , see Fig. 2  in  Sulis et al. 2016 ). This problem is only partially solved in practical approaches where a covariance model is fitted to the data and used to produce residuals that are assumed to be white. For instance,  Delisle et al. (2020)  recently presented an analytical formulation of the p-value resulting from the generalization of  Baluev (2008)  to the case of colored noise when the covariance matrix is known.
Both of these limitations are removed in the present paper. The approach is flexible and can deal with the main characteristics that are encountered in practice with RV detection: irregular sampling and various noise sources with partially unknown noise statistics. The basic principle of the procedure is to propagate errors on the noise model parameters to derive accurate p-values of detection tests by means of intensive Monte Carlo simulations. The choice of the noise models involved in the procedure is entirely left to the user, as is the choice of the periodogram and detection test. We note that without loss of generality, the procedure can be applied to an RV dataset resulting from any extraction process (including, e. g. , the extraction techniques recently described in Collier  Cameron et al.
The choice of which type of RV noise component fits in d or n depends on the assumptions made by the user about the RV time series under test. Under the alternative hypothesis (one or more planets are present), time series x contains the same noise components d and n, plus a deterministic signal s corresponding to the Keplerian signatures of planets (model M s ). The number of planets and their Keplerian parameters θ s are unknown. Throughout this paper, we consider the optional case in which context-driven data of the stochastic colored noise n in Eq. (1) can be made available through realistic simulations, for instance. We call these data the null training sample (NTS). By construction, this NTS is free of any possible contamination by the planetary signal. For example, focusing on the stellar granulation noise,  Sulis et al.
Other examples in which NTS can be obtained are 3D MHD simulations of stellar supergranulation (e. g. ,  Rincon & Rieutord 2018) , empirical simulations of stellar meridional flows  (Meunier & Lagrange 2020) , or specific data-driven observations representative of the instrumental noise (e. g. , microtelluric lines;  Cunha et al. 2014 Seifahrt et al. 2010)  affecting the RV data. In general, all realistic synthetic time series of the stochastic colored noise sources affecting the RV data can be included in the NTS. This setting poses the general question how this NTS might be leveraged to improve the detection process, both in terms of detection power and of the accuracy of the computed p-value. This approach was proposed and analyzed in  Sulis et al. (2017a) , but with d = 0 and a regular sampling for x in model (1).
The resulting dataset constitutes a large set of noise time series from which the oracle reference results can be computed. For the implementation of algorithm 2, the available NTS is composed with a 53-day-long noise time series obtained from 3D MHD simulations of solar granulation  (Bigot et al. , in prep. ). After splitting them into two-day-long time series, 26 granulation noise time series are available, of which we randomly selected L = 5 for the standardization. Before running algorithm 2, we applied the same corrections as for the GOLF data to the NTS obtained from MHD simulations (T 5 ) (i. e. , filtering of the stellar acoustic modes and addition of an instrumental WGN). The NTS was finally sampled as the observations under test (see the three sampling grids detailed below). Algorithm 2 also relies on parameters that set the size of the Monte Carlo simulations, B and b (taken here as B = 100 and b = 10 4 ) and on model M n with associated parameters θ n.
modulated with the stellar rotation period plus long-term trends that are modulated with the stellar cycle. Numerous techniques have been developed to estimate the contribution of magnetic activity to RV data (e. g. , see  Ahrer et al. 2021). We assume that an estimate of the noise activity signature has been obtained by one of these methods in the form of an ancillary time series for d. This ancillary time series is assumed to be the log R HK activity indicator in the following (but other indicators can be used as well, see Table  1 ). The noise component n in Eq. (  1 ) is composed of correlated granulation noise plus WGN. An NTS of n composed with L simulated RV time series obtained from MHD simulations is assumed to be available, except in the last part of this section, in which we relax this assumption.
The remaining section contains four parts. The first two parts describe the synthetic dataset with the computation of oracle p-values, and the validation of the p-value estimation algorithm with the impact of the priors on the computed p-values. In the third part, we study improvements that can be achieved by using generalized extreme values (GEV) to speed up the Monte Carlo simulations in algorithm 2. In the last part, we consider the particular (but practical) case in which no NTS is available for n in Eq. (1).
2015 ) S H (ν + k ; θ n ) := 2 √ 2 π a 2 H b H 1 + ν + k b H c H + σ 2 w , ( 13 ) where the vector θ H = [a H , b H , c H , σ 2 w ] collects the amplitude, characteristic frequency, and power of the Harvey function, and σ 2 w is the variance of the WGN. Notation ν + k means that positive frequencies are considered. We calibrated the parameter vector θ H using a fit of the available MHD RV time series (see Sect. 4). In this case and in the following, we used the lmfit Python package  (Newville et al. 2014) , which makes nonlinear optimizations for curve-fitting problems. This choice was made for simplicity and because the algorithm is fast. For practical RV analyses, the user can optimize the fitting procedure to use a proper Markov chain Monte Carlo estimation procedure, for example. Synthetic time series with a PSD that is exactly given by Eq.
(  13 ) can be simulated with the Fourier transform (FT). To compute a synthetic time series from Eq. (  13 ), we generated a WGN w ∼ N(0, I), computed the fast FT of w, performed a point-wise multiplication with √ S H (ν k ), and finally took the real part of the inverse FT. An example of a synthetic ten-daylong time series obtained using models (  10 ) and (  13 ) is shown in  Fig. 5 (black). From this time series, we created a large central gap between day 2 and day 8 in the time-sampling grid, and we randomly selected N = 288 data points in the two remaining intervals (gray). This synthetic RV time series is the series that we test in the next three subsections. To compute the oracle procedure (which has knowledge of the exact parameters that were used to generate the synthetic time series, i.
Validation of algorithm 2 We applied the 3SD procedure on one of the synthetic time series. For this purpose, we assumed a realistic situation in which the noise models M d and M n that are used as inputs of algorithms 1 and 2 are different from the models that are used to generate the synthetic RV dataset in Sect. 5. 2. Following an example given in  Dumusque et al. (2012)  and  Ahrer et al. (2021) , we used for M d a simple parametric model 4  composed of a linear combination of c and three low-order polynomials, d(t j | θ d ) = β d • c(t j ) + d • t 2 j + ζ d • t j + η d , j = 1,. , N, (14) with θ d = [β d , d , ζ d , η d ] the corresponding parameter vector. For the available NTS T L , we selected the L = 5 MHD time series described in Sect. 4. 2. 1. Using the LSP for P, the Max test for T, T L , the model (  14 ) for M d , no model M n , and the synthetic ancillary series c, we then computed algorithm 1 and obtained a test value t.
We finally set up the size of the Monte Carlo simulations as B = 100 and b = 1000. The p-value estimates resulting from algorithm 2 are shown in Fig. 8. The estimated mean p-values and true p-values match very well, similarly to the case with an NTS (Sect. 5. 3, see left panel of Fig. 6 ). This shows that the p-value can be robustly estimated even when no NTS is available. We anticipate, however, that the performances of detection procedures based on estimates of the covariance structure from the data will probably depend on the RV data (noise sources, data sampling, etc. ). The comparison of specific cases is left to a future paper.
Application to RV exoplanet detection: The debated detection of αCenBb Alpha Centauri Bb is a debated ∼1. 13 Earth-mass (minimum mass) planet whose detection was reported around our solar neighborhood star αCenB with an orbital period of 3. 2 days  (Dumusque et al. 2012). It is challenging to achieve the detection of such a small planet because αCen is a triple star and the planetary RV semi-amplitude (∼0. 51 m s -1 ) was at the limit of the A04, page 12 of 18 Fig. 8. Same as Fig. 6 , but for a practical case without NTS for n in Eq. (  1 ). In this case, the covariance structure of the stochastic noise source is estimated from the data with model M n given in Eq. (  13 ). instrumental precision of HARPS (∼1 m s -1 ). The observed RV campaign contains N = 459 points, irregularly sampled during a time span of 4 yr between 2008 and 2011.
The dataset contains large gaps between the observation years as a result of the visibility of the star, and small gaps that are due to the available nights. The planet detection has been debated in a lively way: using analysis tools different from the detection paper in  Hatzes (2013) , using different stellar noise modeling in  Rajpaul et al. (2016) , and recently using a different technique of randomization inference to measure the p-value of the periodogram peak at 3. 2 days by  Toulis & Bean (2021). In this section, we analyze this RV dataset as a case study for the 3SD procedure. The objective of the second part (Sect. 6. 2) is also to demonstrate that algorithm 2 offers the possibility of investigating the effects of model errors on the frequency analysis and on the estimated p-values.
They also used a different number of harmonics for each of the four RV subsets. We refer to the supplementary material' of  Dumusque et al. (2012)  for the global model that is fit to each of the four RV subsets (see their Eqs. p. 7). In total, m M contains 19 free parameters. The sum of components m B , m C , and m M forms the noise component d in model (1). The authors assumed that component n in (1) is uncorrelated and there is no NTS. We applied the 3SD procedure to the RV data of αCenB with the following setting for algorithm 1: - We then ran algorithm 2 to evaluate the p-value of t with same inputs as algorithm 1 that are listed above. The t values corresponding to mean p-values of 10, 1, and 0. 1% are shown with solid green, blue, and red curves, respectively, in Fig. 9. The 90% intervals are shown with the corresponding colored shaded regions.
The value t := p(3. 2 d) = 16. 03 corresponds to an estimated mean p-value of 0. 47% with a 90% interval of [0. 1%, 0. 7%]. We confirmed that these results are reasonably stable with respect to the prior model π d for the M d model parameters in row 13 of algorithm 2 (e. g. , a Gaussian instead of a uniform prior with interval widths set to 1σ standard error leads to p v (16. 03) = 0. 43% with [0. 1%, 0. 7%] 90% interval). Dumusque et al. (2012)  assumed that the data residuals (without a planet) are white. While the p-value evaluation procedure used in this paper was not specified, we assume that they used the classical bootstrap technique in which the p-values are evaluated by shuffling the dataset and keeping the observing time dates constant. The t values corresponding to the p-values of 10, 1, and 0.
Systematic study of noise model errors When we ran our detection algorithm 1 with this new noise model, we obtained final data residuals of 0. 78 m s -1 standard deviation, and the peak at 3. 2 days disappeared. Similarly to  Rajpaul et al. (2016) , we performed an injection test with a planetary signal at 3. 2 days with an amplitude of 0. 51 m s -1 to verify that the GP noise model does not overfit the planet signal. We found the periodogram peak of the data residuals to be the highest peak, confirming the observations of  Rajpaul et al. (2016)  that the detection outcome can be very sensitive to the choice of the noise model plugged in the detection algorithm. Model errors are unavoidable in practice. For the same dataset, different experts may assume different noise models, and the magnitude of the absolute error resulting from these models can probably be a lower bound of the relative difference between the models.
When the noise model is correct, each frequency has been randomly hit a few times (the holes are caused by frequencies that are removed in the noise model). In contrast, when the noise model is not correct, the maximum peak was found 2504 times at the 3. 2 -day period (compared with two times under no model error), or 1917 times at the 7. 94 -day period (compared with one time without a model error). In conclusion, when 1) the estimation errors on the noise parameters (assuming no model error) are taken into account and 2) the effects of possible realistic errors on the noise model are investigated, the degree of surprise brought by the peak at 3. 2 days decreases substantially. This study of the α CenB dataset supports the conclusion that was reached in previous works  (Hatzes 2013; Rajpaul et al.
6. 2). Our procedure builds on and extends our previous study  (Sulis et al. 2020) , which was limited to the case of regular sampling and was not able to handle magnetic activity signals. This procedure allows deriving in algorithm 2 the p-value corresponding to a test statistic produced in detection algorithm 1 while accounting for uncertainties in the noise model parameters. Periodogram standardization can be implemented using a (possibly simulated) NTS. Examples of simulated NTS can come from MHD simulations of granulation, supergranulation, or any other stellar simulations that are shown to be reliable. This opens future collaborations between stellar modelers and RV exoplanet scientists (see Sect. 4). The NTS can also come from instrumental measurements, independent of the studied RV dataset.
In addition, the procedure can take advantage of ancillary data to deal with nuisance signals such as the stellar magnetic activity (e. g. , logR HK time series). Overall, the proposed detection procedure is versatile in i) the periodograms (or other frequency analysis tools), ii) the detection tests (classical or adaptive), and iii) the noise models that can be plugged in. Examples of input parameters for the three items above are listed in Table  1. Additionally, Python codes are released on GitHub (see Appendix. A). Although not emphasized in this paper, the 3SD procedure also opens the possibility of using adaptive tests such as the higher criticsm or the Berk-Jones tests  (Donoho & Jin 2004; Berk & Jones 1979 ). These tests are more powerful than classical detection tests (as the Max test presented in Eq.
(  6 )) in the case of exotic planet signatures of small amplitudes (e. g. , planets of high eccentricity or multiplanet systems) when the data sampling is regular (see  Sulis et al. 2017a). How these adaptive tests may be incorporated in the proposed 3SD procedure to evaluate their performance in the context of irregular time sampling will be investigated in a further study. We have illustrated how the procedure can be implemented in the presence of instrumental, granulation, and magnetic activity, of long-term drifts of stellar origin (magnetic cycle), and binary noises in model (1). Other RV noise sources can similarly be considered in the procedure when they are identified in the RV data. Implementing the 3SD procedure may present some issues, but these can at least partially be solved.
First, the procedure can be very time consuming owing to several factors (generation of NTS simulations, large number of Monte Carlo simulations, and the complexity scales with the number of parameters of the noise models). We have shown that the GEV framework allows us to reduce this computational cost (Sect. 5. 4). Second, the computed p-values remain dependent on the choice of the input noise models. While this is not specific to our approach, we showed that a hybrid version of the procedure allows us to quantify the robustness of p-value estimates to specific model changes (Sect. 6. 2). Third, the computed p-values are more conservative than the p-values obtained by random shuffling of the best-fit residuals, as is often done in RV data analysis (Sect. 6. 1). This is because they take the main errors into account that are generated during the detection process (estimation error on the parameters and/or specific model error).
Last, when the detection process makes some error in the assumed noise model, estimating and removing a nuisance signal from the RV dataset may lead to a nonuniform distribution of the frequency index where the largest periodogram peak is found (this is visible in the bottom right panel of Fig. 10 ). The reason is that imperfect subtraction of nuisance signals (caused by a model error) leads to residual A04, page 15 of 18 A&A 667, A04 (2022) long-period signals in which the periodicities of the sampling grid are imprinted. Model errors always remain in practice, and the proposed algorithm allows diagnosing the effects of some of them. Finally, throughout this paper, we have illustrated the proposed method on solar data, synthetic datasets, and HARPS data of αCenB. The next step is to analyze some still-to-be confirmed low-amplitude planet detection.
We considered another noise model M d for d. Following Rajpaul et al. (2016;   see their Sect. 4), we still considered a nuisance signal of the form d = m B + m C + m M , but with some modifications. The estimation of the noise model parameters on the RV dataset was now performed in two steps. The binary and longterm trend components m B and m C were fit first. The magnetic activity component m M was fitted in a second step on the data residuals as a Gaussian process with a quasi-periodic covariance kernel of the form of Eq. (.
Acknowledgements. The authors would like to thank the referee for her/his helpful comments, which led to improved versions of this study. S. S. acknowledges support from  CNES. D. M. acknowledges support from the  GDR ISIS  through the Projet exploratoire TASTY. MHD stellar computations have been done on the "Mesocentre SIGAMM" machine, hosted by  Observatoire de la Côte d'Azur. The GOLF instrument onboard SOHO is a cooperative effort of scientists, engineers, and technicians, to whom we are indebted. SOHO is a project of international collaboration between  ESA  and  NASA. We acknowledge  X. Dumusque ,  Astronomy Department Geneva Univ. , Switzerland , for the public HARPS-N data that have been made available at http://cdsarc. u-strasbg. fr/viz-bin/cat/J/A+A/648/A103. We acknowledge support from  PNP  and  PNPS-CNES  for financial support through the project  ACTIVITE.
Edge-cloud computing offloads parts of the computations that traditionally occurs in the cloud to edge nodes, e. g. , CDN servers, in order to get closer to the users and reduce latency. To improve performance even further, WebAssembly is increasingly used in this context. Edge-cloud computing providers, such as Fastly or Cloudflare, let their clients deploy stateless services in the form of WebAssembly binaries, which are then translated to machine code and sandboxed for a safe execution at the edge. In this context, we propose a technique that (i) automatically diversifies WebAssembly binaries that are deployed to the edge and (ii) randomizes execution paths at runtime, turning the execution of the services into a moving target. Given a service to be deployed at the edge, we automatically synthesize functionally equivalent variants for the functions that implement the service.
WebAssembly is a portable binary-code format designed to be lightweight, fast and safe  [6] ,  [7]. After compiling code to a WebAssembly binary, developers can spawn a compute service by deploying their binary on all nodes in an Edge platform. Thanks to its simple memory and computation model, WebAssembly is considered better than virtualization or containerization  [8]. However, We-bAssembly is not perfect and is not exempt of vulnerabilities. Implementations in both browsers and standalone runtimes  [9]  have been found to be vulnerable  [10] ,  [9] , opening the door to different attacks. This means that if one node in an Edge network is vulnerable, all the others are vulnerable is the exact same manner as the same binary is replicated on each node. This illustrates how fragile Edge computing can be as one single vulnerability can affect the whole network, like it happened on June 8, 2021  [11].
In this work, we introduce MEWE, a framework that generates diversified WebAssembly binaries so that no two executions in the edge network are identical. Our solution is inspired by Moving Target Defense  [12]  where the attack surface of a program is constantly moving. Here, our goal is not to remove vulnerabilities but to drastically increase the effort for exploitation through large-scale execution path randomization. MEWE operates in two distinct steps. At compile time, MEWE generates variants for different functions in the program. A function variant is semantically identical to the original function but structurally different, i. e. , binary instructions are in different orders or have been replaced with equivalent ones. All the function variants for one service are then embedded in a single multivariant WebAssembly binary.
A. WebAssembly WebAssembly is a bytecode designed to bring safe, fast, portable and compact low-level code on the Web. The language was first publicly announced in 2015 and formalized by Haas et al. [6]. Since then, most major web browsers have implemented support for the standard. Besides the Web, WebAssembly is independent of any specific hardware, which means that it can run in standalone mode. This allows for the adoption of WebAssembly outside web browsers  [7] , e. g. , for edge computing  [9]. WebAssembly binaries are usually compiled from source code like C/C++ or Rust. Listing 1 and 2 illustrate an example of a C function turned into WebAssembly. Listing 1 presents the C code of one function and Listing 2 shows the result of compiling this function into a WebAssembly module. The WebAssembly code is further interpreted or compiled ahead of time into machine code.
B. Web Assembly and Edge Computing Using Wasm as an intermediate layer is better, in terms of startup and memory usage, than containerization or virtualization  [8] ,  [13]. This has encouraged edge computing platforms like Cloudflare or Fastly to adopt WebAssembly (Wasm) to deploy client applications in a modular and sandboxed manner  [4] ,  [5]. In addition, WebAssembly is a compact representation of code, which saves bandwidth when transporting code over the network. This allows edge-cloud platform providers to deploy the same Wasm binary, for a client application, around the world in a few seconds. Client applications that are designed to be deployed on edge-cloud computing platforms are usually isolated services, Fig. 1 : Deployment to the edge. Client application developers build their application and compile it to WebAssembly before submitting to the Edge-cloud computing platform.