Set of equations Some of **the** variables modelled in **JOREK** **code** are: **the** poloidal flux Ψ, **the** electric potential u, **the** toroidal current density j, **the** toroidal vorticity ω, **the** density ρ, **the** temperature T , and **the** velocity v parallel along magnetic field lines. Depending on **the** model
choosen (hereafter denoted model which is a simulation parameter), **the** number of variables and **the** number of equations on them are setup. At every time-step, this set of reduced MHD equations is solved in weak form as a large sparse implicit system. **The** fully implicit method leads to very large sparse matrices. There are some benefits to this approach: there is no a priori limit on **the** time step, **the** numerical core adapts easily on **the** physics modelled (compared to semi-implicit methods that rely on additional hypothesis). There are also some disadvantages: high computational costs and high memory consumption **for** **the** parallel direct sparse solver (PASTIX or others).

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Mots clés : régressions empilées, estimation efficace, parité des pouvoirs d'achat, coïntégration
ABSTRACT
This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of **the** first differences of **the** regressors and estimating this augmented dynamic **regression** model by feasible generalized least squares using **the** long-run covariance matrix, we obtain an efficient estimator of **the** cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in **the** literature. We apply these new estimators to **the** **testing** of purchasing power parity (PPP) among **the** G-7 countries. **The** test based on **the** efficient estimates rejects **the** PPP hypothesis **for** most countries.

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Mots clés : régressions empilées, estimation efficace, parité des pouvoirs d'achat, coïntégration
ABSTRACT
This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of **the** first differences of **the** regressors and estimating this augmented dynamic **regression** model by feasible generalized least squares using **the** long-run covariance matrix, we obtain an efficient estimator of **the** cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in **the** literature. We apply these new estimators to **the** **testing** of purchasing power parity (PPP) among **the** G-7 countries. **The** test based on **the** efficient estimates rejects **the** PPP hypothesis **for** most countries.

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R s,Aλ ≤ ε, (3)
(ii) (lower bound) **for** any ε ∈ (0, 1) there exists a ε > 0 such that, **for** all 0 < A < a ε ,
R s,Aλ ≥ 1 − ε. (4)
Note that **the** rate λ defined in this way is a **non**-asymptotic minimax rate of **testing** as opposed to **the** classical asymptotic definition that can be found, **for** example, in Ingster and Suslina (2003). It is shown in Collier, Comminges and Tsybakov (2017) that when X is **the** identity matrix and p = n (which corresponds to **the** Gaussian sequence model), **the** **non**-asymptotic minimax rate of **testing** on **the** class B 0 (s) with respect to **the** ℓ 2 -distance has **the** following form:

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a. ICAM, Nantes, France
b. Naomod Team, Universit´ e de Nantes, LS2N (UMR CNRS 6004) c. Naomod Team, IMT Atlantique, LS2N (UMR CNRS 6004)
Abstract In order to ensure that existing functionalities have not been impacted by recent program changes, test cases are regularly executed during **regression** **testing** (RT) phases. **The** RT time becomes problematic as **the** number of test cases is growing. **Regression** test selection (RTS) aims at running only **the** test cases that have been impacted by recent changes. RTS reduces **the** duration of **regression** **testing** and hence its cost. In this paper, we present a model-driven approach **for** RTS. Execution traces are gathered at runtime, and injected in a static source-**code** model. We use this resulting model to identify and select all **the** test cases that have been impacted by changes between two revisions of **the** program. Our MDE approach allows modularity in **the** granularity of changes considered. In addition, it offers better reusability than existing RTS techniques: **the** trace model is persistent and standardised. Furthermore, it enables more interoperability with other model-driven tools, enabling further analysis at different levels of abstraction (e.g. energy consumption).

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5.2.1 Previous Attempts. MBT is a growing research field and many papers in this domain are published each year. **The** latest mapping study on MBT performed by Bernardino et al. illustrates that from 2006 to 2016, approximately 70 MBT supporting tools are proposed by business and academy while some of which are open source [1]. This significant number of tools promotes **the** opportunity to create a repository of existing MBT tools which can be analyzed **for** different purposes, but there is no repository so far. 5.2.2 Opportunities. **The** model-based **testing** is addressed in many papers, but it is not specialized **for** **the** low-**code** context. As we mentioned earlier, low-**code** development platforms are based on particular DSLs and system modeling is inherent in these platforms. Therefore, **for** **the** application of MBT in LCDPs, **the** first step (i. e., selection of a modeling language) is strictly imposed by **the** platform. Accordingly, **for** using MBT in **the** **testing** component of LCDPs, two modes exist:

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In some cases, these optimizations may negatively decrease **the** quality of **the** software and deteriorate application per- formance over time [6]. As a consequence, compiler creators
usually define fixed and program-independent sequence opti- mizations, which are based on their experiences and heuristics. **For** example, in GCC, we can distinguish optimization levels from O1 to O3. Each optimization level involves a fixed list of compiler optimization options and provides different trade- offs in terms of **non**-functional properties. Nevertheless, there is no guarantee that these optimization levels will perform well on untested architectures or **for** unseen applications. Thus, it is necessary to detect possible issues caused by source **code** changes such as performance regressions and help users to validate optimizations that induce performance improvement. We also note that when trying to optimize software perfor- mance, many **non**-functional properties and design constraints must be involved and satisfied simultaneously to better opti- mize **code**. Several research efforts try to optimize a single criterion (usually **the** execution time) [7]–[9] and ignore other important **non**-functional properties, more precisely resource consumption properties (e.g., memory or CPU usage) that must be taken into consideration and can be equally important in relation to **the** performance. Sometimes, improving program execution time can result in a high resource usage which may decrease system performance. **For** example, embedded systems **for** which **code** is generated often have limited resources. Thus, optimization techniques must be applied whenever possible to generate efficient **code** and improve performance (in terms of execution time) with respect to available resources (CPU or memory usage) [10]. Therefore, it is important to construct optimization levels that represent multiple trade-offs between **non**-functional properties, enabling **the** software designer to choose among different optimal solutions which best suit **the** system specifications.

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2 J. Lambert, H. Chouh, G. Rougeron, V. Bergeaud, S. Chatillon, L. Lacassagne, J.C. Iehl, J.P. Farrugia & V. Ostromoukhov / EG L A TEX Author Guidelines
vectorized. Morevover, a single step algorithm avoiding **the** unnecessary storage of temporary data and providing more work **for** each thread has been settled. **The** resulting opti- mized **code** scales well on a 2x12 cores CPU. Its overall per- formance is around 3.5x faster than previous reference im- plementation on a set of representative configurations. **For** **the** simplest ones, it reaches 20 fps.

A rich family of surrogate models consists in data-fitting: an interpolation and/or **regression** is established based on a pre-calculated set of simulation results, i.e., samples. Once **the** sample set is obtained, **the** subsequent data-fitting is far less expensive that **the** true electromagnetic simulation. Among **the** contributions in **the** last years, let us cite [1], where **the** authors combine a radial basis function (RBF) interpolation on optimally scattered samples and particle swarm optimisation (PSO) to efficiently solve EC-NdT inverse problems.

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Criteo - 1.00e-03 - 0.005 - - - - - - 49006.7±1400 37534.6±1600
Criteo - 1.00e-04 - 0.005 - - - - - - 59303.8±1300 42773.9±1000
4 Numerical Experiments
Set-up We now present some numerical studies showing **the** computational gain achieved by our approach. As an inner solver and baseline algorithms, we have considered a proximal algorithm [16] and a block-coordinate descent approach [3]; they are respectively denoted as GIST and BCD. They have been implemented in Python/Numpy and **the** **code** will be shared online upon publica- tion. We have integrated those solvers into **the** maximum-violating constraint (MaxVC) working set approach (algorithm in **the** appendix) and our approach denoted as FireWorks **for** FeasIble REsid- ual WORKing Set). Note that **for** MaxVC, we add **the** same number of constraints in **the** working set as in our algorithm. This is already a better baseline than **the** genuine one proposed in [1] As another baseline, we have considered a solver based on majorization-minimization (MM) approach, which consists in iteratively minimizing a majorization of **the** **non**-convex objective function as in [17, 13, 25]. Each iteration results in a weighted Lasso problem that we solve with a Blitz-based con- vex proximal Lasso or BCD Lasso (up to precision of 10 −5 **for** its optimality conditions). **For** these

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6 Conclusion
We introduce a smooth-transition generalized Pareto **regression** model, useful **for** handling **the** time-
varying effect of risk factors on **the** severity distribution of financial losses. This model has **the**
advantages of accounting explicitly **for** **the** high probability of extreme events and **for** a change in effects of **the** explanatory variables over time. In a simulation study, we highlight **the** good properties of **the** proposed estimation and **testing** procedures. Then, we use our model to conduct an empirical study of **the** dynamics driving operational losses severity at UniCredit. We focus on connecting **the** severity distribution of operational losses and **the** past number of losses (i.e. **the** frequency process), with **the** idea that past operational events proxy **the** quality of internal controls. As transition variable, we use **the** VIX, assuming that **the** uncertainty on **the** financial markets influences **the** link between **the** severity and frequency processes. We find that two different limiting mechanisms drive **the** severity distribution: in high uncertainty periods, we observe that a high number of operational events is followed by less extreme losses. This result suggests a self-inhibition effect, i.e. that **the** monitoring and supervision processes following operational events at UniCredit mitigate **the** likelihood of extremes in subsequent periods. In addition, during such periods of high uncertainty, an increase in **the** financial stability index (FSI), **the** Italian yield spread, and **the** industrial production growth rate are linked with a decrease in **the** likelihood of extreme losses. In light of these effects, we conjecture that these variables are proxies **for** an increase in risk aversion, a tight monetary policy, and **the** counter-cyclical nature of fraud losses, respectively. On **the** contrary, in periods of low uncertainty, only positive economic growth rate and FSI are significantly associated with more severe losses. Potential explanations are related to **the** effect of economic growth on transaction sizes and to **the** impact of low liquidity on timing issues. Several periods in our sample are driven by mixtures of **the** two limiting regimes, suggesting that a continuous transition function is necessary to model **the** data correctly. Finally, we demonstrate that **the** smooth-transition components improve **the** goodness-of-fit with respect to simpler alternatives.

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Remark 3. In some situations, as explained in Section 1, it may happen that **the** con- ditional location function (1.2) **for** a given function J (·) cannot be consistently estimated due to **the** presence of censoring. It is typically **the** case if two conditional means have to be compared, with J (s) = I(0 ≤ s ≤ 1). However, this problem can be avoided in many situations if **the** models (1.1) satisfy stronger assumptions. **For** example, in **the** classical homoscedastic case, where **the** error distribution is **the** same in both models and independent of **the** covariate, **the** null hypothesis is equivalent to **the** equality of two re- gression curves with a function ˜ J (·) (having **the** same properties as J (·)) chosen in an appropriate way. Indeed, **for** j = 1, 2, consider **the** models Y j = m j (X j ) + ε j , where

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static(at equilibrium) refinement strategy **for** **the** 2D version of **the** **JOREK** **code**.
Our dynamic refinement process is intended to increase **the** accuracy of spatial discretization in regions where **the** spatial scales are insufficiently resolved and decrease computing time **for** **the** same resolution with a simulation without refinement, in particular, **the** surfaces which present a deformations due to **the** appearance of instabilities. This technique is developed and imple- mented in 3D **JOREK** **code** to improve **the** simulation of MHD instabilities that are needed to evaluate mechanisms to control **the** energy losses observed in **the** standard tokamak operating scenario(ITER), and numerical simulation of these phenomena becomes crucial **for** better under- standing them. As a consequence, it is important to refine **the** grid as much as possible where instabilities are formed. This should be done adaptively, because **the** location of **the** instabilities can change, as in **the** case of **the** pellets injection.

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In **the** first step, software developers have to define, at de- sign time, **the** software’s behavior using a high-level abstract language (DSLs, models, program, etc). Afterwards, develop- ers can use platform-specific **code** generators to ease **the** soft- ware development and automatically generate **code** **for** dif- ferent languages and platforms. We depict, as an example in Figure 1, three **code** generators from **the** same family capa- ble to generate **code** to three software programming languages (JAVA, C# and C++). **The** first step is to generate **code** from **the** previously designed model. Afterwards, generated soft- ware artifacts (e.g., JAVA, C#, C++, etc.) are compiled, de- ployed and executed across different target platforms (e.g., Android, ARM/Linux, JVM, x86/Linux, etc.). Finally, to per- form **the** **non**-functional **testing** of generated **code**, developers have to collect, visualize and compare information about **the** performance and efficiency of running **code** across **the** differ- ent platforms. Therefore, they generally use several platform- specific profilers, trackers, instrumenting and monitoring tools in order to find some inconsistencies or bugs during **code** ex- ecution [3, 7]. Finding inconsistencies within **code** generators involves analyzing and inspecting **the** **code** and that, **for** each execution platform. **For** example, one way to handle that, is to analyze **the** memory footprint of software execution and find memory leaks [16]. Developers can then inspect **the** generated **code** and find some fragments of **the** **code**-base that have trig- gered this issue. Therefore, software testers generally use to report statistics about **the** performance of generated **code** in order to fix, refactor, and optimize **the** **code** generation pro- cess. Compared to this classical **testing** approach, our pro- posed work seeks to automate **the** last three steps: generate **code**, execute it on top of different platforms, and find **code** generator issues.

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(e-mail: juancp@uvigo.es)
Abstract:
Assume we have two populations satisfying **the** general model Y j = m j (X j ) + ε j , j = 1, 2, where m(·) is a smooth function, ε
has zero location and Y j is possibly right-censored. In this paper, we propose to test **the** null hypothesis H 0 : m 1 = m 2 versus

Rebound Tests
**The** rebound hammer is a surface hardness tester **for** which an empirical correlation has been established between strength and rebound number. **The** only known instrument to make use of **the** rebound principle **for** concrete **testing** is **the** Schmidt hammer, which weighs about 4 lb (1.8 kg) and is suitable **for** both laboratory and field work. It consists of a spring-controlled hammer mass that slides on a plunger within a tubular housing. **The** hammer is forced against **the** surface of **the** concrete by **the** spring and **the** distance of rebound is measured on a scale. **The** test surface can be horizontal, vertical or at any angle but **the** instrument must be calibrated in this position.

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product spaces [3]. In **the** context of uncertainty quantification, **for** problems involving very high stochastic dimension, instead of evaluating **the** coefficients of an expansion in a given approxi- mation basis (e.g. polynomial chaos), function u is approximated in suitable low-dimensional tensor subsets (e.g. rank m tensors) which are low-dimensional manifolds of **the** underlying tensor space. **The** dimensionality of these manifolds typically grows linearly with dimension d and therefore, it addresses **the** curse of dimensionality. Note that a **regression**-based method has already been proposed in [4] **for** **the** construction of tensor approxima- tions of multivariate functionals. Here, we propose an alternative construction of tensor approximations using greedy algorithms and sparse regularization techniques.

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now well established that gene expression is controlled by a balance between **the** joint action of enhancers and promoters increasing transcriptional activity, and silencers having an opposite effect (Kolovos et al. 2012), along with **the** action of many proteins that bind to these DNA regions. A number of studies have been conducted to describe enhancers and link them to their target genes, as enhancers do not necessarily control **the** nearest gene (Yao et al. 2015). Gasperini et al.(2020) recently reviewed biological techniques and recent developments enabling **the** discovery and characterisation of such enhancers. Several huge projects like FANTOM5 (Forrest et al. 2014) or ENCODE (Dunham et al. 2012) have described and annotated regulatory elements of **the** genome and contributed to **the** construction of public databases to share this knowledge. Thanks to these projects, we now have access to a huge amount of information about gene regulation which can be used to identify variants within key regulatory elements that could potentially be linked to diseases (Ma et al. 2015). Other projects such as **the** Roadmap Epigenomics Project (Bernstein et al. 2010) were developed to study epigenomics marks of **the** genome. These marks are very useful to define regulatory elements with, **for** example, **the** mono-methylation of **the** 4 th lysine residue of **the** H3 histone (H3K4m1) being indicative of enhancers or its tri-methylation (H3K4m3) being indicative of promoters. Projects were also conducted to study gene expression in different tissues. **The** GTEx project (GTEx Consortium 2013) **for** example provides information on gene expression in different cell lines. It has enabled **the** identification of expression Quantitative Trait Loci (eQTL) that could be involved in human diseases (Albert and Kruglyak 2015). At a larger scale, **the** characterisation of **the** genome organisation or “3D genome” has also been

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Functional ridge regression estimator FRRE The deﬁnition of the estimator of β in the centered model 2.2 is inspired by the estimator introduced by Hoerl [8] in the Ridge Regularization [r]