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We compute the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane introduced in $\texttt{arXiv:2002.02514}$ assuming that the characteristic is zero.

The interactions between different tools added successively to a block-based video codec are critical to its rate-distortion efficiency. In particular, when deep neural network-based intra prediction modes are inserted into a block-based video codec, as the neural network-based prediction function cannot be easily characterized, the adaptation of the transform selection process to the new modes can hardly be performed manually. That is why this paper presents a combined neural network-based intra prediction and transform selection for a block-based video codec. When putting a single neural network-based intra prediction mode and the learned prediction of the selected LFNST pair index into VTM-8.0, -3.71%, -3.17%, and -3.37% of mean BD-rate reduction in all-intra is obtained.

Context. The recent estimates of the 3D shape of the M/Xe-type triple asteroid system (216) Kleopatra indicated a density of 5 g.cm$^{-3}$. Such a high density implies a high metal content and a low porosity which is not easy to reconcile with its peculiar dumbbell shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, we aim to constrain the mass and the shape of Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of Kleopatra recorded in 2017 and 2018 with archival data, as well as lightcurve, occultation, and delay-Doppler images, to derive its 3D shape model using two different algorithms (ADAM, MPCD). Furthermore, an N-body dynamical model allowed us to retrieve the orbital elements of the two moons as explained in the accompanying paper. Results. The shape of Kleopatra is very close to an equilibrium dumbbell figure with two lobes and a thick neck. Its volume equivalent diameter (118.75$\pm$1.40) km and mass (2.97$\pm$0.32) 10$^{18}$ kg imply a bulk density of (3.38$\pm$0.50) g cm$^{-3}$. Such a low density for a supposedly metal-rich body indicates a substantial porosity within the primary. This porous structure along with its near-equilibrium shape is compatible with a formation scenario including a giant impact followed by reaccumulation. Kleopatra's current rotation period and dumbbell shape imply that it is in a critically rotating state. The low effective gravity along the equator of the body, together with the equatorial orbits of the moons and possibly rubble-pile structure, opens the possibility that the moons formed via mass shedding. Conclusions. Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. It deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission., Comment: Accepted for publication in Astronomy and Astrophysics

The Intergovernmental Panel on Climate Change proposes different mitigation strategies to achieve the net emissions reductions that would be required to follow a pathway that limits global warming to 1.5{\deg}C with no or limited overshoot. The transition towards a carbon-free society goes through an inevitable increase in the share of renewable generation in the energy mix and a drastic decrease in the total consumption of fossil fuels. Therefore, this thesis studies the integration of renewables in power systems by investigating forecasting and decision-making tools. Indeed, in contrast to conventional power plants, renewable energy is subject to uncertainty. Most of the generation technologies based on renewable sources are non-dispatchable, and their production is stochastic and complex to predict in advance. A high share of renewables is challenging for power systems that have been designed and sized for dispatchable units. In this context, probabilistic forecasts, which aim at modeling the distribution of all possible future realizations, have become a vital tool to equip decision-makers, hopefully leading to better decisions in energy applications. This thesis focuses on two main research questions: (1) How to produce reliable probabilistic renewable generation forecasts, consumption, and electricity prices? (2) How to make decisions with uncertainty using probabilistic forecasts? The thesis perimeter is the energy management of "small" systems such as microgrids at a residential scale on a day-ahead basis. It is divided into two main parts to propose directions to address both research questions (1) a forecasting part; (2) a planning and control part., Comment: Ph.D. thesis manuscript

Robotic Process Automation (RPA) is a technology to automate routine work such as copying data across applications or filling in document templates using data from multiple applications. RPA tools allow organizations to automate a wide range of routines. However, identifying and scoping routines that can be automated using RPA tools is time consuming. Manual identification of candidate routines via interviews, walk-throughs, or job shadowing allow analysts to identify the most visible routines, but these methods are not suitable when it comes to identifying the long tail of routines in an organization. This article proposes an approach to discover automatable routines from logs of user interactions with IT systems and to synthesize executable specifications for such routines. The approach starts by discovering frequent routines at a control-flow level (candidate routines). It then determines which of these candidate routines are automatable and it synthetizes an executable specification for each such routine. Finally, it identifies semantically equivalent routines so as to produce a set of non-redundant automatable routines. The article reports on an evaluation of the approach using a combination of synthetic and real-life logs. The evaluation results show that the approach can discover automatable routines that are known to be present in a UI log, and that it identifies automatable routines that users recognize as such in real-life logs., Comment: 41 pages, 6 figures, 10 tables. arXiv admin note: text overlap with arXiv:2008.05782

Greater direct electrification of end-use sectors with a higher share of renewables is one of the pillars to power a carbon-neutral society by 2050. However, in contrast to conventional power plants, renewable energy is subject to uncertainty raising challenges for their interaction with power systems. Scenario-based probabilistic forecasting models have become a vital tool to equip decision-makers. This paper presents to the power systems forecasting practitioners a recent deep learning technique, the normalizing flows, to produce accurate scenario-based probabilistic forecasts that are crucial to face the new challenges in power systems applications. The strength of this technique is to directly learn the stochastic multivariate distribution of the underlying process by maximizing the likelihood. Through comprehensive empirical evaluations using the open data of the Global Energy Forecasting Competition 2014, we demonstrate that this methodology is competitive with other state-of-the-art deep learning generative models: generative adversarial networks and variational autoencoders. The models producing weather-based wind, solar power, and load scenarios are properly compared in terms of forecast value by considering the case study of an energy retailer and quality using several complementary metrics. The numerical experiments are simple and easily reproducible. Thus, we hope it will encourage other forecasting practitioners to test and use normalizing flows in power system applications such as bidding on electricity markets, scheduling power systems with high renewable energy sources penetration, energy management of virtual power plan or microgrids, and unit commitment., Comment: Version accepted to be published on Applied Energy

Forecasting imbalance prices is essential for strategic participation in the short-term energy markets. A novel two-step probabilistic approach is proposed, with a particular focus on the Belgian case. The first step consists of computing the net regulation volume state transition probabilities. It is modeled as a matrix computed using historical data. This matrix is then used to infer the imbalance prices since the net regulation volume can be related to the level of reserves activated and the corresponding marginal prices for each activation level are published by the Belgian Transmission System Operator one day before electricity delivery. This approach is compared to a deterministic model, a multi-layer perceptron, and a widely used probabilistic technique, Gaussian Processes.

This paper addresses the energy management of a grid-connected photovoltaic plant coupled with a battery energy storage device, within the capacity firming specifications of the French Energy Regulatory Commission. The paper contributions are positioned in the continuity of the studies adopting stochastic models for optimizing the bids of renewable energy sources in a day-ahead market by considering a storage device. The proposed deterministic and stochastic approaches are optimization problems formulated as quadratic problems with linear constraints. The case study is a real microgrid with PV production monitored on-site. The results demonstrate the validity of the stochastic formulation by using an ideal predictor that produces unbiased PV scenarios.

Hierarchical microgrid control levels range from distributed device level controllers that run at a high frequency to centralized controllers optimizing market integration that run much less frequently. Centralized controllers are often subdivided into operational planning controllers that optimize decisions over a time horizon of one or several days, and real-time optimization controllers that deal with actions in the current market period. The coordination of these levels is of paramount importance. In this paper, we propose a value function-based approach as a way to propagate information from operational planning to real-time optimization. We apply this method to an environment where operational planning, using day-ahead forecasts, optimizes at a market period resolution the decisions to minimize the total energy cost and revenues, the peak consumption and injection-related costs, and plans for reserve requirements. While real-time optimization copes with the forecast errors and yields implementable actions based on real-time measurements. The approach is compared to a rule-based controller on three use cases, and its sensitivity to forecast error is assessed.

This paper proposes a strategy to size a grid-connected photovoltaic plant coupled with a battery energy storage device within the \textit{capacity firming} specifications of the French Energy Regulatory Commission. In this context, the sizing problem is challenging due to the two-phase engagement control with a day-ahead nomination and an intraday control to minimize deviations from the planning. The two-phase engagement control is modeled with deterministic and stochastic approaches. The optimization problems are formulated as mixed-integer quadratic problems, using a Gaussian copula methodology to generate PV scenarios, to approximate the mixed-integer non-linear problem of the capacity firming. Then, a grid search is conducted to approximate the optimal sizing for a given selling price using both the deterministic and stochastic approaches. The case study is composed of PV production monitored on-site at the Li\`ege University (ULi\`ege), Belgium.

This paper develops probabilistic PV forecasters by taking advantage of recent breakthroughs in deep learning. It tailored forecasting tool, named encoder-decoder, is implemented to compute intraday multi-output PV quantiles forecasts to efficiently capture the time correlation. The models are trained using quantile regression, a non-parametric approach that assumes no prior knowledge of the probabilistic forecasting distribution. The case study is composed of PV production monitored on-site at the University of Li\`ege (ULi\`ege), Belgium. The weather forecasts from the regional climate model provided by the Laboratory of Climatology are used as inputs of the deep learning models. The forecast quality is quantitatively assessed by the continuous ranked probability and interval scores. The results indicate this architecture improves the forecast quality and is computationally efficient to be incorporated in an intraday decision-making tool for robust optimization.

This paper addresses the energy management of a grid-connected renewable generation plant coupled with a battery energy storage device in the capacity firming market, designed to promote renewable power generation facilities in small non-interconnected grids. The core contribution is to propose a probabilistic forecast-driven strategy, modeled as a min-max-min robust optimization problem with recourse. It is solved using a Benders-dual cutting plane algorithm and a column and constraints generation algorithm in a tractable manner. A dynamic risk-averse parameters selection strategy based on the quantile forecasts distribution is proposed to improve the results. A secondary contribution is to use a recently developed deep learning model known as normalizing flows to generate quantile forecasts of renewable generation for the robust optimization problem. This technique provides a general mechanism for defining expressive probability distributions, only requiring the specification of a base distribution and a series of bijective transformations. Overall, the robust approach improves the results over a deterministic approach with nominal point forecasts by finding a trade-off between conservative and risk-seeking policies. The case study uses the photovoltaic generation monitored on-site at the University of Li\`ege (ULi\`ege), Belgium., Comment: Extended version of the paper accepted for publication in IEEE Transactions on Sustainable Energy

To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons, orbiting an extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Consequently, we use a modified $N$-body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order $\ell = 10$. Its convergence was verified against the `brute-force' algorithm. We computed the coefficients $C_{\ell m},S_{\!\ell m}$ for Kleopatra's shape, assuming a~constant bulk density. For solar-system applications, it was also necessary to implement a variable distance and geometry of observations. Our $\chi^2$ metric then accounts for the absolute astrometry, the relative astrometry (2nd moon with respect to 1st), angular velocities, and also silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra's two moons. Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons, $P_1 = (1.822359\pm0.004156)\,{\rm d}$, $P_2 = (2.745820\pm0.004820)\,{\rm d}$. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), so that regular librations of the critical argument are not present. The resulting mass of Kleopatra, $m_1 = (1.49\pm0.16)\cdot10^{-12}\,M_\odot$ or $2.97\cdot10^{18}\,{\rm kg}$, is significantly lower than previously thought. An implication explained in the accompanying paper (Marchis et al.) is that (216) Kleopatra is a critically rotating body., Comment: accepted in A&A

We consider the Trivially Perfect Editing problem, where one is given an undirected graph $G = (V,E)$ and a parameter $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a trivially perfect graph. The related Trivially Perfect Completion and Trivially Perfect Deletion problems are obtained by only allowing edge additions or edge deletions, respectively. Trivially perfect graphs are both chordal and cographs, and have applications related to the tree-depth width parameter and to social network analysis. All variants of the problem are known to be NP-Complete and to admit so-called polynomial kernels. More precisely, the existence of an $O(k^3)$ vertex-kernel for Trivially Perfect Completion was announced by Guo (ISAAC 2007) but without a stand-alone proof. More recently, Drange and Pilipczuk (Algorithmica 2018) provided $O(k^7)$ vertex-kernels for these problems and left open the existence of cubic vertex-kernels. In this work, we answer positively to this question for all three variants of the problem.

Reducing cycle time is a recurrent concern in the field of business process management. Depending on the process, various interventions may be triggered to reduce the cycle time of a case, for example, using a faster shipping service in an order-to-delivery process or giving a phone call to a customer to obtain missing information rather than waiting passively. Each of these interventions comes with a cost. This paper tackles the problem of determining if and when to trigger a time-reducing intervention in a way that maximizes the total net gain. The paper proposes a prescriptive process monitoring method that uses orthogonal random forest models to estimate the causal effect of triggering a time-reducing intervention for each ongoing case of a process. Based on this causal effect estimate, the method triggers interventions according to a user-defined policy. The method is evaluated on two real-life logs.

Enterprise information systems allow companies to maintain detailed records of their business process executions. These records can be extracted in the form of event logs, which capture the execution of activities across multiple instances of a business process. Event logs may be used to analyze business processes at a fine level of detail using process mining techniques. Among other things, process mining techniques allow us to discover a process model from an event log -- an operation known as automated process discovery. Despite a rich body of research in the field, existing automated process discovery techniques do not fully capture the concurrency inherent in a business process. Specifically, the bulk of these techniques treat two activities A and B as concurrent if sometimes A completes before B and other times B completes before A. Typically though, activities in a business process are executed in a true concurrency setting, meaning that two or more activity executions overlap temporally. This paper addresses this gap by presenting a refined version of an automated process discovery technique, namely Split Miner, that discovers true concurrency relations from event logs containing start and end timestamps for each activity. The proposed technique is also able to differentiate between exclusive and inclusive choices. We evaluate the proposed technique relative to existing baselines using 11 real-life logs drawn from different industries.

We present a broadband ferromagnetic resonance study of the Gilbert damping enhancement ($\Delta \alpha$) due to spin pumping in NiFe/Pt bilayers. The bilayers, which have negligible interfacial spin memory loss, are studied as a function of the Pt layer thickness ($t_{\text{Pt}}$) and temperature (100-293 K). Within the framework of diffusive spin pumping theory, we demonstrate that Dyakonov-Perel (DP) or Elliot-Yaffet (EY) spin relaxation mechanisms acting alone are incompatible with our observations. In contrast, if we consider that the relation between spin relaxation characteristic time ($\tau_{\text{s}}$) and momentum relaxation characteristic time ($\tau_{\text{p}}$) is determined by a superposition of DP and EY mechanisms, the qualitative and quantitative agreement with experimental results is excellent. Remarkably, we found that $\tau_{\text{p}}$ must be determined by the out-of-plane electrical resistivity ($\rho$) of the Pt film and hence its spin diffusion length ($\lambda_{\text{Pt}}$) is independent of $t_{\text{Pt}}$. Our work settles the controversy regarding the $t_{\text{Pt}}$ dependence of $\lambda_{\text{Pt}}$ by demonstrating its fundamental connection with $\rho$ considered along the same direction of spin current flow. \end{abstract}, Comment: 7 pages, 4 figures

Business process simulation is a well-known approach to estimate the impact of changes to a process with respect to time and cost measures -- a practice known as what-if process analysis. The usefulness of such estimations hinges on the accuracy of the underlying simulation model. Data-Driven Simulation (DDS) methods leverage process mining techniques to learn process simulation models from event logs. Empirical studies have shown that, while DDS models adequately capture the observed sequences of activities and their frequencies, they fail to accurately capture the temporal dynamics of real-life processes. In contrast, generative Deep Learning (DL) models are better able to capture such temporal dynamics. The drawback of DL models is that users cannot alter them for what-if analysis due to their black-box nature. This paper presents a hybrid approach to learn process simulation models from event logs wherein a (stochastic) process model is extracted via DDS techniques, and then combined with a DL model to generate timestamped event sequences. An experimental evaluation shows that the resulting hybrid simulation models match the temporal accuracy of pure DL models, while partially retaining the what-if analysis capability of DDS approaches., Comment: 16 pages, 4 figures

The applicability of process mining techniques hinges on the availability of event logs capturing the execution of a business process. In some use cases, particularly those involving customer-facing processes, these event logs may contain private information. Data protection regulations restrict the use of such event logs for analysis purposes. One way of circumventing these restrictions is to anonymize the event log to the extent that no individual can be singled out using the anonymized log. This paper addresses the problem of anonymizing an event log in order to guarantee that, upon disclosure of the anonymized log, the probability that an attacker may single out any individual represented in the original log, does not increase by more than a threshold. The paper proposes a differentially private disclosure mechanism, which oversamples the cases in the log and adds noise to the timestamps to the extent required to achieve the above privacy guarantee. The paper reports on an empirical evaluation of the proposed approach using 14 real-life event logs in terms of data utility loss and computational efficiency.

Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics driven weather forecast systems or climate models can be used to forecast their occurrence or predict their probability. The present work explores the use of deep learning architectures, trained using outputs of a climate model, as an alternative strategy to forecast the occurrence of extreme long-lasting heatwaves. This new approach will be useful for several key scientific goals which include the study of climate model statistics, building a quantitative proxy for resampling rare events in climate models, study the impact of climate change, and should eventually be useful for forecasting. Fulfilling these important goals implies addressing issues such as class-size imbalance that is intrinsically associated with rare event prediction, assessing the potential benefits of transfer learning to address the nested nature of extreme events (naturally included in less extreme ones). We train a Convolutional Neural Network, using 1000 years of climate model outputs, with large-class undersampling and transfer learning. From the observed snapshots of the surface temperature and the 500 hPa geopotential height fields, the trained network achieves significant performance in forecasting the occurrence of long-lasting extreme heatwaves. We are able to predict them at three different levels of intensity, and as early as 15 days ahead of the start of the event (30 days ahead of the end of the event)., Comment: 21 pages, 5 figures

Dynamical models of Solar System evolution have suggested that P-/D-type volatile-rich asteroids formed in the outer Solar System and may be genetically related to the Jupiter Trojans, the comets and small KBOs. Indeed, their spectral properties resemble that of anhydrous cometary dust. High-angular-resolution images of P-type asteroid (87) Sylvia with VLT/SPHERE were used to reconstruct its 3D shape, and to study the dynamics of its two satellites. We also model Sylvia's thermal evolution. The shape of Sylvia appears flattened and elongated. We derive a volume-equivalent diameter of 271 +/- 5 km, and a low density of 1378 +/- 45 kg.m-3. The two satellites orbit Sylvia on circular, equatorial orbits. The oblateness of Sylvia should imply a detectable nodal precession which contrasts with the fully-Keplerian dynamics of the satellites. This reveals an inhomogeneous internal structure, suggesting that Sylvia is differentiated. Sylvia's low density and differentiated interior can be explained by partial melting and mass redistribution through water percolation. The outer shell would be composed of material similar to interplanetary dust particles (IDPs) and the core similar to aqueously altered IDPs or carbonaceous chondrite meteorites such as the Tagish Lake meteorite. Numerical simulations of the thermal evolution of Sylvia show that for a body of such size, partial melting was unavoidable due to the decay of long-lived radionuclides. In addition, we show that bodies as small as 130-150 km in diameter should have followed a similar thermal evolution, while smaller objects, such as comets and the KBO Arrokoth, must have remained pristine, in agreement with in situ observations of these bodies. NASA Lucy mission target (617) Patroclus (diameter~140 km) may, however, be differentiated., Comment: Accepted for publication in A&A