Abstract
An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data.

Abstract
Power systems are evolving very rapidly namely in what concerns the technologies used to generate electricity, the diversification of commercial relationships involving different agents and more specifically the empowerment of consumers. In this scope, several countries passed new legislation to induce the installation of Renewable Energy Communities, RECs, to induce new investments at a local level, to empower end consumers and to increase their self-sufficiency. However, the way Local Energy Markets, LEMs, will be integrated into Wholesale Markets, WSM, is not yet fully established. To this end, this paper proposes a design and an optimization model to increase the mentioned self-sufficiency level, to better manage the energy produced locally, also admitting the installation of battery storage units, and to profit as much as possible of them. LEM interaction with WSM, is based on an Agent Based Model architecture equipped with a Q-learning strategy. An economic assessment is also included, in order to get insights if some level of exemption, for instance associated with some components of the Access Tariffs, have to be considered in order to induce the massification of RECs.

Abstract
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Abstract

Abstract
Diabetic foot ulcers (DFU) are one of the most frequent and debilitating complications of diabetes. DFU wound healing is a highly complex process, resulting in significant medical, economic and social challenges. Therefore, early identification of patients with a high-risk profile would be important to adequate treatment and more successful health outcomes. This study explores risk assessment profiles for DFU healing and healing prognosis, using machine learning predictive approaches and decision tree algorithms. Patients were evaluated at baseline (T0; N = 158) and 2 months later (T1; N = 108) on sociodemographic, clinical, biochemical and psychological variables. The performance evaluation of the models comprised F1-score, accuracy, precision and recall. Only profiles with F1-score >0.7 were selected for analysis. According to the two profiles generated for DFU healing, the most important predictive factors were illness representations on T1 IPQ-B (IPQ-B <= 9.5 and < 10.5) and the DFU duration (<= 13 weeks). The two predictive models for DFU healing prognosis suggest that biochemical factors are the best predictors of a favorable healing prognosis, namely IL-6, microRNA-146a-5p and PECAM-1 at T0 and angiopoietin-2 at T1. Illness perception at T0 (IPQ-B <= 39.5) also emerged as a relevant predictor for healing prognosis. The results emphasize the importance of DFU duration, illness perception and biochemical markers as predictors of healing in chronic DFUs. Future research is needed to confirm and test the obtained predictive models.

Abstract
Context. In the Milky Way the central massive black hole, Sgr A*, coexists with a compact nuclear star cluster that contains a sub-parsec concentration of fast-moving young stars called S-stars. Their location and age are not easily explained by current star formation models, and in several scenarios the presence of an intermediate-mass black hole (IMBH) has been invoked.Aims. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2, the best known S-star, to investigate whether a second massive object could be present deep in the Galactic Centre (GC) in the form of an IMBH binary companion to Sgr A*.Methods. To solve the three-body problem, we used a post-Newtonian framework and consider two types of settings: (i) a hierarchical set-up where the star S2 orbits the Sgr A*-IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies outside the S2 orbit. In both cases we explore the full 20-dimensional parameter space by employing a Bayesian dynamic nested sampling method.Results. For the hierarchical case we find the strongest constraints: IMBH masses > 2000 M-circle dot on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case, the chaotic nature of the problem becomes significant: the parameter space contains several pockets of valid IMBH solutions. However, a closer analysis of their impact on the resident stars reveals that IMBHs on semi-major axes larger than S2 tend to disrupt the S-star cluster in less than a million years. This makes the existence of an IMBH among the S-stars highly unlikely.Conclusions. The current S2 data do not formally require the presence of an IMBH. If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2 orbit that moves on a short and significantly inclined trajectory or an IMBH with a semi-major axis > 1 ''. We provide the parameter maps of valid IMBH solutions in the GC and discuss the general structure of our results and how future observations can help to put even stronger constraints on the properties of IMBHs in the GC.