Abstract
Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region is well established, but its neighbouring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g. stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be a scalar field of toroidal distribution, associated with ultralight dark matter particles, surrounding the Kerr black hole. Such a field is a form of 'hair' expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.

Abstract
This paper addresses the participation of an aggregator of small prosumersin the energy and tertiary reserve markets. A two-stage stochastic optimization model is proposed to exploit the load and generation flexibility of the prosumers. The aim is to define energy and tertiary reserve bids to minimize the net cost of the aggregator buying and selling energy in the day-ahead and real-time markets, as well as to maximize the revenue of selling tertiary reserve during the real-time stage. Scenario-based stochastic programming is used to deal with the uncertainties of photovoltaic power generation, electricity demand, outdoor temperature, end-users' behavior, and preferences. A case study of 1000 small prosumers from MIBEL is used to compare the proposed strategy to two other strategies. The numerical results show that the proposed strategy reduces the bidding net cost of the aggregator by 48% when compared to an inflexible strategy typically used by retailers.

Abstract
Retailers need demand forecasts at different levels of aggregation in order to support a variety of decisions along the supply chain. To ensure aligned decision-making across the hierarchy, it is essential that forecasts at the most disaggregated level add up to forecasts at the aggregate levels above. It is not clear if these aggregate forecasts should be generated independently or by using an hierarchical forecasting method that ensures coherent decision-making at the different levels but does not guarantee, at least, the same accuracy. To give guidelines on this issue, our empirical study investigates the relative performance of independent and reconciled forecasting approaches, using real data from a Portuguese retailer. We consider two alternative forecasting model families for generating the base forecasts; namely, state space models and ARIMA. Appropriate models from both families are chosen for each time-series by minimising the bias-corrected Akaike information criteria. The results show significant improvements in forecast accuracy, providing valuable information to support management decisions. It is clear that reconciled forecasts using the Minimum Trace Shrinkage estimator (MinT-Shrink) generally improve on the accuracy of the ARIMA base forecasts for all levels and for the complete hierarchy, across all forecast horizons. The accuracy gains generally increase with the horizon, varying between 1.7% and 3.7% for the complete hierarchy. It is also evident that the gains in forecast accuracy are more substantial at the higher levels of aggregation, which means that the information about the individual dynamics of the series, which was lost due to aggregation, is brought back again from the lower levels of aggregation to the higher levels by the reconciliation process, substantially improving the forecast accuracy over the base forecasts.

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Abstract
Distribution networks are more active due to demand response programs which causes flexible behavior of end-users. This paper proposes an iterative algorithm to transact electricity based on interplay between aggregators and the Distribution Company (DisCo) considering the amount which the bottom-layer of a distribution system can provide from the aggregated end-users. The performance of the proposed trading algorithm was tested on a 33-bus test system for a distribution network. Similations for different scenarios were made to analyze the impact of different flexibility constraints on sustainability of the system and expected cost on distribution grid's player.

Abstract