Load Frequency Control: A Deep Multi-Agent Reinforcement Learning Approach

The paradigm shift in energy generation towards microgrid-based architectures is changing the landscape of the energy control structure heavily in distribution systems. More specifically, distributed generation is deployed in the network demanding decentralised control mechanisms to ensure reliable power system operations. In this work, a Multi-Agent Reinforcement Learning approach is proposed to deliver an agentbased solution to implement load frequency control without the need of a centralised authority. Multi-Agent Deep Deterministic Policy Gradient is used to approximate the frequency control at the primary and the secondary levels. Each generation unit is represented as an agent that is modelled by a Recurrent Neural Network. Agents learn the optimal way of acting and interacting with the environment to maximise their long term performance and to balance generation and load, thus restoring frequency. In this paper we prove using three test systems, with two, four and eight generators, that our Multi-Agent Reinforcement Learning approach can efficiently be used to perform frequency control in a decentralised way

Parallel imports, innovations and national welfare: The role of the sizes of the income classes and national markets for health care.

This paper shows that regardless of any intra-country income differences, parallel imports result in a lower level of health-care innovation but, contrary to popular as well as conventional theoretical wisdom, a lower price in the Third World compared to market-based discrimination. Despite such a lower price, however, parallel imports unambiguously make all buyers in the Third World worse off when intra-country income disparity exists. On the other hand, even discarding the MNC's profit, there will be cases in which the richer country prefers price discrimination as well. That is, in those cases, no countries will have any incentive under the welfare criterion to undo price discrimination, contrary to Richardso

Cooler and bigger than thought? Planetary host stellar parameters from the InfraRed Flux Method

Effective temperatures and radii for 92 planet-hosting stars as determined from the InfraRed Flux Method (IRFM) are presented and compared with those given by other authors using different approaches. The IRFM temperatures we have derived are systematically lower than those determined from the spectroscopic condition of excitation equilibrium, the mean difference being as large as 110 K. They are, however, consistent with previous IRFM studies and with the colors derived from Kurucz and MARCS model atmospheres. Comparison with direct measurements of stellar diameters for 7 dwarf stars, which approximately cover the range of temperatures of the planet-hosting stars, suggest that the IRFM radii and temperatures are reliable in an absolute scale. A better understanding of the fundamental properties of the stars with planets will be achieved once this discrepancy between the IRFM and the spectroscopic temperature scales is resolved.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics

We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized non-linear abelian gauge models in three space dimensions. These models are defined by lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of non-linear electrodynamics supporting ESS non-topological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviours of their ESS solutions in flat space (or, equivalently, by the behaviour of the lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordstr\"om case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the ADM mass, the charge and the soliton energy. Most of the results concerning well known models, such as the electrodynamics of Maxwell, Born-Infeld and the Euler-Heisenberg effective lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.Comment: 11 pages, revtex4, 4 figures; added references; introduction, conclusions and several sections extended, 2 additional figures included, title change

The relationship of drug reimbursement with the price and the quality of pharmaceutical innovations

This paper studies the strategic interaction between pharmaceutical firms' pricing decisions and government agencies' reimbursement decisions which discriminate between patients by giving reimbursement rights to patients for whom the drug is most effective. We show that if the reimbursement decision preceeds the pricing decision, the agency only reimburses some patients if the private and public health benefits from the new drug diverge. That is, when (i) there are large externalities of consuming the drug and (ii) the difference in costs between the new drug and the alternative treatment is large. Alternatively, if the firm can commit to a price in advance of the reimbursement decision, we identify a strategic effect which implies that by committing to a high price ex ante, the firm can force a listing outcome and make the agency more willing to reimburse than in the absence of commitment