Rodriguezgleason5399

21; 95% CI, 1.08-1.37 for each additional enhancer), and having ≥3 enhancers represents an optimum threshold for incremental prediction (C statistic, 0.766; net reclassification index, 0.041; integrated discrimination index, 0.010; P≤0.007). On the other hand, CAC was superior to individual enhancers (C statistic, 0.774; net reclassification index, 0.073; integrated discrimination index, 0.010; P less then 0.001), reliably reclassifies intermediate-risk participants with less then 3 risk enhancers (event rate, 3.5% if no CAC and 9.8% if positive CAC), but offered no reclassification among participants with ≥3 enhancers. Conclusions The individual risk enhancers evaluated in this study provided no or only marginal incremental information added to the pooled cohort equation. However, the presence of ≥3 risk enhancers reliably identified intermediate-risk patients that will benefit from statin therapy, and further CAC testing may be considered among those with less then 3 risk enhancers.We examine how different pricing frameworks deal with non-convex features typical of day-ahead energy prices when the power system is hydro-dominated, like in Brazil. For the system operator, requirements of minimum generation translate into feasibility issues that are fundamental to carry the generated power through the network. When utilities are remunerated at a price depending on Lagrange multipliers computed for a system with fixed commitment, the corresponding values sometimes fail to capture a signal that recovers costs. Keeping in mind recent discussions for the Brazilian power system, we analyse mechanisms that provide a compromise between the needs of the generators and those of the system operator. After characterizing when a price supports a generation plan, we explain in simple terms dual prices and related concepts, such as minimal uplifts and bi-dual problems. We present a new pricing mechanism that guarantees cost recovery to all agents, without over-compensations. Instead of using Lagrange multipliers, the price is defined as the solution to an optimization problem. The behaviour of the new rule is compared to two other proposals in the literature on illustrative examples, including a small, yet representative, hydro-thermal system. This article is part of the theme issue 'The mathematics of energy systems'.The increased penetration of renewable energy sources into existing power systems induces challenges in supply-demand balancing. Demand-side flexibility is seen as an option to accommodate variability and limited predictability from renewable energy generation. Heat pumps at residential level, if well coordinated, can be one of those flexibility sources. The complexity involved is high though, since their coordinated operation combines control, population effects and the fact agents may actually not behave as rational decision-makers. We describe here a coordinated control framework that accounts for those aspects altogether. Decentralized model predictive control for large populations of heterogeneous agents is employed. As the cost to be minimized is affected by the population behaviour as a whole through the electricity price, the decentralized control is re-thought as a mean-field game. Existence and uniqueness of a Nash equilibrium are discussed while the Picard-Banach algorithm is used as a solution approach. It is extended to the case of bounded-rational agents. The impact on system dynamics of modelling agents as bounded rational is illustrated through numerical simulations. This article is part of the theme issue 'The mathematics of energy systems'.This paper develops an econometric price model with fundamental impacts for intraday electricity markets of 15-min contracts. A unique dataset of intradaily updated forecasts of renewable power generation is analysed. We use a threshold regression model to examine how 15-min intraday trading depends on the slope of the merit order curve. Our estimation results reveal strong evidence of mean reversion in the price formation mechanism of 15-min contracts. BTK inhibitor Additionally, prices of neighbouring contracts exhibit strong explanatory power and a positive impact on prices of a given contract. We observe an asymmetric effect of renewable forecast changes on intraday prices depending on the merit-order-curve slope. In general, renewable forecasts have a higher explanatory power at noon than in the morning and evening, but price information is the main driver of 15-min intraday trading. This article is part of the theme issue 'The mathematics of energy systems'.This paper advocates for a progressive rethinking of the day-ahead/intra-day power system security management practice in the low-carbon energy transition era. As a starting point, the need for coordination between multi-area transmission system operators in order to efficiently exploit the value of grid flexibility towards operating the low-carbon, multi-area power system securely and economically is emphasized. On this basis, the core proposal of this paper is the adoption of a new approach to day-ahead/intra-day multi-area power system security management, inspired by the principles of cooperative game theory. The proposed approach relies on counterfactual analysis to evaluate the (positive and/or negative) impact of each distinctive control area to the common security of the multi-area system, thus providing clear economic incentives to achieve the required coordination. This proposal is not a marginal approach and notably facilitates the integration of more detailed physical modelling (including the non-convexities of the power system) in the inter-TSO settlement of the multi-area interconnected system security management cost. The proposed framework allows some level of subsidiarity and the definition of hedging products to cover ex-post costs. Further from the blueprint of the proposed approach, the paper presents a demonstrative implementation in the context of static N-1 security management and discusses prominent research and development pathways in order to progressively put such vision into practice. This article is part of the theme issue 'The mathematics of energy systems'.