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The Shapley value for a fair division of group discounts for coordinating cooling loads.

ABSTRACT: We consider a demand response program in which a block of apartments receive a discount from their electricity supplier if they ensure that their aggregate load from air conditioning does not exceed a predetermined threshold. The goal of the participants is to obtain the discount, while ensuring that their individual temperature preferences are also satisfied. As such, the apartments need to collectively optimise their use of air conditioning so as to satisfy these constraints and minimise their costs. Given an optimal cooling profile that secures the discount, the problem that the apartments face then is to divide the total discounted cost in a fair way. To achieve this, we take a coalitional game approach and propose the use of the Shapley value from cooperative game theory, which is the normative payoff division mechanism that offers a unique set of desirable fairness properties. However, applying the Shapley value in this setting presents a novel computational challenge. This is because its calculation requires, as input, the cost of every subset of apartments, which means solving an exponential number of collective optimisations, each of which is a computationally intensive problem. To address this, we propose solving the optimisation problem of each subset suboptimally, to allow for acceptable solutions that require less computation. We show that, due to the linearity property of the Shapley value, if suboptimal costs are used rather than optimal ones, the division of the discount will be fair in the following sense: each apartment is fairly "rewarded" for its contribution to the optimal cost and, at the same time, is fairly "penalised" for its contribution to the discrepancy between the suboptimal and the optimal costs. Importantly, this is achieved without requiring the optimal solutions.

SUBMITTER: Maleki S

PROVIDER: S-EPMC6953874 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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The Shapley value for a fair division of group discounts for coordinating cooling loads.

Maleki Sasan S Rahwan Talal T Ghosh Siddhartha S Malibari Areej A Alghazzawi Daniyal D Rogers Alex A Beigy Hamid H Jennings Nicholas R NR

PloS one 20200110 1

We consider a demand response program in which a block of apartments receive a discount from their electricity supplier if they ensure that their aggregate load from air conditioning does not exceed a predetermined threshold. The goal of the participants is to obtain the discount, while ensuring that their individual temperature preferences are also satisfied. As such, the apartments need to collectively optimise their use of air conditioning so as to satisfy these constraints and minimise their ...[more]

PMID: 31923244

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Project description:UnlabelledCell division in bacteria is driven by a cytoskeletal ring structure, the Z ring, composed of polymers of the tubulin-like protein FtsZ. Z-ring formation must be tightly regulated to ensure faithful cell division, and several mechanisms that influence the positioning and timing of Z-ring assembly have been described. Another important but as yet poorly understood aspect of cell division regulation is the need to coordinate division with cell growth and nutrient availability. In this study, we demonstrated for the first time that cell division is intimately linked to central carbon metabolism in the model Gram-positive bacterium Bacillus subtilis. We showed that a deletion of the gene encoding pyruvate kinase (pyk), which produces pyruvate in the final reaction of glycolysis, rescues the assembly defect of a temperature-sensitive ftsZ mutant and has significant effects on Z-ring formation in wild-type B. subtilis cells. Addition of exogenous pyruvate restores normal division in the absence of the pyruvate kinase enzyme, implicating pyruvate as a key metabolite in the coordination of bacterial growth and division. Our results support a model in which pyruvate levels are coupled to Z-ring assembly via an enzyme that actually metabolizes pyruvate, the E1? subunit of pyruvate dehydrogenase. We have shown that this protein localizes over the nucleoid in a pyruvate-dependent manner and may stimulate more efficient Z-ring formation at the cell center under nutrient-rich conditions, when cells must divide more frequently.ImportanceHow bacteria coordinate cell cycle processes with nutrient availability and growth is a fundamental yet unresolved question in microbiology. Recent breakthroughs have revealed that nutritional information can be transmitted directly from metabolic pathways to the cell cycle machinery and that this can serve as a mechanism for fine-tuning cell cycle processes in response to changes in environmental conditions. Here we identified a novel link between glycolysis and cell division in Bacillus subtilis. We showed that pyruvate, the final product of glycolysis, plays an important role in maintaining normal division. Nutrient-dependent changes in pyruvate levels affect the function of the cell division protein FtsZ, most likely by modifying the activity of an enzyme that metabolizes pyruvate, namely, pyruvate dehydrogenase E1?. Ultimately this system may help to coordinate bacterial division with nutritional conditions to ensure the survival of newborn cells.

Project description:BackgroundIn gene expression analysis, statistical tests for differential gene expression provide lists of candidate genes having, individually, a sufficiently low p-value. However, the interpretation of each single p-value within complex systems involving several interacting genes is problematic. In parallel, in the last sixty years, game theory has been applied to political and social problems to assess the power of interacting agents in forcing a decision and, more recently, to represent the relevance of genes in response to certain conditions.ResultsIn this paper we introduce a Bootstrap procedure to test the null hypothesis that each gene has the same relevance between two conditions, where the relevance is represented by the Shapley value of a particular coalitional game defined on a microarray data-set. This method, which is called Comparative Analysis of Shapley value (shortly, CASh), is applied to data concerning the gene expression in children differentially exposed to air pollution. The results provided by CASh are compared with the results from a parametric statistical test for testing differential gene expression. Both lists of genes provided by CASh and t-test are informative enough to discriminate exposed subjects on the basis of their gene expression profiles. While many genes are selected in common by CASh and the parametric test, it turns out that the biological interpretation of the differences between these two selections is more interesting, suggesting a different interpretation of the main biological pathways in gene expression regulation for exposed individuals. A simulation study suggests that CASh offers more power than t-test for the detection of differential gene expression variability.ConclusionCASh is successfully applied to gene expression analysis of a data-set where the joint expression behavior of genes may be critical to characterize the expression response to air pollution. We demonstrate a synergistic effect between coalitional games and statistics that resulted in a selection of genes with a potential impact in the regulation of complex pathways.

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The Shapley value for a fair division of group discounts for coordinating cooling loads.

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The Shapley value for a fair division of group discounts for coordinating cooling loads.

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