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A model of Edgeworthian economies is studied, in which participants are randomly chosen at each period to exchange two goods to increase their utilities, as described by the Cobb-Douglas utility function. Participants can trade deviating from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. The article aims to study the convergence to equilibrium in a situation where individuals or small groups of participants trade in a market, and prices are determined by interactions between the participants rather than by demand and supply alone. A dynamic matching and bargaining game is considered, with statistical duality imposed on the market game, ensuring that each participant has a counterpart with opposite preferences. This guaranties that there is sufficient incentive for trade. It is shown that, in each period, the expected logarithm of the trading price in the Edgeworthian economy equals the expected Walrasian price. This demonstrates that, under symmetry conditions, the trading price in the Edgeworthian economy is related to the Walrasian price, indicating convergence of the trading price in the Edgeworthian economy towards the Walrasian price. The study suggests that, under the right conditions, the decentralized trading model leads to price convergence similar to what would be expected in a more classical Walrasian economy, where prices balance demand and supply.

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Background/Objectives: Type 2 diabetes mellitus (T2DM) is a chronic condition marked by hyperglycemia, which can affect metabolic, vascular, and hematological parameters. A low-carbohydrate, high-fat (LCHF) diet has been shown to improve glycemic control and blood pressure regulation. Exercise in hypoxia (EH) enhances insulin sensitivity, erythropoiesis, and angiogenesis. The combination of LCHF and EH may offer a promising strategy for managing T2DM and hypertension (HTN), although evidence remains limited. This study aimed to assess the effects of an eight-week normobaric EH intervention at 3000 m simulated altitude combined with an LCHF diet on hematological and lipid profiles, inflammation, and blood pressure in older patients with T2DM and HTN. Methods: Forty-two diabetic patients with HTN were randomly assigned to three groups: (1) control group (control diet + exercise in normoxia), (2) EH group (control diet + EH), and (3) intervention group (EH+LCHF) Baseline and eight-week measurements included systolic, diastolic, and mean blood pressure (SBP, DBP, MAP), hematological and lipid profiles, and inflammation biomarkers. Results: Blood pressure decreased after the intervention (p < 0.001), with no significant differences between groups (SBP: p = 0.151; DBP: p = 0.124; MAP: p = 0.18). No differences were observed in lipid profile or C-reactive protein levels (p > 0.05). Mean corpuscular hemoglobin (MCH) increased in the EH group (p = 0.027), while it decreased in the EH+LCHF group (p = 0.046). Conclusions: Adding hypoxia or restricting carbohydrates did not provide additional benefits on blood pressure in T2DM patients with HTN. Further elucidation of the mechanisms underlying hematological adaptations is imperative.

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Introdução: Os hábitos alimentares são uma das principais causas modificáveis de doenças crónicas não transmissíveis. A Dieta Mediterrânica é conhecida por ser um padrão alimentar protetor da saúde e sustentável. Nas últimas décadas, Portugal, tem-se distanciado deste padrão alimentar e aumentado o consumo de alimentos ultraprocessados. Objetivos: Avaliar a adesão ao Padrão Alimentar Mediterrânico, o consumo de alimentos ultraprocessados e fatores associados, em crianças e adolescentes. Metodologia: Estudo transversal, observacional descritivo. Aplicou-se um questionário, que incluía a versão portuguesa do Índice KIDMED e um Índice de consumo de alimentos ultraprocessados construído para este projeto, a uma amostra de conveniência de crianças e adolescentes com idades entre os 10 e os 19 anos. Os dados foram tratados e analisados no programa estatístico SPSS® com um nível de confiança de 95%. Resultados: A amostra incluiu 506 participantes, sendo 54,3% do sexo feminino, com uma idade média de 14,1 anos (dp = 2,5). A adesão ao Padrão Alimentar Mediterrânico correlacionou-se com o consumo de alimentos ultraprocessados (r = 0,447; p < 0,001). Verificou-se uma elevada adesão ao Padrão Alimentar Mediterrânico por 47,8% dos participantes, média adesão por 47,2% e baixa adesão por 4,9%, sendo mais elevada nos indivíduos fisicamente ativos (?2p = 0,012; p = 0,021), nos que têm hábitos de sono à semana adequados (?2p = 0,009; p = 0,045) e nos mais novos (r = -0,112; p = 0,003). O consumo de alimentos ultraprocessados revelou uma pontuação média de 21,8 (dp = 4,8), sendo o sexo masculino (?2p = 0,031; p < 0,001) e os que passam mais tempo em frente ao ecrã (?2p = 0,170; p = 0,005) quem mais consome este tipo de alimentos. Conclusões: Observa-se a necessidade de intervir ao nível da promoção e difusão da Dieta Mediterrânica, uma vez que parece ter impacto na diminuição do consumo de alimentos ultraprocessados, de promover a atividade física, estimular hábitos de sono adequados e mitigar o tempo que as crianças e adolescentes passam em frente aos ecrãs.

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In the original publication [1], there was a minor error in Figure 1 and Table 6. Unfortunately, Figure 1 presented a smaller text size than appropriate, making it difficult for the reader, in addition to the abbreviation “FiO2” instead of “FiO2”. Then, in Table 6, the basal lactate values between the groups were corrected and the lactate peak values were included. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated. © 2024 by the authors.

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