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We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

Pulmonary arterial hypertension (PAH) is a fatal disease with a well-established sexual dimorphism. Activated inflammatory response and altered redox homeostasis, both known to manifest in a sex-specific manner, are implicated in the pathogenic mechanisms involved in PAH development. This study aimed to evaluate the impact of sex and plasma redox status on circulating cytokine profiles. Plasma oxidation-reduction potential (ORP), as a substitute measure of redox status, was analyzed in male and female Group 1 PAH and healthy subjects. The profiles of 27 circulating cytokines were compared in 2 PAH groups exhibiting the highest and lowest quartile for plasma ORP, correlated with clinical parameters, and used to predict patient survival. The analysis of the PAH groups with the highest and lowest ORP revealed a correlation between elevated cytokine levels and increased oxidative stress in females. In contrast, in males, cytokine expressions were increased in the lower oxidative environment (except for IL-1b). Correlations of the increased cytokine expressions with PAH severity were highly sex-dependent and corresponded to the increase in PAH severity in males and less severe PAH in females. Machine learning algorithms trained on the combined cytokine and redox profiles allowed the prediction of PAH mortality with 80% accuracy. We conclude that the profile of circulating cytokines in PAH patients is redox- and sex-dependent, suggesting the vital need to stratify the patient cohort subjected to anti-inflammatory therapies. Combined cytokine and/or redox profiling showed promising value for predicting the patients' survival., (Copyright © 2022 The Author(s). Published by Elsevier Inc. All rights reserved.)