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Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow
Figalli, Alessio,Kang, Moon-Jin,Morales, Javier Springer-Verlag 2018 Archive for rational mechanics and analysis Vol.227 No.3
<P>We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.</P>
( Alejandra García-garcía ),( Luis A. Alvarez-sala-walther ),( Hae-young Lee ),( Cristina Sierra ),( Domingo Pascual-figal ),( Miguel Camafort ) 대한내과학회 2022 The Korean Journal of Internal Medicine Vol.37 No.1
The incidence and prevalence of heart failure (HF) is increasing worldwide, leading to high morbidity and mortality. The global management of HF involves lifestyle changes in addition to pharmacological treatments. Changes include exercise and dietary recommendations, mainly salt and fluid restriction, but without any clear evidence. We conducted a systematic review to analyse the degree of evidence for these dietary recommendations in HF. Only randomized controlled trials (RCT), and observational studies in humans were selected. Studies were considered eligible if they included participants with HF and sodium and/or fluid restriction. Publications in languages other than English or Spanish were excluded. We included 15 studies related to sodium or fluid restriction. Nine RCT and six observational studies showed some improvements in symptoms and quality of life and a degree of reduction in new hospitalizations, but the results are based on limited population groups, applying different methodologies, and with different restriction goals. We found a lack of clear evidence of the benefits of sodium/fluid restriction in chronic HF. The evidence is limited to few studies with conflicting results. Randomized clinical trials are needed to fill this gap in our knowledge.