Global well-posedness for a coupled modified kdv system

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modi ed Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura's Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura's Transform that takes a KdV system to the system we are considering. To overcome this di culty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura's Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.Fundação para a Ciência e a Tecnologia (FCT

Autoantibodies targeting G protein-coupled receptors: an evolving history in autoimmunity. Report of the 4th international symposium

G protein-coupled receptors (GPCR) are involved in various physiological and pathophysiological processes. Functional autoantibodies targeting GPCRs have been associated with multiple disease manifestations in this context. Here we summarize and discuss the relevant findings and concepts presented in the biennial International Meeting on autoantibodies targeting GPCRs (the 4th Symposium), held in Lübeck, Germany, 15-16 September 2022. The symposium focused on the current knowledge of these autoantibodies' role in various diseases, such as cardiovascular, renal, infectious (COVID-19), and autoimmune diseases (e.g., systemic sclerosis and systemic lupus erythematosus). Beyond their association with disease phenotypes, intense research related to the mechanistic action of these autoantibodies on immune regulation and pathogenesis has been developed, underscoring the role of autoantibodies targeting GPCRs on disease outcomes and etiopathogenesis. The observation repeatedly highlighted that autoantibodies targeting GPCRs could also be present in healthy individuals, suggesting that anti-GPCR autoantibodies play a physiologic role in modeling the course of diseases. Since numerous therapies targeting GPCRs have been developed, including small molecules and monoclonal antibodies designed for treating cancer, infections, metabolic disorders, or inflammatory conditions, anti-GPCR autoantibodies themselves can serve as therapeutic targets to reduce patients' morbidity and mortality, representing a new area for the development of novel therapeutic interventions