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A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first-order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE-based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019 (COVID-19) and its associated severity have been linked to uncontrolled inflammation and may be associated with changes in the microbiome of mucosal sites including the gastrointestinal tract and oral cavity. These sites play an important role in host-microbe homeostasis, and disruption of epithelial barrier integrity during COVID-19 may potentially lead to exacerbated inflammation and immune dysfunction. Outcomes in COVID-19 are highly disparate, ranging from asymptomatic to fatal, and the impact of microbial dysbiosis on disease severity is unclear. Here, we obtained plasma, rectal swabs, oropharyngeal swabs, and nasal swabs from 86 patients hospitalized with COVID-19 and 12 healthy volunteers. We performed 16S rRNA sequencing to characterize the microbial communities in the mucosal swabs and measured concentrations of circulating cytokines, markers of gut barrier integrity, and fatty acids in the plasma samples. We compared these plasma concentrations and microbiomes between healthy volunteers and COVID-19 patients, some of whom had unfortunately died by the end of the study enrollment, and performed a correlation analysis between plasma variables and bacterial abundances. Rectal swabs of COVID-19 patients had reduced abundances of several commensal bacteria including Faecalibacterium prausnitzii and an increased abundance of the opportunistic pathogens Eggerthella lenta and Hungatella hathewayi . Furthermore, the oral pathogen Scardovia wiggsiae was more abundant in the oropharyngeal swabs of COVID-19 patients who died. The abundance of both H. hathewayi and S. wiggsiae correlated with circulating inflammatory markers including IL-6, highlighting the possible role of the microbiome in COVID-19 severity and providing potential therapeutic targets for managing COVID-19.IMPORTANCEOutcomes in coronavirus disease 2019 (COVID-19) are highly disparate and are associated with uncontrolled inflammation; however, the individual factors that lead to this uncontrolled inflammation are not fully understood. Here, we report that severe COVID-19 is associated with systemic inflammation, microbial translocation, and microbial dysbiosis. The rectal and oropharyngeal microbiomes of COVID-19 patients were characterized by a decreased abundance of commensal bacteria and an increased abundance of opportunistic pathogens, which positively correlated with markers of inflammation and microbial translocation. These microbial perturbations may, therefore, contribute to disease severity in COVID-19 and highlight the potential for microbiome-based interventions in improving COVID-19 outcomes., Competing Interests: The authors declare no conflict of interest.