The most critical step during viral infection is when viruses enter the cell. A novel coronavirusSARS-CoV-2 penetrates into alveolar cells through the transmembrane serine proteaseTMPRSS2. Extensive studies show that a clinically approved drug from Japan and South Korea,camostat mesylate inactivates TMPRSS2 in order to prevent the infection. However, these basicstudies have not been translated to “bedside”, and their effectiveness has not been clinicallyconfirmed yet. Here, we describe another potential antiviral substance, commonly used in theclinical practice as a mucolytics – bromhexine hydrochloride. Causing only few mild sideeffects, it may serve as either a new therapeutic strategy during early stages of the disease or apreventive agent blocking SARS-CoV-2 entry into alveolar cells through TMPRSS2.Therefore, in this review, we discuss these possible approaches based on the current data.
Splice type surface singularities, introduced in 2002 by Neumann and Wahl, provide all examples known so far of integral homology spheres which appear as links of isolated complete intersections of dimension two. They are determined, up to equisingularity, by decorated trees called splice diagrams. In 2005, Neumann and Wahl formulated their Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a special kind of decomposition into pieces of the Milnor fibers of the associated singularities. These pieces are constructed from the Milnor fibers of the splice type singularities determined by the subdiagrams on both sides of the chosen edge. In this paper we give an overview of this conjecture and a detailed outline of its proof, based on techniques from tropical geometry and log geometry in the sense of Fontaine and Illusie. The crucial log geometric ingredient is the operation of rounding of a complex logarithmic space introduced in 1999 by Kato and Nakayama. It is a functorial generalization of the operation of real oriented blowup. The use of the latter to study Milnor fibrations was pioneered by A'Campo in 1975.
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