RESUMO
The set of singular values of a digraph with respect to a vertex-degree based topological index is the set of all singular values of its general adjacency matrix. The spectral norm is the largest singular value and the energy the sum of the singular values. In this paper we characterize the digraphs which have exactly one singular value different from zero and the digraphs for which all singular values are equal. As a consequence, we deduce sharp upper and lower bounds for the spectral norm and energy of digraphs. In addition to being a natural generalization, proving the results in the general setting of digraphs allows us to deduce new results on graph energy.
RESUMO
New antiviral treatments are needed to deal with the unpredictable emergence of viruses. Furthermore, vaccines and antivirals are only available for just a few viral infections, and antiviral drug resistance is an increasing concern. Cyanidin (a natural product also called A18), a key flavonoid that is present in red berries and other fruits, attenuates the development of several diseases, through its anti-inflammatory effects. Regarding its mechanism of action, A18 was identified as an IL-17A inhibitor, resulting in the attenuation of IL-17A signaling and associated diseases in mice. Importantly, A18 also inhibits the NF-κB signaling pathway in different cell types and conditions in vitro and in vivo. In this study, we report that A18 restricts RSV, HSV-1, canine coronavirus, and SARS-CoV-2 multiplication, indicating a broad-spectrum antiviral activity. We also found that A18 can control cytokine and NF-κB induction in RSV-infected cells independently of its antiviral activity. Furthermore, in mice infected with RSV, A18 not only significantly reduces viral titers in the lungs, but also diminishes lung injury. Thus, these results provide evidence that A18 could be used as a broad-spectrum antiviral and may contribute to the development of novel therapeutic targets to control these viral infections and pathogenesis.