Abstract-Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent results have shown that structural balance is necessary for polarization in networks with fixed, strongly connected neighbor relationships when the opinion dynamics are described by DeGroot-type averaging rules. We develop this line of research in this paper in two steps. First, we consider fixed, not necessarily strongly connected, neighbor relationships. It is shown that if the network includes a strongly connected subnetwork containing mistrust, which influences the rest of the network, then no opinion clustering is possible when that subnetwork is not structurally balanced; all the opinions become neutralized in the end. In contrast, it is shown that when that subnetwork is indeed structurally balanced, the agents of the subnetwork evolve into two polarized camps and the opinions of all other agents in the network spread between these two polarized opinions. Second, we consider time-varying neighbor relationships. We show that the opinion separation criteria carry over if the conditions for fixed graphs are extended to joint graphs. The results are developed for both discrete-time and continuous-time models.
The emergence of multi-drug-resistant
pathogens threatens the healthcare
systems world-wide. Recent advances in phototherapy (PT) approaches
mediated by photo-antimicrobials (PAMs) provide new opportunities
for the current serious antibiotic resistance. During the PT treatment,
reactive oxygen species or heat produced by PAMs would react with
the cell membrane, consequently leaking cytoplasm components and effectively
eradicating different pathogens like bacteria, fungi, viruses, and
even parasites. This Perspective will concentrate on the development
of different organic photo-antimicrobials (OPAMs) and their application
as practical therapeutic agents into therapy for local infections,
wound dressings, and removal of biofilms from medical devices. We
also discuss how to design highly efficient OPAMs by modifying the
chemical structure or conjugating with a targeting component. Moreover,
this Perspective provides a discussion of the general challenges and
direction for OPAMs and what further needs to be done. It is hoped
that through this overview, OPAMs can prosper and will be more widely
used for microbial infections in the future, especially at a time
when the global COVID-19 epidemic is getting more serious.
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