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Spike proteins, 1200 amino acids, are divided into two nearly equal parts, S1 and S2. We review here phase transition theory, implemented quantitatively by thermodynamic scaling. The theory explains the evolution of Coronavirus extremely high contagiousness caused by a few mutations from CoV2003 to CoV2019 identified among hundreds in S1. The theory previously predicted the unprecedented success of spike-based vaccines. Here we analyze impressive successes by McClellan et al., 2020, in stabilizing their original S2P vaccine to Hexapro. Hexapro has expanded the two proline mutations of S2P, 2017, to six combined proline mutations in S2. Their four new mutations are the result of surveying 100 possibilities in their detailed structure-based context Our analysis, based on only sparse publicly available data, suggests new proline mutations could improve the Hexapro combination to Octapro or beyond.
Modern technology unintentionally provides resources that enable the trust of everyday interactions to be undermined. Some authentication schemes address this issue using devices that give unique outputs in response to a challenge. These signatures a
Antibody therapeutics and vaccines are among our last resort to end the raging COVID-19 pandemic. They, however, are prone to over 5,000 mutations on the spike (S) protein uncovered by a Mutation Tracker based on over 200,000 genome isolates. It is i
We consider pressing sequences, a certain kind of transformation of graphs with loops into empty graphs, motivated by an application in phylogenetics. In particular, we address the question of when a graph has precisely one such pressing sequence, th
A matching $M$ in a graph $G$ is said to be uniquely restricted if there is no other matching in $G$ that matches the same set of vertices as $M$. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted matching i
In this paper we generalize the concept of uniquely $K_r$-saturated graphs to hypergraphs. Let $K_r^{(k)}$ denote the complete $k$-uniform hypergraph on $r$ vertices. For integers $k,r,n$ such that $2le k <r<n$, a $k$-uniform hypergraph $H$ with $n$