Structural and functional characterizations of altered infectivity and immune evasion of SARS-CoV-2 Omicron variant

The SARS-CoV-2 Omicron with increased fitness is spreading rapidly worldwide. Analysis of cryo-EM structures of the Spike (S) from Omicron reveals amino acid substitutions forging new interactions that stably maintain an active conformation for receptor recognition. The relatively more compact domain organization confers improved stability and enhances attachment but compromises the efficiency of viral fusion step. Alterations in local conformation, charge and hydrophobic microenvironments underpin the modulation of the epitopes such that they are not recognized by most NTD- and RBD-antibodies, facilitating viral immune escape. Apart from already existing mutations, we have identified three new immune escape sites: 1) Q493R, 2) G446S and 3) S371L/S373P/S375F that confers greater resistance to five of the six classes of RBD-antibodies. Structure of the Omicron S bound with human ACE2, together with analysis of sequence conservation in ACE2 binding region of 25 sarbecovirus members as well as heatmaps of the immunogenic sites and their corresponding mutational frequencies sheds light on conserved and structurally restrained regions that can be used for the development of broad-spectrum vaccines and therapeutics.

Semiflexible Polymer Enclosed in a 3D Compact Domain

The conformational states of a semiflexible polymer enclosed in a volume V:=ℓ3 are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever 3ℓ/ℓp>1, where ℓp is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz–Wang–type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to-end distance. This shape transition provides evidence of a universal signature of the behavior of a semiflexible polymer confined in a compact domain.

Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions

<p style='text-indent:20px;'>In this paper we present a rigorous derivation of the Boltzmann equation in a compact domain with {isotropic} boundary conditions. We consider a system of <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> hard spheres of diameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> in a box <inline-formula><tex-math id="M3">\begin{document}$ \Lambda : = [0, 1]\times(\mathbb{R}/\mathbb{Z})^2 $\end{document}</tex-math></inline-formula>. When a particle meets the boundary of the domain, it is instantaneously reinjected into the box with a random direction, {but} conserving kinetic energy. We prove that the first marginal of the process converges in the scaling <inline-formula><tex-math id="M4">\begin{document}$ N\epsilon^2 = 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \epsilon\rightarrow 0 $\end{document}</tex-math></inline-formula> to the solution of the Boltzmann equation, with the same short time restriction of Lanford's classical theorem.</p>

Gap theorems for compact almost Ricci-harmonic solitons

Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.

A Partitioning Algorithm for Maximum Common Subgraph Problems

We introduce a new branch and bound algorithm for the maximum common subgraph and maximum common connected subgraph problems which is based around vertex labelling and partitioning. Our method in some ways resembles a traditional constraint programming approach, but uses a novel compact domain store and supporting inference algorithms which dramatically reduce the memory and computation requirements during search, and allow better dual viewpoint ordering heuristics to be calculated cheaply. Experiments show a speedup of more than an order of magnitude over the state of the art, and demonstrate that we can operate on much larger graphs without running out of memory.

Invariant density estimation for a reflected diffusion using an Euler scheme

We give an explicit error bound between the invariant density of an elliptic reflected diffusion in a smooth compact domain and the kernel estimator built on the symmetric Euler scheme introduced in [