Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

Combining Effects and Coeffects via Grading

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the Association for Computing Machinery.$\textit{Effects}$ and $\textit{coeffects}$ are two general, complementary aspects of program behaviour. They roughly correspond to computations which change the execution context (effects) versus computations which make demands on the context (coeffects). Effectful features include partiality, non-determinism, input-output, state, and exceptions. Coeffectful features include resource demands, variable access, notions of linearity, and data input requirements. The effectful or coeffectful behaviour of a program can be captured and described via type-based analyses, with fine grained information provided by monoidal effect annotations and semiring coeffects. Various recent work has proposed models for such typed calculi in terms of $\textit{graded (strong) monads}$ for effects and $\textit{graded (monoidal) comonads}$ for coeffects. Effects and coeffects have been studied separately so far, but in practice many computations are both effectful and coeffectful, e.g., possibly throwing exceptions but with resource requirements. To remedy this, we introduce a new general calculus with a combined $\textit{effect-coeffect system}$. This can describe both the $\textit{changes}$ and $\textit{requirements}$ that a program has on its context, as well as interactions between these effectful and coeffectful features of computation. The effect-coeffect system has a denotational model in terms of effect-graded monads and coeffect-graded comonads where interaction is expressed via the novel concept of $\textit{graded distributive laws}$. This graded semantics unifies the syntactic type theory with the denotational model. We show that our calculus can be instantiated to describe in a natural way various different kinds of interaction between a program and its evaluation context.Orchard was supported by EPSRC grant EP/M026124/1 and EP/K011715/1 (whilst previously at Imperial College London), Katsumata by JSPS KAKENHI grant JP15K00014, Uustalu by Estonian Min. of Educ. and Res. grant IUT33-13 and Estonian Sci. Found. grant 9475. Gaboardi’s work was done in part while at the University of Dundee, UK supported by EPSRC grant EP/M022358/1

SARS-CoV-2 Omicron-B.1.1.529 leads to widespread escape from neutralizing antibody responses

On 24th November 2021, the sequence of a new SARS-CoV-2 viral isolate Omicron-B.1.1.529 was announced, containing far more mutations in Spike (S) than previously reported variants. Neutralization titers of Omicron by sera from vaccinees and convalescent subjects infected with early pandemic Alpha, Beta, Gamma, or Delta are substantially reduced, or the sera failed to neutralize. Titers against Omicron are boosted by third vaccine doses and are high in both vaccinated individuals and those infected by Delta. Mutations in Omicron knock out or substantially reduce neutralization by most of the large panel of potent monoclonal antibodies and antibodies under commercial development. Omicron S has structural changes from earlier viruses and uses mutations that confer tight binding to ACE2 to unleash evolution driven by immune escape. This leads to a large number of mutations in the ACE2 binding site and rebalances receptor affinity to that of earlier pandemic viruses