A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01261-9.

Multilinear maps have many cryptographic applications. The first candidate construction of multilinear maps was proposed by Garg, Gentry, and Halevi (GGH13) in 2013, and a bit later another candidate was suggested by Coron, Lepoint, and Tibouchi (CLT13) over the integers. However, both of them turned out to be insecure from so-called zeroizing attack (HJ15, CHL15). As a fix of CLT13, Coron, Lep...

the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

Let z = (z1, z2, · · · , zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be a unital commutative ring of any characteristic and Ft(z) = z−Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉 ×n and o(Ht(z)) ≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F (z) := z−Ht=1(z) when it makes sense. The inverse map Gt(z) of Ft(z) can always be written as Gt(...

Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program de nitions. Furthermore, tabling often improves computational performance. Rational term are terms with one or more in nite subterms but with a nite representation. Rational terms can be generated in Prolog by omitting the occurs check when unifying two ...