This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. One of the main results of this paper states that if for every m the first m digits of a real number α ≥ 4 are computable in time ≤ C22Cm for some constant C > 0 then nα is equivalent (“big O”) to the Dehn function of a finitely presented group. The smallest isodiametric f...

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely cutpoints, generalizing existing results nearest-neighbour random walks to adapted with bounded increments satisfying appropriate conditional increment moments conditions. apply one of these deduce that a class transient zero-drift Markov chains in $\mathbb{R}^d$, $d \geq 2$, poss...

We show that the analytic continuations of Helson zeta functions ζ χ ( s ) = ∑ 1 ∞ n − $ \zeta _\chi (s)= \sum _1^{\infty }\chi (n)n^{-s}$ can have essentially arbitrary poles and zeroes in strip 21 / 40 < ℜ 21/40 \Re 1$ (unconditionally), whole critical 2 1/2 <1$ under Riemann Hypothesis, with function \chi$ taking values cubic roots unity. If sets are symmetric respect to real axis, same be a...

Precise spatiotemporal gene regulation is paramount for the establishment and maintenance of cell-specific programmes. Although there is evidence that chromatin neighbourhoods, formed by the zinc-finger protein CTCF, can sequester enhancers and their target genes, there is limited in vivo evidence for CTCF demarcating super-enhancers and preventing cross talk between distinct regulatory element...

The continuous incorporation of new neurons in the dentate gyrus of the adult hippocampus raises exciting questions about memory and learning, and has inspired new computational models to understand the function of adult neurogenesis. These theoretical approaches suggest distinct roles for new neurons as they slowly integrate into the existing dentate gyrus network: immature adult-born neurons ...

The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...