Polymer ejection from strong spherical confinement

We examine the ejection of an initially strongly confined flexible polymer from a spherical capsid through a nanoscale pore. We use molecular dynamics for unprecedentedly high initial monomer densities. We show that the time for an individual monomer to eject grows exponentially with the number of ejected monomers. By measurements of the force at the pore we show this dependence to be a consequence of the excess free energy of the polymer due to confinement growing exponentially with the number of monomers initially inside the capsid. This growth relates closely to the divergence of mixing energy in the Flory-Huggins theory at large concentration. We show that the pressure inside the capsid driving the ejection dominates the process that is characterized by the ejection time growing linearly with the lengths of different polymers. Waiting time profiles would indicate that the superlinear dependence obtained for polymers amenable to computer simulations results from a finite-size effect due to the final retraction of polymers' tails from capsids.Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev. E, increased readability from previous versio

Polishness of some topologies related to word or tree automata

We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.Comment: This paper is an extended version of a paper which appeared in the proceedings of the 26th EACSL Annual Conference on Computer Science and Logic, CSL 2017. The main addition with regard to the conference paper consists in the study of the B\"uchi topology and of the Muller topology in the case of a space of trees, which now forms Section

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

An Upper Bound on the Complexity of Recognizable Tree Languages

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\bf\Delta}^1\_2$