Asymptotics of the number of threshold functions on a two-dimensional rectangular grid

Let $m,n\ge 2$, $m\le n$. It is well-known that the number of (two-dimensional) threshold functions on an $m\times n$ rectangular grid is {eqnarray*} t(m,n)=\frac{6}{\pi^2}(mn)^2+O(m^2n\log{n})+O(mn^2\log{\log{n}})= \frac{6}{\pi^2}(mn)^2+O(mn^2\log{m}). {eqnarray*} We improve the error term by showing that $$ t(m,n)=\frac{6}{\pi^2}(mn)^2+O(mn^2). $

Polymer dynamics in time-dependent periodic potentials

Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state non-symmetric flashing potential and symmetric traveling potential. Rich non-linear behavior of these observables is found. By varying the polymer length, we find current inversions caused by the rebound effect that is only present for molecules with internal structure. These results depend strongly on the polymer type. We also notice increased transport coherence for longer polymers.Comment: 22 pages, 7 figure

The arithmetic derivative and Leibniz-additive functions

An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$f(mn)=f(m)h_f(n)+f(n)h_f(m)$$ for all positive integers $m$ and $n$. A motivation for the present study is the fact that Leibniz-additive functions are generalizations of the arithmetic derivative $D$; namely, $D$ is Leibniz-additive with $h_D(n)=n$. In this paper, we study the basic properties of Leibniz-additive functions and, among other things, show that a Leibniz-additive function $f$ is totally determined by the values of $f$ and $h_f$ at primes. We also consider properties of Leibniz-additive functions with respect to the usual product, composition and Dirichlet convolution of arithmetic functions

‘At least they are welcome in my home!’ : Contentious hospitality in home accommodation of asylum seekers in Finland

This article discusses hospitality towards asylum seekers as a political and contentious act. Accommodating asylum seekers in local homes is one of the pro-asylum mobilisations that emerged across Europe following the 'summer of migration'. Based on interviews with local hosts in Finland, this article demonstrates that offering accommodation is often motivated by an explicit mistrust in state asylum policies and a will to make a statement in support of the right to asylum. Home accommodation challenges the norm of housing asylum seekers in reception centres, isolated from the rest of society. Thus, it provides valuable social and spatial resources in the struggle for asylum. Departing from the understanding that questions of asylum and home are inherently political, and following feminist citizenship theorisation that connects the domestic with the political, this article and the concept contentious hospitality contribute to challenging the discursive division between public and private.Peer reviewe