Irreducible pseudo 2-factor isomorphic cubic bipartite graphs

A bipartite graph is {\em pseudo 2--factor isomorphic} if all its 2--factors have the same parity of number of circuits. In \cite{ADJLS} we proved that the only essentially 4--edge-connected pseudo 2--factor isomorphic cubic bipartite graph of girth 4 is $K_{3,3}$, and conjectured \cite[Conjecture 3.6]{ADJLS} that the only essentially 4--edge-connected cubic bipartite graphs are $K_{3,3}$, the Heawood graph and the Pappus graph. There exists a characterization of symmetric configurations $n_3$ %{\bf decide notation and how to use it in the rest of the paper} due to Martinetti (1886) in which all symmetric configurations $n_3$ can be obtained from an infinite set of so called {\em irreducible} configurations \cite{VM}. The list of irreducible configurations has been completed by Boben \cite{B} in terms of their {\em irreducible Levi graphs}. In this paper we characterize irreducible pseudo 2--factor isomorphic cubic bipartite graphs proving that the only pseudo 2--factor isomorphic irreducible Levi graphs are the Heawood and Pappus graphs. Moreover, the obtained characterization allows us to partially prove the above Conjecture

Efficiency of a Brownian information machine

A Brownian information machine extracts work from a heat bath through a feedback process that exploits the information acquired in a measurement. For the paradigmatic case of a particle trapped in a harmonic potential, we determine how power and efficiency for two variants of such a machine operating cyclically depend on the cycle time and the precision of the positional measurements. Controlling only the center of the trap leads to a machine that has zero efficiency at maximum power whereas additional optimal control of the stiffness of the trap leads to an efficiency bounded between 1/2, which holds for maximum power, and 1 reached even for finite cycle time in the limit of perfect measurements.Comment: 9 pages, 2 figure

On the absorption and production cross sections of KK and K∗K^*

We have computed the isospin and spin averaged cross sections of the processes $\pi K^*\to \rho K$ and $\rho K^*\to \pi K$, which are crucial in the determination of the abundances of $K^*$ and $K$ in heavy ion collisions. Improving previous calculations, we have considered several mechanisms which were missing, such as the exchange of axial and vector resonances ($K_1(1270)$, $K^*_2(1430)$, $h_1(1170)$, etc...) and also other processes such as $\pi K^*\to \omega K, \phi K$ and $\omega K^*,\,\phi K^*\to \pi K$. We find that some of these mechanisms give important contributions to the cross section. Our results also suggest that, in a hadron gas, $K^*$ production might be more important than its absorption