Runtime verification for biochemical programs

The biochemical paradigm is well-suited for modelling autonomous systems and new programming languages are emerging from this approach. However, in order to validate such programs, we need to define precisely their semantics and to provide verification techniques. In this paper, we consider a higher-order biochemical calculus that models the structure of system states and its dynamics thanks to rewriting abstractions, namely rules and strategies. We extend this calculus with a runtime verification technique in order to perform automatic discovery of property satisfaction failure. The property specification language is a subclass of LTL safety and liveness properties

Free-fall accretion and emitting caustics in wind-fed X-ray sources

In wind-fed X-ray binaries the accreting matter is Compton cooled and falls freely onto the compact object. The matter has a modest angular momentum $l$ and accretion is quasi-spherical at large distances from the compact object. Initially small non-radial velocities grow in the converging supersonic flow and become substantial in the vicinity of the accretor. The streamlines with $l>(GMR_*)^{1/2}$ (where $M$ and $R_*$ are the mass and radius of the compact object) intersect outside $R_*$ and form a two-dimensional caustic which emits X-rays. The streamlines with low angular momentum, $l<(GMR_*)^{1/2}$, run into the accretor. If the accretor is a neutron star, a large X-ray luminosity results. We show that the distribution of accretion rate/luminosity over the star surface is sensitive to the angular momentum distribution of the accreting matter. The apparent luminosity depends on the side from which the star is observed and can change periodically with the orbital phase of the binary. The accretor then appears as a `Moon-like' X-ray source.Comment: 8 pages, accepted to MNRA

Physical picture of the gapped excitation spectrum of the one-dimensional Hubbard model

A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis" for complex momenta and derive an exact formulation of the Bethe-Ansatz equations including all states. Among other things we show that all gapped eigenstates have the Bethe-Ansatz form, contrary to assertions in the literature. The simplest excitations in the upper Hubbard band are computed: we find an unusual dispersion close to half-filling.Comment: 22 pages, revtex, 4 eps-figure