Varieties of Cost Functions.

Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring

Molecular Signatures in the Near Infrared Dayside Spectrum of HD 189733b

We have measured the dayside spectrum of HD 189733b between 1.5 and 2.5 microns using the NICMOS instrument on the Hubble Space Telescope. The emergent spectrum contains significant modulation, which we attribute to the presence of molecular bands seen in absorption. We find that water (H2O), carbon monoxide (CO), and carbon dioxide (CO2) are needed to explain the observations, and we are able to estimate the mixing ratios for these molecules. We also find temperature decreases with altitude in the ~0.01 < P < ~1 bar region of the dayside near-infrared photosphere and set an upper limit to the dayside abundance of methane (CH4) at these pressures.Comment: 13 pages, 3 figures. accepted in Astrophysical Journal Letter

Deriving relativistic momentum and energy. II. Three-dimensional case

We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.Comment: 7 page

Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA