Computing Quantiles in Markov Reward Models

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with non-negative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in time polynomial in the size of the chain and the maximum reward.Comment: 17 pages, 1 figure; typo in example correcte

Electric Dipole Moments and Polarizability in the Quark-Diquark Model of the Neutron

For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, viewed as a bound state of ten electrons two protons and an oxygen nucleus, both have zero mean electric dipole moments. Yet, the water molecule is said to have a nonzero dipole moment strength $d=e\Lambda$ with $\Lambda_{H_2O} \approx 0.385\ \dot{A}$. The neutron may also be said to have an electric dipole moment strength with $\Lambda_{neutron} \approx 0.612\ fm$. The neutron analysis can be made experimentally consistent, if one employs a quark-diquark model of neutron structure.Comment: four pages, two figure

Multiwavelength analysis of the young open cluster NGC 2362

We present a multiwavelength analysis of the young open cluster NGC 2362. UBVRcIc CCD photometric observations, together with available data in the Chandra data base, near infrared data from the Two Micron All Sky Survey (2MASS), and recently published Halpha spectroscopy were used to get information about the evolutionary stage of the cluster and the main physical properties of its stellar content. Cluster membership is estimated for every individual star by means of ZAMS and isochrone fitting. The cluster is confirmed to host a richly populated pre-main sequence (PMS), and to contain a large amount of X-ray emitting stars, which reach from the PMS members of GK spectral type, up to the most luminous OB type main sequence (MS) members. The PMS cluster members show no significant age spread, and the comparison to both PMS and post-MS isochrones suggests a younger age for the more massive MS than for lower mass PMS members. The analysis allows to asses the validity of currently used pre-main sequence evolutionary models, and supports the suggestion of a well defined positive correlation of the X-ray emission from PMS stars with their bolometric luminosity. Clear differences are found on the other hand, between the X-ray activity properties of MS and PMS cluster members, both in the relation between X-ray luminosity and bolometric luminosity, and in spectral properties as well.Comment: 1 gzipped file: 1 tex file with 9 pages text. 5 ps files with figures. Submitted to Astrophysical Journa

BV formulation of higher form gauge theories in a superspace

We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for two and three form gauge theories. Further we develop the superspace formulation for the BV actions for these theories. We show that the extended BRST invariant BV action for these theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. On the hand a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories.Comment: 30 pages, No figure, version to appear in EPJ