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

The Itzykson-Zuber Integral for U(m|n)

We compute the Itzykson-Zuber (IZ) integral for the superunitary group U(m|n). As a consequence, we are able to find the non-zero correlations of superunitary matricesComment: Latex, 16 page

Granular activated carbons from avocado seeds

Avocado seeds have proven to be an excellent raw material for the production of Granular Activated Carbons (GAC). This residue, generated in large amounts in centralized facilities dedicated to the transformation of avocado fruit, has no commercial value at present. GAC have been produced by partial gasification of ground seeds under mildly oxidizing conditions (steam/nitrogen mixture). Optimum activation conditions were achieved at 1000 ºC and residence times between 120-150 min, resulting in burn off rates between 34-37 wt% and carbon yields between 12.4-13.0 wt%. These GAC exhibited type IV N2 gas adsorption isotherm, characteristic of materials containing a mixture of micro and mesopores. Avocado seed GACs exhibited BET surface areas up to 700 m2 /g, CO2 surface areas up to 900 m 2 /g and micro-pore volumes up to 0.31 cm3 /g. This porous structure provided these GAC with a remarkable aqueous adsorption capacity for methylene blue (Langmuir qm = 153.8 mg/g and Freundlich Kf = 113.0 mg/g), which was greater than that determined for a range of GAC commercialized for the treatment of waste and drinking waters