Probabilistic regular graphs

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents $\beta/\nu$, $\gamma /\nu$ and $(1-\alpha)/\nu$ are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied.Comment: LaTeX file with EPJB macro package, 11 pages, 16 postscript figures, to appear in Eur. Phys. J.

Network Effects and Infrastructure Productivity in Developing Countries

This paper proposes to investigate the threshold effects of the productivity of infrastructure investment in developing countries within a panel data framework. Various speci.cations of an augmented production function that allow for endogenous thresholds are considered. The overwhelming outcome is the presence of strong threshold effects in the relationship between output and private and public inputs. Whatever the transition mechanism used, the testing procedures lead to strong rejection of the linearity of this relationship. In particular, the productivity of infrastructure investment generally exhibits some network effects. When the available stock of infrastructure is very low, investment in this sector has the same productivity as non-infrastructure investment. On the contrary, when a minimumnetwork is available, the marginal productivity of infrastructure investment is generally largely greater than the productivity of other investments. Finally, when the main network is achieved, its marginal productivity becomes similar to the productivity of other investment.financial economics and financial management ;

Mechanism for the {\alpha} -> {\epsilon} phase transition in iron

The mechanism of the {\alpha}-{\epsilon} transition in iron is reconsidered. A path in the Burgers description of the bcc/hcp transition different from those previously considered is proposed. It relies on the assumption that shear and shuffle are decoupled and requires some peculiar magnetic order, different from that of {\alpha} and {\epsilon} phases as found in Density-Functional Theory. Finally, we put forward an original mechanism for this transition, based on successive shuffle motion of layers, which is akin to a nucleation-propagation process rather than to some uniform motion.Comment: 6 pages, 5 figure

Backtesting Value-at-Risk: A GMM Duration-Based Test

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e. the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christoffersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.Value-at-Risk; backtesting; GMM; duration-based test

Backtesting Value-at-Risk: A GMM Duration-based Test

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e., the geometric distribution) is applied to the case of VaR forecast validity. Using simple J-statistics based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated with duration based backtesting procedures. In particular, it is among the first to take into account problems induced by the estimation risk in duration-based backtesting tests and to other a sub-sampling approach for robust inference derived from Escanciano and Olmo (2009). An empirical application of the method to Nasdaq returns confirms that using the GMM test has major consequences for the ex-post evaluation of risk by regulation regulatory authorities.Economics ;