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

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio

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

A Finite Quantum Gravity Field Theory Model

We discuss the quantization of Delta gravity, a two symmetric tensors model of gravity. This model, in Cosmology, shows accelerated expansion without a cosmological constant. We present the $\tilde{\delta}$ transformation which defines the geometry of the model. Then we show that all delta type models live at one loop only. We apply this to General Relativity and we calculate the one loop divergent part of the Effective Action showing its null contribution in vacuum, implying a finite model. Then we proceed to study the existence of ghosts in the model. Finally, we study the form of the finite quantum corrections to the classical action of the model.Comment: Latex, 33 page

Drought affects the performance of native oak seedlings more strongly than competition with invasive crested wattle seedlings

Two of the most important processes threatening vulnerable plant species are competitive displacement by invasive alien species and water stress due to global warming. Quercus lusitanica, an oak shrub species with remarkable conservation interest, could be threatened by the expansion of the invasive alien tree Paraserianthes lophantha. However, it is unclear how competition would interact with predicted reductions in water availability due to global climate change. We set up a full factorial experiment to examine the direct interspecific competition between P. lophantha and Q. lusitanica seedlings under control and water-limited conditions. • We measured seed biomass, germination, seedling emergence, leaf relative growth rate, biomass, root/shoot ratio, predawn shoot water potential and mortality to assess the individual and combined effects of water stress and interspecific competition on both species. • Our results indicate that, at seedling stage, both species experience competitive effects and responses. However, water stress exhibited a stronger overall effect than competition. Although both species responded strongly to water stress, the invasive P. lophantha exhibited significantly less drought stress than the native Q. lusitanica based on predawn shoot water potential measurements. • The findings of this study suggest that the competition with invasive P. lophantha in the short term must not be dismissed, but that the long-term conservation of the native shrub Q. lusitanica could be compromised by increased drought as a result of global change. Our work sheds light on the combined effects of biological invasions and climate change that can negatively affect vulnerable plant species

Generalized Penner models to all genera

We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to investigate the scaling behaviour of the model in the vicinity of these points. We carry out an analysis of the critical behaviour to all genera addressing all types of multi-critical points. In certain regions of the coupling constant space the model must be defined via analytical continuation. We show in detail how this works for the Penner model. Using analytical continuation it is possible to reach the fermionic 1-matrix model. We show that the critical points of the fermionic 1-matrix model can be indexed by an integer, $m$, as it was the case for the ordinary hermitian 1-matrix model. Furthermore the $m$'th multi-critical fermionic model has to all genera the same value of $\gamma_{str}$ as the $m$'th multi-critical hermitian model. However, the coefficients of the topological expansion need not be the same in the two cases. We show explicitly how it is possible with a fermionic matrix model to reach a $m=2$ multi-critical point for which the topological expansion has alternating signs, but otherwise coincides with the usual Painlev\'{e} expansion.Comment: 27 pages, PostScrip

Field-enlarging transformations and chiral theories

A field-enlarging transformation in the chiral electrodynamics is performed. This introduces an additional gauge symmetry to the model that is unitary and anomaly-free and allows for comparison of different models discussed in the literature. The problem of superfluous degrees of freedom and their influence on quantization is discussed. Several "mysteries" are explained from this point of view.Comment: 14 pages, LaTeX-file, BI-TP 93/0

Spin Flavor Conversion of Neutrinos in Loop Quantum Gravity

Loop quantum gravity theory incorporates a new scale length ${\cal L}$ which induces a Lorentz invariance breakdown. This scale can be either an universal constant or can be fixed by the momentum of particles (${\cal L}\sim p^{-1}$). Effects of the scale parameter ${\cal L}$ and helicity terms occurring in the dispersion relation of fermions are reviewed in the framework of spin-flip conversion of neutrino flavors.Comment: 7 pages, no figur

Current conservation, screening and the magnetic moment of the Δ\Delta resonance. -- 1. Formulation without quark degrees of freedom

The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is studied in a new form of current conservation. According to this condition, the internal and external particle radiation parts of the $\pi N$ radiation amplitude have opposite signs, i.e., they contain terms which must cancel each other. Therefore, one has a screening of the internal and external particle radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex cancel against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances and the anomalous magnetic moment of the proton $\mu_p$ is obtained, where $\mu_{\Delta}$ is expressed by $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement with the values extracted from the fit for the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.Comment: 37 pages, 2 figures and 1 tabl