Extensions of discrete classical orthogonal polynomials beyond the orthogonality

It is well known that the family of Hahn polynomials $\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $\Delta$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all n\in \XX N_0. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.Comment: 2 figures, 20 page

A Survey on q-Polynomials and their Orthogonality Properties

In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW)) for almost any complex value of the parameters and for all non-negative integers degrees. We state the degenerate version of Favard's theorem, which is one of the keys of the paper, that allow us to extend the orthogonality properties valid up to some integer degree N to Sobolev type orthogonality properties. We also present, following an analogous process that applied in [16], tables with the factorization and the discrete Sobolev-type orthogonality property for those families which satisfy a finite orthogonality property, i.e. it consists in sum of finite number of masspoints, such as q-Racah (qR), q-Hahn (qH), dual q-Hahn (dqH), and q-Krawtchouk polynomials (qK), among others. -- [16] R. S. Costas-Santos and J. F. Sanchez-Lara. Extensions of discrete classical orthogonal polynomials beyond the orthogonality. J. Comp. Appl. Math., 225(2) (2009), 440-451Comment: 3 Figures, 3 tables, in a 22 pages manuscrip

Biopesticide activity from drimanic compounds to control tomato pathogens

Indexación: Scopus.Tomato crops can be affected by several infectious diseases produced by bacteria, fungi, and oomycetes. Four phytopathogens are of special concern because of the major economic losses they generate worldwide in tomato production; Clavibacter michiganensis subsp. michiganensis and Pseudomonas syringae pv. tomato, causative agents behind two highly destructive diseases, bacterial canker and bacterial speck, respectively; fungus Fusarium oxysporum f. sp. lycopersici that causes Fusarium Wilt, which strongly affects tomato crops; and finally, Phytophthora spp., which affect both potato and tomato crops. Polygodial (1), drimenol (2), isonordrimenone (3), and nordrimenone (4) were studied against these four phytopathogenic microorganisms. Among them, compound 1, obtained from Drimys winteri Forst, and synthetic compound 4 are shown here to have potent activity. Most promisingly, the results showed that compounds 1 and 4 affect Clavibacter michiganensis growth at minimal inhibitory concentrations (MIC) values of 16 and 32 μg/mL, respectively, and high antimycotic activity against Fusarium oxysporum and Phytophthora spp. with MIC of 64 μg/mL. The results of the present study suggest novel treatment alternatives with drimane compounds against bacterial and fungal plant pathogens. © 2018 by the authors.https://www.mdpi.com/1420-3049/23/8/205

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium of G where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is restricting the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively.Comment: 23 pages; revised versio

Not so different after all: Properties and spatial structure of column density peaks in the pipe and Orion A clouds

We present a comparative study of the physical properties and the spatial distribution of column density peaks in two giant molecular clouds (GMCs), the Pipe Nebula and Orion A, which exemplify opposite cases of star cluster formation stages. The density peaks were extracted from dust extinction maps constructed from Herschel/SPIRE far-infrared images. We compare the distribution functions for dust temperature, mass, equivalent radius, and mean volume density of peaks in both clouds, and made a more fair comparison by isolating the less active Tail region in Orion A and by convolving the Pipe Nebula map to simulate placing it at a distance similar to that of the Orion Complex. The peak mass distributions for Orion A, the Tail, and the convolved Pipe have similar ranges, sharing a maximum near 5 M and a similar power-law drop above 10 M. Despite the clearly distinct evolutive stage of the clouds, there are very important similarities in the physical and spatial distribution properties of the column density peaks, pointing to a scenario where they form as a result of uniform fragmentation of filamentary structures across the various scales of the cloud, with density being the parameter leading the fragmentation, and with clustering being a direct result of thermal fragmentation at different spatial scales. Our work strongly supports the idea that the formation of clusters in GMC could be the result of the primordial organization of pre-stellar material

Algorithms for Game Metrics

Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative {\mu}-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n^4) for both turn-based games and MDPs; improving the previously best known O(n^9\cdot log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(|G|^O(|G|^5)) time complexity, improving the previously known reduction, which yielded O(|G|^O(|G|^7)) time complexity. These algorithms can be iterated to approximate the metrics using binary search.Comment: 27 pages. Full version of the paper accepted at FSTTCS 200

Blackwell-Optimal Strategies in Priority Mean-Payoff Games

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes

Decision Problems for Nash Equilibria in Stochastic Games

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we single out several decidable restrictions of the problem. First, restricting the search space to stationary, or pure stationary, equilibria results in problems that are typically contained in PSPACE and NP, respectively. Second, we show that the existence of an equilibrium with a binary payoff (i.e. an equilibrium where each player either wins or loses with probability 1) is decidable. We also establish that the existence of a Nash equilibrium with a certain binary payoff entails the existence of an equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio

Deterministic Priority Mean-payoff Games as Limits of Discounted Games

International audienceInspired by the paper of de Alfaro, Henzinger and Majumdar about discounted $\mu$-calculus we show new surprising links between parity games and different classes of discounted games

Anomalous Commutator Algebra for Conformal Quantum Mechanics

The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.Comment: 23 pages. A few typos corrected in the final version (which agrees with the published Phys. Rev. D article