Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure

Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.Comment: 5 pages RevTeX, 3 figures (.eps

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

Dynamic Recursive Petri Nets

International audienceIn the early two-thousands, Recursive Petri nets (RPN) have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. While having a great expressive power, RPN suffer two limitations: (1) they do not include more general features for transitions like reset arcs, transfer arcs, etc. (2) the initial marking associated the recursive "call" only depends on the calling transition and not on the current marking of the caller. Here we introduce Dynamic Recursive Petri nets (DRPN) which address these issues. We show that the standard extensions of Petri nets for which decidability of the coverability problem is preserved are particular cases of DPRN. Then we establish that w.r.t. coverability languages, DRPN are strictly more expressive than RPN. Finally we prove that the coverability problem is still decidable for DRPN

Bounded Determinization of Timed Automata with Silent Transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.Comment: 25 page

Quantum and random walks as universal generators of probability distributions

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time- and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without loosing coherence, as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin.Comment: 8 pages, 2 figures; revised and enlarged versio

Low-dose ketamine for children and adolescents with acute sickle cell disease related pain: A single center experience

Background: Opioids are the mainstay of therapy for painful vasoocclusive episodes (VOEs) in sickle cell disease (SCD). Based on limited studies, low-dose ketamine could be a useful adjuvant analgesic for refractory SCD pain, but its safety and efficacy has not been evaluated in pediatric SCD. Procedure: Using retrospective chart review we recorded and compared characteristics of hospitalizations of 33 children with SCD hospitalized with VOE who were treated with low-dose ketamine and opioid PCA vs. a paired hospitalization where the same patients received opioid PCA without ketamine. We seek to 1) describe a single center experience using adjuvant low-dose ketamine with opioid PCA for sickle cell related pain, 2) retrospectively explore the safety and efficacy of adjuvant low-dose ketamine for pain management, and 3) determine ketamine’s effect on opioid consumption in children and adolescents hospitalized with VOE. Results: During hospitalizations where patients received ketamine, pain scores and opioid use were higher (6.48 vs. 5.99; p=0.002 and 0.040 mg/kg/h vs. 0.032 mg/kg/h; p=0.004 respectively) compared to hospitalizations without ketamine. In 3 patients, ketamine was discontinued due to temporary and reversible psychotomimetic effects. There were no additional short term side effects of ketamine. Conclusions: Low-dose ketamine has an acceptable short-term safety profile for patients with SCD hospitalized for VOE. Lack of an opioid sparing effect of ketamine likely represents use of low-dose ketamine for patients presenting with more severe VOE pain. Prospective randomized studies of adjuvant low-dose ketamine for SCD pain are warranted to determine efficacy and long-term safety