509 research outputs found
Polynomial Interrupt Timed Automata
Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where
reachability and some variants of timed model checking are decidable even in
presence of parameters. They are well suited to model and analyze real-time
operating systems. Here we extend ITA with polynomial guards and updates,
leading to the class of polynomial ITA (PolITA). We prove the decidability of
the reachability and model checking of a timed version of CTL by an adaptation
of the cylindrical decomposition method for the first-order theory of reals.
Compared to previous approaches, our procedure handles parameters and clocks in
a unified way. Moreover, we show that PolITA are incomparable with stopwatch
automata. Finally additional features are introduced while preserving
decidability
Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
y formally diagonalizing with accuracy the Hamiltonian of electrons
in a crystal subject to electromagnetic perturbations, we resolve the debate on
the Hamiltonian nature of semiclassical equations of motion with Berry-phase
corrections, and therefore confirm the validity of the Liouville theorem. We
show that both the position and momentum operators acquire a Berry-phase
dependence, leading to a non-canonical Hamiltonian dynamics. The equations of
motion turn out to be identical to the ones previously derived in the context
of electron wave-packets dynamics.Comment: 4 page
A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
An explicit series solution is proposed for the inversion of the spherical
mean Radon transform. Such an inversion is required in problems of thermo- and
photo- acoustic tomography. Closed-form inversion formulae are currently known
only for the case when the centers of the integration spheres lie on a sphere
surrounding the support of the unknown function, or on certain unbounded
surfaces. Our approach results in an explicit series solution for any closed
measuring surface surrounding a region for which the eigenfunctions of the
Dirichlet Laplacian are explicitly known - such as, for example, cube, finite
cylinder, half-sphere etc. In addition, we present a fast reconstruction
algorithm applicable in the case when the detectors (the centers of the
integration spheres) lie on a surface of a cube. This algorithm reconsrtucts
3-D images thousands times faster than backprojection-type methods
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of
hybrid automata well suited to the description of timed multi-task systems with
interruptions in a single processor environment. While the reachability problem
is undecidable for hybrid automata we show that it is decidable for ITA. More
precisely we prove that the untimed language of an ITA is regular, by building
a finite automaton as a generalized class graph. We then establish that the
reachability problem for ITA is in NEXPTIME and in PTIME when the number of
clocks is fixed. To prove the first result, we define a subclass ITA- of ITA,
and show that (1) any ITA can be reduced to a language-equivalent automaton in
ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without
any class graph). In the next step, we investigate the verification of real
time properties over ITA. We prove that model checking SCL, a fragment of a
timed linear time logic, is undecidable. On the other hand, we give model
checking procedures for two fragments of timed branching time logic. We also
compare the expressive power of classical timed automata and ITA and prove that
the corresponding families of accepted languages are incomparable. The result
also holds for languages accepted by controlled real-time automata (CRTA), that
extend timed automata. We finally combine ITA with CRTA, in a model which
encompasses both classes and show that the reachability problem is still
decidable. Additionally we show that the languages of ITA are neither closed
under complementation nor under intersection
From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
In 1990, Dyson published a proof due to Feynman of the Maxwell equations
assuming only the commutation relations between position and velocity. With
this minimal assumption, Feynman never supposed the existence of Hamiltonian or
Lagrangian formalism. In the present communication, we review the study of a
relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's
magnetic angular momentum and Dirac magnetic monopole are the consequences of
the structure of the Lorentz Lie algebra defined by the Feynman's brackets.
Then, we extend these ideas to the dual momentum space by considering
noncommutative quantum mechanics. In this context, we show that the
noncommutativity of the coordinates is responsible for a new effect called the
spin Hall effect. We also show its relation with the Berry phase notion. As a
practical application, we found an unusual spin-orbit contribution of a
nonrelativistic particle that could be experimentally tested. Another practical
application is the Berry phase effect on the propagation of light in
inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland,
U.S.A., August 2006
Intrauterine crowding impairs formation and growth of secondary myofibers in pigs
There are indications that intrauterine crowding may cause intrauterine growth retardation with the possibility of an impaired myofiber hyperplasia. The aim of the study was to confirm this by generating large differences in uterine space using sows that were unilaterally hysterectomized-ovariectomized (HO; crowded) or unilaterally oviduct ligated (OL; non-crowded). In the study, seven HO and seven OL Swiss Large White third parity sows were used. At farrowing, litter size and litter birth weight were determined. Subsequently, within each litter two male and two female progenies each with the respectively lowest (L) and highest (H) birth weight were sacrificed. Internal organs and brain were weighed, and longissimus (LM) and semitendinosus muscle (SM) samples were collected. Histological analyses were performed in both muscles using mATPase staining after preincubation at pH 4.3 and 10.2. Myosin heavy chain (MyHC) polymorphism was determined in the LM by means of SDS-PAGE. The number of piglets born alive was similar in both sow groups, but litter size expressed per uterine horn was lower (P < 0.05) in OL than HO sows. Consequently, OL progeny were markedly heavier (P < 0.01). Regardless of gender, the organs, the brain and the SM were heavier (P < 0.001) in OL and H compared with HO and L offspring, respectively. Compared with HO pigs, the SM of OL offspring tended (P < 0.1) to have more myofibers, which were of larger (P < 0.05) size. However, myofiber density appeared to be lower (P < 0.1) in the SM of OL than HO pigs. The impact of birth weight on myofiber characteristics was limited to the lower (P < 0.05) myofiber density in the SM and the larger (P < 0.01) myofiber size in the light portion of the SM of H than L offspring, whereas myofiber hyperplasia did not differ between birth weight categories. The SM, but not the LM, of male offspring had a greater (P < 0.05) myofiber density. This did not affect total SM myofiber number. The relative abundance of fetal and type I MyHC in the LM was lower (P < 0.05) and that of type II MyHC was greater (P < 0.001) in OL than HO pigs. The current data suggest that regardless of birth weight and gender, in the LM and SM of individuals born from a crowded environment, not only hyperplasia but also hypertrophy of myofibers is impaired and their maturity seems delaye
Last passage percolation and traveling fronts
We consider a system of N particles with a stochastic dynamics introduced by
Brunet and Derrida. The particles can be interpreted as last passage times in
directed percolation on {1,...,N} of mean-field type. The particles remain
grouped and move like a traveling wave, subject to discretization and driven by
a random noise. As N increases, we obtain estimates for the speed of the front
and its profile, for different laws of the driving noise. The Gumbel
distribution plays a central role for the particle jumps, and we show that the
scaling limit is a L\'evy process in this case. The case of bounded jumps
yields a completely different behavior
Inverse problem and Bertrand's theorem
The Bertrand's theorem can be formulated as the solution of an inverse
problem for a classical unidimensional motion. We show that the solutions of
these problems, if restricted to a given class, can be obtained by solving a
numerical equation. This permit a particulary compact and elegant proof of
Bertrand's theorem.Comment: 11 pages, 3 figure
Language Emptiness of Continuous-Time Parametric Timed Automata
Parametric timed automata extend the standard timed automata with the
possibility to use parameters in the clock guards. In general, if the
parameters are real-valued, the problem of language emptiness of such automata
is undecidable even for various restricted subclasses. We thus focus on the
case where parameters are assumed to be integer-valued, while the time still
remains continuous. On the one hand, we show that the problem remains
undecidable for parametric timed automata with three clocks and one parameter.
On the other hand, for the case with arbitrary many clocks where only one of
these clocks is compared with (an arbitrary number of) parameters, we show that
the parametric language emptiness is decidable. The undecidability result
tightens the bounds of a previous result which assumed six parameters, while
the decidability result extends the existing approaches that deal with
discrete-time semantics only. To the best of our knowledge, this is the first
positive result in the case of continuous-time and unbounded integer
parameters, except for the rather simple case of single-clock automata
Testing real-time systems using TINA
The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts
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