831 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
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
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
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
Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
To build genuine generators of the rotations group in noncommutative quantum
mechanics, we show that it is necessary to extend the noncommutative parameter
to a field operator, which one proves to be only momentum dependent.
We find consequently that this field must be obligatorily a dual Dirac monopole
in momentum space. Recent experiments in the context of the anomalous Hall
effect provide for a monopole in the crystal momentum space. We suggest a
connection between the noncommutative field and the Berry curvature in momentum
space which is at the origine of the anomalous Hall effect.Comment: 4 page
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
In the main theorem of this paper we treat the problem of existence of
minimizers of the isoperimetric problem under the assumption of small volumes.
Applications of the main theorem to asymptotic expansions of the isoperimetric
problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted
Quantitative information flow, with a view
We put forward a general model intended for assessment of system security against passive eavesdroppers, both quantitatively ( how much information is leaked) and qualitatively ( what properties are leaked). To this purpose, we extend information hiding systems ( ihs ), a model where the secret-observable relation is represented as a noisy channel, with views : basically, partitions of the state-space. Given a view W and n independent observations of the system, one is interested in the probability that a Bayesian adversary wrongly predicts the class of W the underlying secret belongs to. We offer results that allow one to easily characterise the behaviour of this error probability as a function of the number of observations, in terms of the channel matrices defining the ihs and the view W . In particular, we provide expressions for the limit value as n â â, show by tight bounds that convergence is exponential, and also characterise the rate of convergence to predefined error thresholds. We then show a few instances of statistical attacks that can be assessed by a direct application of our model: attacks against modular exponentiation that exploit timing leaks, against anonymity in mix-nets and against privacy in sparse datasets
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
- âŠ