33,214 research outputs found
A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)
For a right-invariant and controllable driftless system on SU(n), we consider
a time-periodic reference trajectory along which the linearized control system
generates su(n): such trajectories always exist and constitute the basic
ingredient of Coron's Return Method. The open-loop controls that we propose,
which rely on a left-invariant tracking error dynamics and on a fidelity-like
Lyapunov function, are determined from a finite number of left-translations of
the tracking error and they assure global asymptotic convergence towards the
periodic reference trajectory. The role of these translations is to avoid being
trapped in the critical region of this Lyapunov-like function. The convergence
proof relies on a periodic version of LaSalle's invariance principle and the
control values are determined by numerical integration of the dynamics of the
system. Simulations illustrate the obtained controls for and the
generation of the C--NOT quantum gate.Comment: Submitte
Gravitation as Anholonomy
A gravitational field can be seen as the anholonomy of the tetrad fields.
This is more explicit in the teleparallel approach, in which the gravitational
field-strength is the torsion of the ensuing Weitzenboeck connection. In a
tetrad frame, that torsion is just the anholonomy of that frame. The infinitely
many tetrad fields taking the Lorentz metric into a given Riemannian metric
differ by point-dependent Lorentz transformations. Inertial frames constitute a
smaller infinity of them, differing by fixed-point Lorentz transformations.
Holonomic tetrads take the Lorentz metric into itself, and correspond to
Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and
sees the electromagnetic field strength with an additional term.Comment: RevTeX4, 10 pages, no figures. To appear in Gen. Rel. Gra
The Equivalence Principle Revisited
A precise formulation of the strong Equivalence Principle is essential to the
understanding of the relationship between gravitation and quantum mechanics.
The relevant aspects are reviewed in a context including General Relativity,
but allowing for the presence of torsion. For the sake of brevity, a concise
statement is proposed for the Principle: "An ideal observer immersed in a
gravitational field can choose a reference frame in which gravitation goes
unnoticed". This statement is given a clear mathematical meaning through an
accurate discussion of its terms. It holds for ideal observers (time-like
smooth non-intersecting curves), but not for real, spatially extended
observers. Analogous results hold for gauge fields. The difference between
gravitation and the other fundamental interactions comes from their distinct
roles in the equation of force.Comment: RevTeX, 18 pages, no figures, to appear in Foundations of Physic
Influence of chirping the Raman lasers in an atom gravimeter: phase shifts due to the Raman light shift and to the finite speed of light
We present here an analysis of the influence of the frequency dependence of
the Raman laser light shifts on the phase of a Raman-type atom gravimeter.
Frequency chirps are applied to the Raman lasers in order to compensate gravity
and ensure the resonance of the Raman pulses during the interferometer. We show
that the change in the Raman light shift when this chirp is applied only to one
of the two Raman lasers is enough to bias the gravity measurement by a fraction
of Gal (Gal~=~~m/s). We also show that this effect is
not compensated when averaging over the two directions of the Raman wavevector
. This thus constitutes a limit to the rejection efficiency of the
-reversal technique. Our analysis allows us to separate this effect from the
effect of the finite speed of light, which we find in perfect agreement with
expected values. This study highlights the benefit of chirping symmetrically
the two Raman lasers
Confidence Statements for Ordering Quantiles
This work proposes Quor, a simple yet effective nonparametric method to
compare independent samples with respect to corresponding quantiles of their
populations. The method is solely based on the order statistics of the samples,
and independence is its only requirement. All computations are performed using
exact distributions with no need for any asymptotic considerations, and yet can
be run using a fast quadratic-time dynamic programming idea. Computational
performance is essential in high-dimensional domains, such as gene expression
data. We describe the approach and discuss on the most important assumptions,
building a parallel with assumptions and properties of widely used techniques
for the same problem. Experiments using real data from biomedical studies are
performed to empirically compare Quor and other methods in a classification
task over a selection of high-dimensional data sets
Quantitative assessment of geosites with national and international relevance in Portugal: methodological procedures
During the last years geoscientists of
various institutions have developed a
project aiming the establishment of a
geoconservation strategy in Portugal.
One of the main goals of this project was the
inventory of the most important Portuguese
the definition of the frameworks representing
the most important geological features in
Portugal and considering all geodiversity.
With the participation of more than seventy geoscientists, twenty-seven geological
frameworks were defined according to their
scientific value at both national and international levels. The scientific value together with the vulnerability was numerically assessed in order to obtain a sorted list of all
geosites with scientific value. The first step geosites. The Portuguese geosites inventory will be used in nature conservation policies and land-use strategies in different levels of country's administration
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