307,645 research outputs found
Randomization Adaptive Self-Stabilization
We present a scheme to convert self-stabilizing algorithms that use
randomization during and following convergence to self-stabilizing algorithms
that use randomization only during convergence. We thus reduce the number of
random bits from an infinite number to a bounded number. The scheme is
applicable to the cases in which there exits a local predicate for each node,
such that global consistency is implied by the union of the local predicates.
We demonstrate our scheme over the token circulation algorithm of Herman and
the recent constant time Byzantine self-stabilizing clock synchronization
algorithm by Ben-Or, Dolev and Hoch. The application of our scheme results in
the first constant time Byzantine self-stabilizing clock synchronization
algorithm that uses a bounded number of random bits
Self-stabilization of extra dimensions
We show that the problem of stabilization of extra dimensions in Kaluza-Klein
type cosmology may be solved in a theory of gravity involving high-order
curvature invariants. The method suggested (employing a slow-change
approximation) can work with rather a general form of the gravitational action.
As examples, we consider pure gravity with Lagrangians quadratic and cubic in
the scalar curvature and some more complex ones in a simple Kaluza-Klein
framework. After a transition to the 4D Einstein conformal frame, this results
in effective scalar field theories with certain effective potentials, which in
many cases possess positive minima providing stable small-size extra
dimensions. Estimates made in the original (Jordan) conformal frame show that
the problem of a small value of the cosmological constant in the present
Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections,
accepted at Phys. Rev.
Bounding the Impact of Unbounded Attacks in Stabilization
Self-stabilization is a versatile approach to fault-tolerance since it
permits a distributed system to recover from any transient fault that
arbitrarily corrupts the contents of all memories in the system. Byzantine
tolerance is an attractive feature of distributed systems that permits to cope
with arbitrary malicious behaviors. Combining these two properties proved
difficult: it is impossible to contain the spatial impact of Byzantine nodes in
a self-stabilizing context for global tasks such as tree orientation and tree
construction. We present and illustrate a new concept of Byzantine containment
in stabilization. Our property, called Strong Stabilization enables to contain
the impact of Byzantine nodes if they actually perform too many Byzantine
actions. We derive impossibility results for strong stabilization and present
strongly stabilizing protocols for tree orientation and tree construction that
are optimal with respect to the number of Byzantine nodes that can be tolerated
in a self-stabilizing context
Large deviations and a Kramers' type law for self-stabilizing diffusions
We investigate exit times from domains of attraction for the motion of a
self-stabilized particle traveling in a geometric (potential type) landscape
and perturbed by Brownian noise of small amplitude. Self-stabilization is the
effect of including an ensemble-average attraction in addition to the usual
state-dependent drift, where the particle is supposed to be suspended in a
large population of identical ones. A Kramers' type law for the particle's exit
from the potential's domains of attraction and a large deviations principle for
the self-stabilizing diffusion are proved. It turns out that the exit law for
the self-stabilizing diffusion coincides with the exit law of a potential
diffusion without self-stabilization and a drift component perturbed by average
attraction. We show that self-stabilization may substantially delay the exit
from domains of attraction, and that the exit location may be completely
different.Comment: Published in at http://dx.doi.org/10.1214/07-AAP489 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Noise Stabilization of Self-Organized Memories
We investigate a nonlinear dynamical system which ``remembers'' preselected
values of a system parameter. The deterministic version of the system can
encode many parameter values during a transient period, but in the limit of
long times, almost all of them are forgotten. Here we show that a certain type
of stochastic noise can stabilize multiple memories, enabling many parameter
values to be encoded permanently. We present analytic results that provide
insight both into the memory formation and into the noise-induced memory
stabilization. The relevance of our results to experiments on the
charge-density wave material is discussed.Comment: 29 pages, 6 figures, submitted to Physical Review
Partially incoherent optical vortices in self-focusing nonlinear media
We observe stable propagation of spatially localized single- and
double-charge optical vortices in a self-focusing nonlinear medium. The
vortices are created by self-trapping of partially incoherent light carrying a
phase dislocation, and they are stabilized when the spatial incoherence of
light exceeds a certain threshold. We confirm the vortex stabilization effect
by numerical simulations and also show that the similar mechanism of
stabilization applies to higher-order vortices.Comment: 4 pages and 6 figures (including 3 experimental figures
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