14,913 research outputs found
Analysis of Large Urn Models with Local Mean-Field Interactions
The stochastic models investigated in this paper describe the evolution of a
set of identical balls scattered into urns connected by an underlying
symmetrical graph with constant degree . After some random amount of time
{\em all the balls} of any urn are redistributed locally, among the urns
of its neighborhood. The allocation of balls is done at random according to a
set of weights which depend on the state of the system. The main original
features of this context is that the cardinality of the range of
interaction is not necessarily linear with respect to as in a classical
mean-field context and, also, that the number of simultaneous jumps of the
process is not bounded due to the redistribution of all balls of an urn at the
same time. The approach relies on the analysis of the evolution of the local
empirical distributions associated to the state of urns located in the
neighborhood of a given urn. Under convenient conditions, by taking an
appropriate Wasserstein distance and by establishing several technical
estimates for local empirical distributions, we are able to prove mean-field
convergence results.
When the load per node goes to infinity, a convergence result for the
invariant distribution of the associated McKean-Vlasov process is obtained for
several allocation policies. For the class of power of choices policies, we
show that the associated invariant measure has an asymptotic finite support
property under this regime. This result differs somewhat from the classical
double exponential decay property usually encountered in the literature for
power of choices policies
Analysis of Large Unreliable Stochastic Networks
In this paper a stochastic model of a large distributed system where users'
files are duplicated on unreliable data servers is investigated. Due to a
server breakdown, a copy of a file can be lost, it can be retrieved if another
copy of the same file is stored on other servers. In the case where no other
copy of a given file is present in the network, it is definitively lost. In
order to have multiple copies of a given file, it is assumed that each server
can devote a fraction of its processing capacity to duplicate files on other
servers to enhance the durability of the system.
A simplified stochastic model of this network is analyzed. It is assumed that
a copy of a given file is lost at some fixed rate and that the initial state is
optimal: each file has the maximum number of copies located on the servers
of the network. Due to random losses, the state of the network is transient and
all files will be eventually lost. As a consequence, a transient
-dimensional Markov process with a unique absorbing state describes
the evolution this network. By taking a scaling parameter related to the
number of nodes of the network. a scaling analysis of this process is
developed. The asymptotic behavior of is analyzed on time scales of
the type for . The paper derives asymptotic
results on the decay of the network: Under a stability assumption, the main
results state that the critical time scale for the decay of the system is given
by . When the stability condition is not satisfied, it is
shown that the state of the network converges to an interesting local
equilibrium which is investigated. As a consequence it sheds some light on the
role of the key parameters , the duplication rate and , the maximal
number of copies, in the design of these systems
Identification and adaptive control of a high-contrast focal plane wavefront correction system
All coronagraphic instruments for exoplanet high-contrast imaging need
wavefront correction systems to reject optical aberrations and create
sufficiently dark holes. Since the most efficient wavefront correction
algorithms (controllers and estimators) are usually model-based, the modeling
accuracy of the system influences the ultimate wavefront correction
performance. Currently, wavefront correction systems are typically approximated
as linear systems using Fourier optics. However, the Fourier optics model is
usually biased due to inaccuracies in the layout measurements, the imperfect
diagnoses of inherent optical aberrations, and a lack of knowledge of the
deformable mirrors (actuator gains and influence functions). Moreover, the
telescope optical system varies over time because of instrument instabilities
and environmental effects. In this paper, we present an
expectation-maximization (E-M) approach for identifying and real-time adapting
the linear telescope model from data. By iterating between the E-step (a Kalman
filter and a Rauch smoother) and the M-step (analytical or gradient-based
optimization), the algorithm is able to recover the system even if the model
depends on the electric fields, which are unmeasurable hidden variables.
Simulations and experiments in Princeton's High Contrast Imaging Lab
demonstrate that this algorithm improves the model accuracy and increases the
efficiency and speed of the wavefront correction
Multi-Objective Optimization for Power Efficient Full-Duplex Wireless Communication Systems
In this paper, we investigate power efficient resource allocation algorithm
design for multiuser wireless communication systems employing a full-duplex
(FD) radio base station for serving multiple half-duplex (HD) downlink and
uplink users simultaneously. We propose a multi-objective optimization
framework for achieving two conflicting yet desirable system design objectives,
i.e., total downlink transmit power minimization and total uplink transmit
power minimization, while guaranteeing the quality-of-service of all users. To
this end, the weighted Tchebycheff method is adopted to formulate a
multi-objective optimization problem (MOOP). Although the considered MOOP is
non-convex, we solve it optimally by semidefinite programming relaxation.
Simulation results not only unveil the trade-off between the total downlink and
the total uplink transmit power, but also confirm that the proposed FD system
provides substantial power savings over traditional HD systems.Comment: Accepted for presentation at the IEEE Globecom 2015, San Diego, CA,
USA, Dec. 201
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