40 research outputs found
The Single Server Queue and the Storage Model: Large Deviations and Fixed Points
We consider the coupling of a single server queue and a storage model defined
as a Queue/Store model in Draief et al. 2004. We establish that if the input
variables, arrivals at the queue and store, satisfy large deviations principles
and are linked through an {\em exponential tilting} then the output variables
(departures from each system) satisfy large deviations principles with the same
rate function. This generalizes to the context of large deviations the
extension of Burke's Theorem derived in Draief et al. 2004.Comment: 20 page
Viral processes by random walks on random regular graphs
We study the SIR epidemic model with infections carried by particles
making independent random walks on a random regular graph. Here we assume
, where is the number of vertices in the random graph,
and is some sufficiently small constant. We give an edge-weighted
graph reduction of the dynamics of the process that allows us to apply standard
results of Erd\H{o}s-R\'{e}nyi random graphs on the particle set. In
particular, we show how the parameters of the model give two thresholds: In the
subcritical regime, particles are infected. In the supercritical
regime, for a constant determined by the parameters of the
model, get infected with probability , and get
infected with probability . Finally, there is a regime in which all
particles are infected. Furthermore, the edge weights give information
about when a particle becomes infected. We exploit this to give a completion
time of the process for the SI case.Comment: Published in at http://dx.doi.org/10.1214/13-AAP1000 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust On-line Matrix Completion on Graphs
We study online robust matrix completion on graphs. At each iteration a
vector with some entries missing is revealed and our goal is to reconstruct it
by identifying the underlying low-dimensional subspace from which the vectors
are drawn. We assume there is an underlying graph structure to the data, that
is, the components of each vector correspond to nodes of a certain (known)
graph, and their values are related accordingly. We give algorithms that
exploit the graph to reconstruct the incomplete data, even in the presence of
outlier noise. The theoretical properties of the algorithms are studied and
numerical experiments using both synthetic and real world datasets verify the
improved performance of the proposed technique compared to other state of the
art algorithms
The single server queue and the storage model: Large deviations and fixed points
We consider the coupling of a single server queue and a storage
model defined as a queue/store model. We establish that if the
input variables, arrivals at the queue and store, satisfy large
deviations principles and are linked through an
exponential tilting, then the output variables
(departures from each system) satisfy large deviations principles
with the same rate function.Peer Reviewe