40,338 research outputs found
Discrete time quantum walks on percolation graphs
Randomly breaking connections in a graph alters its transport properties, a
model used to describe percolation. In the case of quantum walks, dynamic
percolation graphs represent a special type of imperfections, where the
connections appear and disappear randomly in each step during the time
evolution. The resulting open system dynamics is hard to treat numerically in
general. We shortly review the literature on this problem. We then present our
method to solve the evolution on finite percolation graphs in the long time
limit, applying the asymptotic methods concerning random unitary maps. We work
out the case of one dimensional chains in detail and provide a concrete, step
by step numerical example in order to give more insight into the possible
asymptotic behavior. The results about the case of the two-dimensional integer
lattice are summarized, focusing on the Grover type coin operator.Comment: 22 pages, 3 figure
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
Large-Scale Sensor Network Localization via Rigid Subnetwork Registration
In this paper, we describe an algorithm for sensor network localization (SNL)
that proceeds by dividing the whole network into smaller subnetworks, then
localizes them in parallel using some fast and accurate algorithm, and finally
registers the localized subnetworks in a global coordinate system. We
demonstrate that this divide-and-conquer algorithm can be used to leverage
existing high-precision SNL algorithms to large-scale networks, which could
otherwise only be applied to small-to-medium sized networks. The main
contribution of this paper concerns the final registration phase. In
particular, we consider a least-squares formulation of the registration problem
(both with and without anchor constraints) and demonstrate how this otherwise
non-convex problem can be relaxed into a tractable convex program. We provide
some preliminary simulation results for large-scale SNL demonstrating that the
proposed registration algorithm (together with an accurate localization scheme)
offers a good tradeoff between run time and accuracy.Comment: 5 pages, 8 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
Distributed Local Linear Parameter Estimation using Gaussian SPAWN
We consider the problem of estimating local sensor parameters, where the
local parameters and sensor observations are related through linear stochastic
models. Sensors exchange messages and cooperate with each other to estimate
their own local parameters iteratively. We study the Gaussian Sum-Product
Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief
propagation, but uses fixed size broadcast messages at each sensor instead.
Compared with the popular diffusion strategies for performing network parameter
estimation, whose communication cost at each sensor increases with increasing
network density, the gSPAWN algorithm allows sensors to broadcast a message
whose size does not depend on the network size or density, making it more
suitable for applications in wireless sensor networks. We show that the gSPAWN
algorithm converges in mean and has mean-square stability under some technical
sufficient conditions, and we describe an application of the gSPAWN algorithm
to a network localization problem in non-line-of-sight environments. Numerical
results suggest that gSPAWN converges much faster in general than the diffusion
method, and has lower communication costs, with comparable root mean square
errors
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