4,296 research outputs found
Information In The Non-Stationary Case
Information estimates such as the ``direct method'' of Strong et al. (1998)
sidestep the difficult problem of estimating the joint distribution of response
and stimulus by instead estimating the difference between the marginal and
conditional entropies of the response. While this is an effective estimation
strategy, it tempts the practitioner to ignore the role of the stimulus and the
meaning of mutual information. We show here that, as the number of trials
increases indefinitely, the direct (or ``plug-in'') estimate of marginal
entropy converges (with probability 1) to the entropy of the time-averaged
conditional distribution of the response, and the direct estimate of the
conditional entropy converges to the time-averaged entropy of the conditional
distribution of the response. Under joint stationarity and ergodicity of the
response and stimulus, the difference of these quantities converges to the
mutual information. When the stimulus is deterministic or non-stationary the
direct estimate of information no longer estimates mutual information, which is
no longer meaningful, but it remains a measure of variability of the response
distribution across time
Cooperation and Storage Tradeoffs in Power-Grids with Renewable Energy Resources
One of the most important challenges in smart grid systems is the integration
of renewable energy resources into its design. In this work, two different
techniques to mitigate the time varying and intermittent nature of renewable
energy generation are considered. The first one is the use of storage, which
smooths out the fluctuations in the renewable energy generation across time.
The second technique is the concept of distributed generation combined with
cooperation by exchanging energy among the distributed sources. This technique
averages out the variation in energy production across space. This paper
analyzes the trade-off between these two techniques. The problem is formulated
as a stochastic optimization problem with the objective of minimizing the time
average cost of energy exchange within the grid. First, an analytical model of
the optimal cost is provided by investigating the steady state of the system
for some specific scenarios. Then, an algorithm to solve the cost minimization
problem using the technique of Lyapunov optimization is developed and results
for the performance of the algorithm are provided. These results show that in
the presence of limited storage devices, the grid can benefit greatly from
cooperation, whereas in the presence of large storage capacity, cooperation
does not yield much benefit. Further, it is observed that most of the gains
from cooperation can be obtained by exchanging energy only among a few energy
harvesting sources
Optimal Beamforming for Physical Layer Security in MISO Wireless Networks
A wireless network of multiple transmitter-user pairs overheard by an
eavesdropper, where the transmitters are equipped with multiple antennas while
the users and eavesdropper are equipped with a single antenna, is considered.
At different levels of wireless channel knowledge, the problem of interest is
beamforming to optimize the users' quality-of-service (QoS) in terms of their
secrecy throughputs or maximize the network's energy efficiency under users'
QoS. All these problems are seen as very difficult optimization problems with
many nonconvex constraints and nonlinear equality constraints in beamforming
vectors. The paper develops path-following computational procedures of
low-complexity and rapid convergence for the optimal beamforming solution.
Their practicability is demonstrated through numerical examples
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