48,244 research outputs found
On Multi-Step Sensor Scheduling via Convex Optimization
Effective sensor scheduling requires the consideration of long-term effects
and thus optimization over long time horizons. Determining the optimal sensor
schedule, however, is equivalent to solving a binary integer program, which is
computationally demanding for long time horizons and many sensors. For linear
Gaussian systems, two efficient multi-step sensor scheduling approaches are
proposed in this paper. The first approach determines approximate but close to
optimal sensor schedules via convex optimization. The second approach combines
convex optimization with a \BB search for efficiently determining the optimal
sensor schedule.Comment: 6 pages, appeared in the proceedings of the 2nd International
Workshop on Cognitive Information Processing (CIP), Elba, Italy, June 201
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
Quantitative Riemann existence theorem over a number field
Given a covering of the projective line with ramifications defined over a
number field, we define a plain model of the algebraic curve realizing the
Riemann existence theorem for this covering, and bound explicitly the defining
equation of this curve and its definition field.Comment: 23 pages, version 4, minor change
Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
We study non-asymptotic fundamental limits for transmitting classical
information over memoryless quantum channels, i.e. we investigate the amount of
classical information that can be transmitted when a quantum channel is used a
finite number of times and a fixed, non-vanishing average error is permissible.
We consider the classical capacity of quantum channels that are image-additive,
including all classical to quantum channels, as well as the product state
capacity of arbitrary quantum channels. In both cases we show that the
non-asymptotic fundamental limit admits a second-order approximation that
illustrates the speed at which the rate of optimal codes converges to the
Holevo capacity as the blocklength tends to infinity. The behavior is governed
by a new channel parameter, called channel dispersion, for which we provide a
geometrical interpretation.Comment: v2: main results significantly generalized and improved; v3: extended
to image-additive channels, change of title, journal versio
A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels
This paper shows that the logarithm of the epsilon-error capacity (average
error probability) for n uses of a discrete memoryless channel is upper bounded
by the normal approximation plus a third-order term that does not exceed 1/2
log n + O(1) if the epsilon-dispersion of the channel is positive. This matches
a lower bound by Y. Polyanskiy (2010) for discrete memoryless channels with
positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm
of the epsilon-error capacity is upper bounded by the n times the capacity plus
a constant term except for a small class of DMCs and epsilon >= 1/2.Comment: published versio
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