2,741 research outputs found
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Graded quantization for multiple description coding of compressive measurements
Compressed sensing (CS) is an emerging paradigm for acquisition of compressed
representations of a sparse signal. Its low complexity is appealing for
resource-constrained scenarios like sensor networks. However, such scenarios
are often coupled with unreliable communication channels and providing robust
transmission of the acquired data to a receiver is an issue. Multiple
description coding (MDC) effectively combats channel losses for systems without
feedback, thus raising the interest in developing MDC methods explicitly
designed for the CS framework, and exploiting its properties. We propose a
method called Graded Quantization (CS-GQ) that leverages the democratic
property of compressive measurements to effectively implement MDC, and we
provide methods to optimize its performance. A novel decoding algorithm based
on the alternating directions method of multipliers is derived to reconstruct
signals from a limited number of received descriptions. Simulations are
performed to assess the performance of CS-GQ against other methods in presence
of packet losses. The proposed method is successful at providing robust coding
of CS measurements and outperforms other schemes for the considered test
metrics
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
Trie-Compressed Adaptive Set Intersection
We introduce space- and time-efficient algorithms and data structures for the offline set intersection problem. We show that a sorted integer set S ? [0..u) of n elements can be represented using compressed space while supporting k-way intersections in adaptive O(k?lg(u/?)) time, ? being the alternation measure introduced by Barbay and Kenyon. Our experimental results suggest that our approaches are competitive in practice, outperforming the most efficient alternatives (Partitioned Elias-Fano indexes, Roaring Bitmaps, and Recursive Universe Partitioning (RUP)) in several scenarios, offering in general relevant space-time trade-offs
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