68,724 research outputs found
Distributed Maximum Likelihood for Simultaneous Self-localization and Tracking in Sensor Networks
We show that the sensor self-localization problem can be cast as a static
parameter estimation problem for Hidden Markov Models and we implement fully
decentralized versions of the Recursive Maximum Likelihood and on-line
Expectation-Maximization algorithms to localize the sensor network
simultaneously with target tracking. For linear Gaussian models, our algorithms
can be implemented exactly using a distributed version of the Kalman filter and
a novel message passing algorithm. The latter allows each node to compute the
local derivatives of the likelihood or the sufficient statistics needed for
Expectation-Maximization. In the non-linear case, a solution based on local
linearization in the spirit of the Extended Kalman Filter is proposed. In
numerical examples we demonstrate that the developed algorithms are able to
learn the localization parameters.Comment: shorter version is about to appear in IEEE Transactions of Signal
Processing; 22 pages, 15 figure
Data Imputation through the Identification of Local Anomalies
We introduce a comprehensive and statistical framework in a model free
setting for a complete treatment of localized data corruptions due to severe
noise sources, e.g., an occluder in the case of a visual recording. Within this
framework, we propose i) a novel algorithm to efficiently separate, i.e.,
detect and localize, possible corruptions from a given suspicious data instance
and ii) a Maximum A Posteriori (MAP) estimator to impute the corrupted data. As
a generalization to Euclidean distance, we also propose a novel distance
measure, which is based on the ranked deviations among the data attributes and
empirically shown to be superior in separating the corruptions. Our algorithm
first splits the suspicious instance into parts through a binary partitioning
tree in the space of data attributes and iteratively tests those parts to
detect local anomalies using the nominal statistics extracted from an
uncorrupted (clean) reference data set. Once each part is labeled as anomalous
vs normal, the corresponding binary patterns over this tree that characterize
corruptions are identified and the affected attributes are imputed. Under a
certain conditional independency structure assumed for the binary patterns, we
analytically show that the false alarm rate of the introduced algorithm in
detecting the corruptions is independent of the data and can be directly set
without any parameter tuning. The proposed framework is tested over several
well-known machine learning data sets with synthetically generated corruptions;
and experimentally shown to produce remarkable improvements in terms of
classification purposes with strong corruption separation capabilities. Our
experiments also indicate that the proposed algorithms outperform the typical
approaches and are robust to varying training phase conditions
Quantum Network Models and Classical Localization Problems
A review is given of quantum network models in class C which, on a suitable
2d lattice, describe the spin quantum Hall plateau transition. On a general
class of graphs, however, many observables of such models can be mapped to
those of a classical walk in a random environment, thus relating questions of
quantum and classical localization. In many cases it is possible to make
rigorous statements about the latter through the relation to associated
percolation problems, in both two and three dimensions.Comment: 23 pages. To appear in '50 years of Anderson Localization', E
Abrahams, ed. (World Scientific)
Role of the impurity-potential range in disordered d-wave superconductors
We analyze how the range of disorder affects the localization properties of
quasiparticles in a two-dimensional d-wave superconductor within the standard
non-linear sigma-model approach to disordered systems. We show that for purely
long-range disorder, which only induces intra-node scattering processes, the
approach is free from the ambiguities which often beset the disordered
Dirac-fermion theories, and gives rise to a Wess-Zumino-Novikov-Witten action
leading to vanishing density of states and finite conductivities. We also study
the crossover induced by internode scattering due to a short range component of
the disorder, thus providing a coherent non-linear sigma-model description in
agreement with all the various findings of different approaches.Comment: 38 pages, 1 figur
Connection Between System Parameters and Localization Probability in Network of Randomly Distributed Nodes
This article deals with localization probability in a network of randomly
distributed communication nodes contained in a bounded domain. A fraction of
the nodes denoted as L-nodes are assumed to have localization information while
the rest of the nodes denoted as NL nodes do not. The basic model assumes each
node has a certain radio coverage within which it can make relative distance
measurements. We model both the case radio coverage is fixed and the case radio
coverage is determined by signal strength measurements in a Log-Normal
Shadowing environment. We apply the probabilistic method to determine the
probability of NL-node localization as a function of the coverage area to
domain area ratio and the density of L-nodes. We establish analytical
expressions for this probability and the transition thresholds with respect to
key parameters whereby marked change in the probability behavior is observed.
The theoretical results presented in the article are supported by simulations.Comment: To appear on IEEE Transactions on Wireless Communications, November
200
Griffiths phases and localization in hierarchical modular networks
We study variants of hierarchical modular network models suggested by Kaiser
and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional
brain connectivity, using extensive simulations and quenched mean-field theory
(QMF), focusing on structures with a connection probability that decays
exponentially with the level index. Such networks can be embedded in
two-dimensional Euclidean space. We explore the dynamic behavior of the contact
process (CP) and threshold models on networks of this kind, including
hierarchical trees. While in the small-world networks originally proposed to
model brain connectivity, the topological heterogeneities are not strong enough
to induce deviations from mean-field behavior, we show that a Griffiths phase
can emerge under reduced connection probabilities, approaching the percolation
threshold. In this case the topological dimension of the networks is finite,
and extended regions of bursty, power-law dynamics are observed. Localization
in the steady state is also shown via QMF. We investigate the effects of link
asymmetry and coupling disorder, and show that localization can occur even in
small-world networks with high connectivity in case of link disorder.Comment: 18 pages, 20 figures, accepted version in Scientific Report
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
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