10,849 research outputs found
On the Coherence Properties of Random Euclidean Distance Matrices
In the present paper we focus on the coherence properties of general random
Euclidean distance matrices, which are very closely related to the respective
matrix completion problem. This problem is of great interest in several
applications such as node localization in sensor networks with limited
connectivity. Our results can directly provide the sufficient conditions under
which an EDM can be successfully recovered with high probability from a limited
number of measurements.Comment: 5 pages, SPAWC 201
Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees
This paper addresses the problem of ad hoc microphone array calibration where
only partial information about the distances between microphones is available.
We construct a matrix consisting of the pairwise distances and propose to
estimate the missing entries based on a novel Euclidean distance matrix
completion algorithm by alternative low-rank matrix completion and projection
onto the Euclidean distance space. This approach confines the recovered matrix
to the EDM cone at each iteration of the matrix completion algorithm. The
theoretical guarantees of the calibration performance are obtained considering
the random and locally structured missing entries as well as the measurement
noise on the known distances. This study elucidates the links between the
calibration error and the number of microphones along with the noise level and
the ratio of missing distances. Thorough experiments on real data recordings
and simulated setups are conducted to demonstrate these theoretical insights. A
significant improvement is achieved by the proposed Euclidean distance matrix
completion algorithm over the state-of-the-art techniques for ad hoc microphone
array calibration.Comment: In Press, available online, August 1, 2014.
http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal
Processing, 201
Adaptive Mantel Test for AssociationTesting in Imaging Genetics Data
Mantel's test (MT) for association is conducted by testing the linear
relationship of similarity of all pairs of subjects between two observational
domains. Motivated by applications to neuroimaging and genetics data, and
following the succes of shrinkage and kernel methods for prediction with
high-dimensional data, we here introduce the adaptive Mantel test as an
extension of the MT. By utilizing kernels and penalized similarity measures,
the adaptive Mantel test is able to achieve higher statistical power relative
to the classical MT in many settings. Furthermore, the adaptive Mantel test is
designed to simultaneously test over multiple similarity measures such that the
correct type I error rate under the null hypothesis is maintained without the
need to directly adjust the significance threshold for multiple testing. The
performance of the adaptive Mantel test is evaluated on simulated data, and is
used to investigate associations between genetics markers related to
Alzheimer's Disease and heatlhy brain physiology with data from a working
memory study of 350 college students from Beijing Normal University
Distinguishability of generic quantum states
Properties of random mixed states of order distributed uniformly with
respect to the Hilbert-Schmidt measure are investigated. We show that for large
, due to the concentration of measure, the trace distance between two random
states tends to a fixed number , which yields the
Helstrom bound on their distinguishability. To arrive at this result we apply
free random calculus and derive the symmetrized Marchenko--Pastur distribution,
which is shown to describe numerical data for the model of two coupled quantum
kicked tops. Asymptotic values for the fidelity, Bures and transmission
distances between two random states are obtained. Analogous results for quantum
relative entropy and Chernoff quantity provide other bounds on the
distinguishablity of both states in a multiple measurement setup due to the
quantum Sanov theorem.Comment: 13 pages including supplementary information, 6 figure
Subnormalized states and trace-nonincreasing maps
We investigate the set of completely positive, trace-nonincreasing linear
maps acting on the set M_N of mixed quantum states of size N. Extremal point of
this set of maps are characterized and its volume with respect to the
Hilbert-Schmidt (Euclidean) measure is computed explicitly for an arbitrary N.
The spectra of partially reduced rescaled dynamical matrices associated with
trace-nonincreasing completely positive maps belong to the N-cube inscribed in
the set of subnormalized states of size N. As a by-product we derive the
measure in M_N induced by partial trace of mixed quantum states distributed
uniformly with respect to HS-measure in .Comment: LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 tabl
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