3,825 research outputs found
A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence
A novel framework for a unifying treatment of quaternion valued adaptive
filtering algorithms is introduced. This is achieved based on a rigorous
account of quaternion differentiability, the proposed I-gradient, and the use
of augmented quaternion statistics to account for real world data with
noncircular probability distributions. We first provide an elegant solution for
the calculation of the gradient of real functions of quaternion variables
(typical cost function), an issue that has so far prevented systematic
development of quaternion adaptive filters. This makes it possible to unify the
class of existing and proposed quaternion least mean square (QLMS) algorithms,
and to illuminate their structural similarity. Next, in order to cater for both
circular and noncircular data, the class of widely linear QLMS (WL-QLMS)
algorithms is introduced and the subsequent convergence analysis unifies the
treatment of strictly linear and widely linear filters, for both proper and
improper sources. It is also shown that the proposed class of HR gradients
allows us to resolve the uncertainty owing to the noncommutativity of
quaternion products, while the involution gradient (I-gradient) provides
generic extensions of the corresponding real- and complex-valued adaptive
algorithms, at a reduced computational cost. Simulations in both the strictly
linear and widely linear setting support the approach
In-ear EEG biometrics for feasible and readily collectable real-world person authentication
The use of EEG as a biometrics modality has been investigated for about a
decade, however its feasibility in real-world applications is not yet
conclusively established, mainly due to the issues with collectability and
reproducibility. To this end, we propose a readily deployable EEG biometrics
system based on a `one-fits-all' viscoelastic generic in-ear EEG sensor
(collectability), which does not require skilled assistance or cumbersome
preparation. Unlike most existing studies, we consider data recorded over
multiple recording days and for multiple subjects (reproducibility) while, for
rigour, the training and test segments are not taken from the same recording
days. A robust approach is considered based on the resting state with eyes
closed paradigm, the use of both parametric (autoregressive model) and
non-parametric (spectral) features, and supported by simple and fast cosine
distance, linear discriminant analysis and support vector machine classifiers.
Both the verification and identification forensics scenarios are considered and
the achieved results are on par with the studies based on impractical on-scalp
recordings. Comprehensive analysis over a number of subjects, setups, and
analysis features demonstrates the feasibility of the proposed ear-EEG
biometrics, and its potential in resolving the critical collectability,
robustness, and reproducibility issues associated with current EEG biometrics
Thermodynamics of small superconductors with fixed particle number
The Variation After Projection approach is applied for the first time to the
pairing hamiltonian to describe the thermodynamics of small systems with fixed
particle number. The minimization of the free energy is made by a direct
diagonalization of the entropy. The Variation After Projection applied at
finite temperature provides a perfect reproduction of the exact canonical
properties of odd or even systems from very low to high temperature.Comment: 4 pages, 3 figure
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