328,123 research outputs found
Data-driven multivariate and multiscale methods for brain computer interface
This thesis focuses on the development of data-driven multivariate and multiscale methods
for brain computer interface (BCI) systems. The electroencephalogram (EEG), the
most convenient means to measure neurophysiological activity due to its noninvasive nature,
is mainly considered. The nonlinearity and nonstationarity inherent in EEG and its
multichannel recording nature require a new set of data-driven multivariate techniques to
estimate more accurately features for enhanced BCI operation. Also, a long term goal
is to enable an alternative EEG recording strategy for achieving long-term and portable
monitoring.
Empirical mode decomposition (EMD) and local mean decomposition (LMD), fully
data-driven adaptive tools, are considered to decompose the nonlinear and nonstationary
EEG signal into a set of components which are highly localised in time and frequency. It
is shown that the complex and multivariate extensions of EMD, which can exploit common
oscillatory modes within multivariate (multichannel) data, can be used to accurately
estimate and compare the amplitude and phase information among multiple sources, a
key for the feature extraction of BCI system. A complex extension of local mean decomposition
is also introduced and its operation is illustrated on two channel neuronal
spike streams. Common spatial pattern (CSP), a standard feature extraction technique
for BCI application, is also extended to complex domain using the augmented complex
statistics. Depending on the circularity/noncircularity of a complex signal, one of the
complex CSP algorithms can be chosen to produce the best classification performance
between two different EEG classes.
Using these complex and multivariate algorithms, two cognitive brain studies are
investigated for more natural and intuitive design of advanced BCI systems. Firstly, a Yarbus-style auditory selective attention experiment is introduced to measure the user
attention to a sound source among a mixture of sound stimuli, which is aimed at improving
the usefulness of hearing instruments such as hearing aid. Secondly, emotion experiments
elicited by taste and taste recall are examined to determine the pleasure and displeasure
of a food for the implementation of affective computing. The separation between two
emotional responses is examined using real and complex-valued common spatial pattern
methods.
Finally, we introduce a novel approach to brain monitoring based on EEG recordings
from within the ear canal, embedded on a custom made hearing aid earplug. The new
platform promises the possibility of both short- and long-term continuous use for standard
brain monitoring and interfacing applications
Autonomous Navigation for an Unmanned Aerial Vehicle by the Decomposition Coordination Method
This paper introduces a new approach for solving the navigation problem of Unmanned Aerial Vehicles (UAV) by studying its rotational and translational dynamics and then solving the nonlinear model by the Decomposition Coordination method. The objective is to reach a destination goal by the mean of an autonomous computed  optimal path calculated  through optimal control sequence. Solving such complex systems often requires a great amount of computation. However, the approach considered herein is based on the Decomposition Coordination principle, which allows the nonlinearity to be treated at a local level, thus offering a low computing time. The stability of the method is discussed with sufficient conditions for convergence. A numerical application is given in consolidation the theoretical results
Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications
The quantitative characterization of the microstructure of random
heterogeneous media in -dimensional Euclidean space via a
variety of -point correlation functions is of great importance, since the
respective infinite set determines the effective physical properties of the
media. In particular, surface-surface and surface-void
correlation functions (obtainable from radiation scattering experiments)
contain crucial interfacial information that enables one to estimate transport
properties of the media (e.g., the mean survival time and fluid permeability)
and complements the information content of the conventional two-point
correlation function. However, the current technical difficulty involved in
sampling surface correlation functions has been a stumbling block in their
widespread use. We first present a concise derivation of the small-
behaviors of these functions, which are linked to the \textit{mean curvature}
of the system. Then we demonstrate that one can reduce the computational
complexity of the problem by extracting the necessary interfacial information
from a cut of the system with an infinitely long line. Accordingly, we devise
algorithms based on this idea and test them for two-phase media in continuous
and discrete spaces. Specifically for the exact benchmark model of overlapping
spheres, we find excellent agreement between numerical and exact results. We
compute surface correlation functions and corresponding local surface-area
variances for a variety of other model microstructures, including hard spheres
in equilibrium, decorated "stealthy" patterns, as well as snapshots of evolving
pattern formation processes (e.g., spinodal decomposition). It is demonstrated
that the precise determination of surface correlation functions provides a
powerful means to characterize a wide class of complex multiphase
microstructures
Engineering analysis of biological variables: An example of blood pressure over 1 day
Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the handling of the local mean is of predominant importance. It is shown that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times. The process of deriving this series is called the “empirical mode decomposition method.” Conventionally, Fourier analysis represents the data by sine and cosine functions, but no instantaneous frequency can be defined. In the new way, the data are represented by intrinsic mode functions, to which Hilbert transform can be used. Titchmarsh [Titchmarsh, E. C. (1948) Introduction to the Theory of Fourier Integrals (Oxford Univ. Press, Oxford)] has shown that a signal and i times its Hilbert transform together define a complex variable. From that complex variable, the instantaneous frequency, instantaneous amplitude, Hilbert spectrum, and marginal Hilbert spectrum have been defined. In addition, the Gumbel extreme-value statistics are applied. We present all of these features of the blood pressure records here for the reader to see how they look. In the future, we have to learn how these features change with disease or interventions
Kaehler submanifolds with parallel pluri-mean curvature
We investigate the local geometry of a class of K\"ahler submanifolds which generalize surfaces of constant mean curvature. The role of
the mean curvature vector is played by the -part (i.e. the -components) of the second fundamental form , which we call the
pluri-mean curvature. We show that these K\"ahler submanifolds are
characterized by the existence of an associated family of isometric
submanifolds with rotated second fundamental form. Of particular interest is
the isotropic case where this associated family is trivial. We also investigate
the properties of the corresponding Gauss map which is pluriharmonic.Comment: Plain TeX, 21 page
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