Spectral and coherence methodologies are ubiquitous for the analysis of multiple time series. Partial coherence analysis may be used to try to determine graphical models for brain functional connectivity. The outcome of such an analysis may be considerably influenced by factors such as the degree of spectral smoothing, line and interference removal, matrix inversion stabilization and the suppression of effects caused by side-lobe leakage , the combination of results from different epochs and people, and multiple hypothesis testing. This paper examines each of these steps in turn and provides a possible path which produces relatively 'clean' connectivity plots. In particular we show how spectral matrix diagonal upweighting can simultaneously stabilize spectral matrix inversion and reduce effects caused by side-lobe leakage, and use the stepdown multiple hypothesis test procedure to help formulate an interaction strength.
If, as is widely believed, schizophrenia is characterised by abnormalities of brain functional connectivity, then it seems reasonable to expect that different subtypes of schizophrenia could be discriminated in the same way. However, evidence for differences in functional connectivity between the subtypes of schizophrenia is largely lacking and, where it exists, it could be accounted for by clinical differences between the patients (e.g. medication) or by the limitations of the measures used. In this study, we measured EEG functional connectivity in unmedicated male patients diagnosed with either positive or negative syndrome schizophrenia and compared them with age and sex matched healthy controls.Using new methodology (Medkour et al., 2009) based on partial coherence, brain connectivity plots were constructed for positive and negative syndrome patients and controls. Reliable differences in the pattern of functional connectivity were found with both syndromes showing not only an absence of some of the connections that were seen in controls but also the presence of connections that the controls did not show. Comparing connectivity graphs using the Hamming distance, the negative-syndrome patients were found to be more distant from the controls than were the positive syndrome patients. Bootstrap distributions * Corresponding author.Tel: (0)20 7594 8524; Fax: (0)20 7594 8517; e-mail: a.walden@imperial.ac.uk Preprint submitted to NeuroscienceJune 8, 2010 of these distances were created which showed a significant difference in the mean distances that was consistent with the observation that negative-syndrome diagnosis is associated with a more severe form of schizophrenia. We conclude that schizophrenia is characterised by widespread changes in functional connectivity with negative syndrome patients showing a more extreme pattern of abnormality than positive syndrome patients.
a singular distribution. In particular, if the input signal is predictable, it was shown that the output of the filter is simply a discrete random variable. Computer experiments in order to verify the theoretical results have been realized and discussed. For this purpose, a specific model of linear Markovian signal of order one was introduced, and the experimental results are in complete agreement with the theory. Finally, a model of Bernoulli input ensuring that the output contains a discrete and a singular part was introduced, and here also the experimental results are in perfect agreement with the theory. REFERENCES Statistical Properties of the Estimated Degree of PolarizationT. Medkour and A. T. Walden, Member, IEEE Abstract-We derive important and useful new statistical properties of the estimated degree of polarization in the two-dimensional case. We find its distribution function and show how it may be used to construct confidence intervals. We also find an expression for any moment of the distribution, and derive an exact unbiasing formula for the estimator of the squared coefficient. Further we discuss a test for partial polarization. Our statistical analyses enable identification of elliptical polarization for an ultra low frequency wave in the solar magnetic field.
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