Conversations with Kenelm

In a celebratory moment of the Paradiso, Dante has Thomas go round the circle of sage spirits identifying each in turn in point of proper calling and confirming how it is that self is everywhere present to the other-than-self as a co-efficient of being in the endless and endlessly varied instantiation of that being. The image, at once perfectly Dantean and perfectly resplendent, underlies and informs these conversations of mine with Kenelm; for if in reading and rereading the cherished text, I have from time to time felt the need to enter a qualification, it is a matter here, as in the high consistory of paradise, of otherness as both contained and as authorized by sameness, as conditioned and set free by it for a life of its own. Never, in other words, is it a question in what follows of the stark alternativism of the sed contra, but instead a matter of formed friendship, of the kind of friendship which, conceived in love, makes for a sweet choreography of the spirit. (DOI: 10.5334/baa

Segment Parameter Labelling in MCMC Mean-Shift Change Detection

This work addresses the problem of segmentation in time series data with respect to a statistical parameter of interest in Bayesian models. It is common to assume that the parameters are distinct within each segment. As such, many Bayesian change point detection models do not exploit the segment parameter patterns, which can improve performance. This work proposes a Bayesian mean-shift change point detection algorithm that makes use of repetition in segment parameters, by introducing segment class labels that utilise a Dirichlet process prior. The performance of the proposed approach was assessed on both synthetic and real world data, highlighting the enhanced performance when using parameter labelling

Dante and Aquinas

Christopher Ryan’s study of Dante and Aquinas, touching on issues of nature and grace, of explicit and implicit faith, and of desire and destiny, is intended to mark the difference between them in key areas of theological sensibility. Re-shaped and revised by John Took on the basis of papers made available to him from Christopher Ryan’s estate, it seeks to deepen our understanding of one of the great cultural encounters in European letters. (DOI: 10.5334/bad

Quaternion singular spectrum analysis of electroencephalogram With application in sleep analysis

A novel quaternion-valued singular spectrum analysis (SSA) is introduced for multichannel analysis of electroencephalogram (EEG). The analysis of EEG typically requires the decomposition of data channels into meaningful components despite the notoriously noisy nature of EEG - which is the aim of SSA. However, the singular value decomposition involved in SSA implies the strict orthogonality of the decomposed components, which may not reflect accurately the sources which exhibit similar neural activities. To allow for the modelling of such co-channel coupling, the quaternion domain is considered for the first time to formulate the SSA using the augmented statistics. As an application, we demonstrate how the augmented quaternion-valued SSA (AQSSA) can be used to extract the sources, even at a signal-to-noise ratio as low as -10 dB. To illustrate the usefulness of our quaternion-valued SSA in a rehabilitation setting, we employ the proposed SSA for sleep analysis to extract statistical descriptors for five-stage classification (Awake, N1, N2, N3 and REM). The level of agreement using these descriptors was 74% as quantified by the Cohen's kappa

Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure