Kyle Hasenstab, Aaron Scheffler, Donatello Telesca
et al.
Summary The electroencephalography (EEG) data created in event-related potential (ERP) experiments have a complex high-dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functional data. The experiments are made up of sequences of multiple trials, resulting in longitudinal functional data and moreover, responses are recorded at multiple electrodes on the scalp, adding an electrode dimension. Traditional EEG analyses involve multiple simplifications of this structure to increase the signal-to-noise ratio, effectively collapsing the functional and longitudinal components by identifying key features of the ERPs and averaging them across trials. Motivated by an implicit learning paradigm used in autism research in which the functional, longitudinal, and electrode components all have critical interpretations, we propose a multidimensional functional principal components analysis (MD-FPCA) technique which does not collapse any of the dimensions of the ERP data. The proposed decomposition is based on separation of the total variation into subject and subunit level variation which are further decomposed in a two-stage functional principal components analysis. The proposed methodology is shown to be useful for modeling longitudinal trends in the ERP functions, leading to novel insights into the learning patterns of children with Autism Spectrum Disorder (ASD) and their typically developing peers as well as comparisons between the two groups. Finite sample properties of MD-FPCA are further studied via extensive simulations.
Abstract A mosaic of siliciclastic and mixed carbonate‐siliciclastic sediments and authigenic minerals occurs at shelf and slope depths (30–1015 m water depth) on the open, wave‐dominated north Kaipara continental margin (NKCM) off northern New Zealand. Texture and composition define five surficial sediment facies. Facies 1 (siliciclastic sand) comprises generally well‐sorted fine sands that extend to outer shelf depths. Facies 2 (glauconitic sand) is composed of 30–95% authigenic glauconite grains at 150–400 m water depth in central to northern portions of NKCM. Facies 3 (mixed bryozoan‐siliciclastic sand) occurs only in northernmost NKCM and involves a conspicuous (>40%) bryozoan carbonate content. Facies 4 (pelletal mud) occupies the mid shelf (100–150 m water depth) in northern NKCM and consists of muddy sediment with >30% mixed carbonate‐siliciclastic pellets of probable fecal origin. Facies 5 (foraminiferal mud and sand) contains >30% foraminiferal tests at slope depths in southern NKCM and at both slope and mid‐outer shelf depths towards the north. The siliciclastic mineralogy is consistent with mainly distant provenances to the south of the NKCM in central North Island and northern South Island, while much of the bryozoan material is likely reworked from the Three Kings carbonate platform to the north. No single shelf sedimentation model explains the complex facies distributions on the NKCM because the deposits record the interplay of several present and past hydrodynamic and sediment supply controls. While truly modern deposits may occur inshore, the bulk of NKCM surficial sediments are mainly palimpsest and/or relict deposits.