Parametric Models Analysed with Linear Maps

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational burden. Assuming that the parametric entity takes values in a linear space, we show how is is associated to a linear map or operator. This provides a general point of view on how to consider and analyse different representations of such entities. Analysis of the associated linear map in turn connects such representations with reproducing kernel Hilbert spaces and affine- / linear-representations in terms of tensor products. A generalised correlation operator is defined through the associated linear map, and its spectral analysis helps to shed light on the approximation properties of ROMs. This point of view thus unifies many such representations under a functional analytic roof, leading to a deeper understanding and making them available for appropriate analysis.Comment: 22 pages, no figure

Synchronisation schemes for two dimensional discrete systems

In this work we consider two models of two dimensional discrete systems subjected to three different types of coupling and analyse systematically the performance of each in realising synchronised states.We find that linear coupling effectively introduce control of chaos along with synchronisation,while synchronised chaotic states are possible with an additive parametric coupling scheme both being equally relevant for specific applications.The basin leading to synchronisationin the initial value plane and the choice of parameter values for synchronisation in the parameter plane are isolatedin each case.Comment: 17 pages 8 figures. submitted to physica script

Low-frequency oscillatory correlates of auditory predictive processing in cortical-subcortical networks: a MEG-study

Emerging evidence supports the role of neural oscillations as a mechanism for predictive information processing across large-scale networks. However, the oscillatory signatures underlying auditory mismatch detection and information flow between brain regions remain unclear. To address this issue, we examined the contribution of oscillatory activity at theta/alpha-bands (4–8/8–13 Hz) and assessed directed connectivity in magnetoencephalographic data while 17 human participants were presented with sound sequences containing predictable repetitions and order manipulations that elicited prediction-error responses. We characterized the spectro-temporal properties of neural generators using a minimum-norm approach and assessed directed connectivity using Granger Causality analysis. Mismatching sequences elicited increased theta power and phase-locking in auditory, hippocampal and prefrontal cortices, suggesting that theta-band oscillations underlie prediction-error generation in cortical-subcortical networks. Furthermore, enhanced feedforward theta/alpha-band connectivity was observed in auditory-prefrontal networks during mismatching sequences, while increased feedback connectivity in the alpha-band was observed between hippocampus and auditory regions during predictable sounds. Our findings highlight the involvement of hippocampal theta/alpha-band oscillations towards auditory prediction-error generation and suggest a spectral dissociation between inter-areal feedforward vs. feedback signalling, thus providing novel insights into the oscillatory mechanisms underlying auditory predictive processing

Semiparametric Bayesian models for human brain mapping

Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility

Implementation and evaluation of simultaneous video-electroencephalography and functional magnetic resonance imaging

The objective of this study was to demonstrate that the addition of simultaneous and synchronised video to electroencephalography (EEG)-correlated functional magnetic resonance imaging (fMRI) could increase recorded information without data quality reduction. We investigated the effect of placing EEG, video equipment and their required power supplies inside the scanner room, on EEG, video and MRI data quality, and evaluated video-EEG-fMRI by modelling a hand motor task. Gradient-echo, echo-planner images (EPI) were acquired on a 3-T MRI scanner at variable camera positions in a test object [with and without radiofrequency (RF) excitation], and human subjects. EEG was recorded using a commercial MR-compatible 64-channel cap and amplifiers. Video recording was performed using a two-camera custom-made system with EEG synchronization. An in-house script was used to calculate signal to fluctuation noise ratio (SFNR) from EPI in test object with variable camera positions and in human subjects with and without concurrent video recording. Five subjects were investigated with video-EEG-fMRI while performing hand motor task. The fMRI time series data was analysed using statistical parametric mapping, by building block design general linear models which were paradigm prescribed and video based. Introduction of the cameras did not alter the SFNR significantly, nor did it show any signs of spike noise during RF off conditions. Video and EEG quality also did not show any significant artefact. The Statistical Parametric Mapping{T} maps from video based design revealed additional blood oxygen level-dependent responses in the expected locations for non-compliant subjects compared to the paradigm prescribed design. We conclude that video-EEG-fMRI set up can be implemented without affecting the data quality significantly and may provide valuable information on behaviour to enhance the analysis of fMRI data

Ten simple rules for reporting voxel-based morphometry studies

Voxel-based morphometry [Ashburner, J. and Friston, K.J., 2000. Voxel-based morphometry—the methods. NeuroImage 11(6 Pt 1), 805–821] is a commonly used tool for studying patterns of brain change in development or disease and neuroanatomical correlates of subject characteristics. In performing a VBM study, many methodological options are available; if the study is to be easily interpretable and repeatable, the processing steps and decisions must be clearly described. Similarly, unusual methods and parameter choices should be justified in order to aid readers in judging the importance of such options or in comparing the work with other studies. This editorial suggests core principles that should be followed and information that should be included when reporting a VBM study in order to make it transparent, replicable and useful

Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map

We analyse the chaotic motion and its shape dependence in a piecewise linear map using Fujisaka's characteristic function method. The map is a generalization of the one introduced by R. Artuso. Exact expressions for diffusion coefficient are obtained giving previously obtained results as special cases. Fluctuation spectrum relating to probability density function is obtained in a parametric form. We also give limiting forms of the above quantities. Dependence of diffusion coefficient and probability density function on the shape of the map is examined.Comment: 4 pages,4 figure