arXiv subjects

Paolo Victor Redondo

Publications and source records attributed to Paolo Victor Redondo.

3 recordsLinked to original sources

arXiv2025

Nonlinear Coherence for Vector Time Series: Defining Region-to-Region Functional Brain Connectivity

Alterations in functional brain connectivity characterize neurodegenerative disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD). As a non-invasive and cost-effective technique, electroencephalography (EEG) is gaining increasing attention for its potential to identify reliable biomarkers for early detection and differential diagnosis of AD and FTD. Considering the behavioral similarities of signals from adjacent EEG channels, we propose a new spectral dependence measure, the nonlinear vector coherence (NVC), to capture beyond-linear interactions between oscillations of two multivariate time series observed from distinct brain regions. This addresses the limitations of conventional channel-to-channel approaches and defines a more natural region-to-region connectivity framework in the frequency domain. As a result, the NVC measure offers a new approach to investigate dependence between brain regions, which then enables to identify altered functional connectivity dynamics associated with AD and FTD. We further introduce a rank-based inference procedure that enables fast and distribution-free estimation of the proposed measure, as well as a fully nonparametric test for spectral independence. The empirical performance of our proposed inference methodology is demonstrated through extensive numerical experiments. An application to resting-state EEG data reveals that our novel NVC measure uncovers distinct and diagnostically meaningful connectivity patterns which effectively discriminate healthy individuals from those with AD and FTD.

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arXiv2025

Functional-Coefficient Models for Multivariate Time Series in Designed Experiments: with Applications to Brain Signals

To study the neurophysiological basis of attention deficit hyperactivity disorder (ADHD), clinicians use electroencephalography (EEG) which record neuronal electrical activity on the cortex. Instead of focusing on single-channel spectral power, a novel framework for investigating interactions (dependence) between channels in the entire network is proposed. Although dependence measures such as coherence and partial directed coherence (PDC) are well explored in studying brain connectivity, these measures only capture linear dependence. Moreover, in designed clinical experiments, these dependence measures are observed to vary across subjects even within a homogeneous group. To address these limitations, we propose the mixed-effects functional-coefficient autoregressive (MXFAR) model which captures between-subject variation by incorporating subject-specific random effects. The advantages of the MXFAR model are the following: (i) it captures potential non-linear dependence between channels; (ii) it is nonparametric and hence flexible and robust to model mis-specification; (iii) it can capture differences between groups when they exist; (iv) it accounts for variation across subjects; (v) the framework easily incorporates well-known inference methods from mixed-effects models; (vi) it can be generalized to accommodate various covariates and factors. Then, we formulate a novel non-linear spectral measure, the functional partial directed coherence (fPDC), to extract dynamic cross-dependence patterns at different frequency oscillations. Finally, we apply the proposed MXFAR-fPDC framework to analyze multichannel EEG signals and report novel findings on altered brain functional networks in ADHD patients.

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arXiv2024

Measuring Information Transfer Between Nodes in a Brain Network through Spectral Transfer Entropy

Brain connectivity characterizes interactions between different regions of a brain network during resting-state or performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), one formal approach to investigating connectivity is through an information-theoretic causal measure called transfer entropy (TE). To enhance the functionality of TE in brain signal analysis, we propose a novel methodology that captures cross-channel information transfer in the frequency domain. Specifically, we introduce a new measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a band-specific oscillation of one channel to another band-specific oscillation of another channel. The main advantage of our proposed approach is that it formulates TE in a novel way to perform inference on band-specific oscillations while maintaining robustness to the inherent problems associated with filtering. In addition, an advantage of STE is that it allows adjustments for multiple comparisons to control false positive rates. Another novel contribution is a simple yet efficient method for estimating STE using vine copula theory. This method can produce an exact zero estimate of STE (which is the boundary point of the parameter space) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, thus enabling straightforward significance testing through standard resampling. Lastly, we demonstrate the advantage of the proposed STE measure through numerical experiments and provide interesting and novel findings on the analysis of EEG data in a visual-memory experiment.

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