Cristina Rueda

Electroencephalographic (EEG) recordings often exhibit strong interchannel correlations due to scalp potentials reflecting electric fields generated by localized neural sources commonly modeled as current dipoles. Despite this physiological basis, many widely used approaches (e.g., independent component analysis) are largely data-driven, may require many components, and offer limited interpretability and limited support for assessing physiological assumptions. We propose a physiologically guided multichannel model built on a parametric Frequency-Modulated Möbius (FMM) formulation, where each electrode signal is expressed as a linear combination of a small number of latent dipole-related sources with parametrically described trajectories. The resulting framework captures temporal and spatial structure with high accuracy and enables likelihood-based testing of the fixed dipole-orientation assumption through a reduced-rank formulation. Using publicly available EEG data, we illustrate that the proposed approach explains interchannel dependence with few latent sources and provides statistical evidence regarding the plausibility of fixed orientation.

The Frequency Modulated Möbius (FMM) approach is a contemporary and versatile tool for analyzing oscillatory signals. Within the functional data analysis framework, the FMM model offers an accurate alternative for comprehending multidimensional synchronized oscillatory signals, which are common in various fields including biology and medicine. This approach decomposes the signals into scaled Möbius waves formulated in terms of four parameters, interpreted as measures of location and shape variation. Among these parameters, two are specific to individual signals, while the remaining two are global and describe the interconnections between signals. In this paper we extend the utility of the FMM by developing inferential procedures based on likelihood estimations for nonlinear models. These procedures cover the core parameters, the signals themselves, and their derivatives. We explore various techniques, including the Gauss–Seidel approach and profile likelihood, for obtaining estimators and their asymptotic properties. Our methodology undergoes rigorous validation, drawing on a combination of theoretical insights and numerical experiments. Furthermore, as our research is primarily motivated by the analysis of biomedical oscillatory signals, we apply this methodology to address two pertinent real-world problems involving electrocardiogram and pattern-reversal visual evoked potential data. These applications illustrate the practical efficacy of the new paradigm.

The circadian system drives near-24-h oscillations in behaviors and biological processes. The underlying core molecular clock regulates the expression of other genes, and it has been shown that the expression of more than 50 percent of genes in mammals displays 24-h rhythmic patterns, with the specific genes that cycle varying from one tissue to another. Determining rhythmic gene expression patterns in human tissues sampled as single timepoints has several challenges, including the reconstruction of temporal order of highly noisy data. Previous methodologies have attempted to address these challenges in one or a small number of tissues for which rhythmic gene evolutionary conservation is assumed to be preserved. Here we introduce CIRCUST, a novel CIRCular-robUST methodology for analyzing molecular rhythms, that relies on circular statistics, is robust against noise, and requires fewer assumptions than existing methodologies. Next, we validated the method against four controlled experiments in which sampling times were known, and finally, CIRCUST was applied to 34 tissues from the Genotype-Tissue Expression (GTEx) dataset with the aim towards building a comprehensive daily rhythm gene expression atlas in humans. The validation and application shown here indicate that CIRCUST provides a flexible framework to formulate and solve the issues related to the analysis of molecular rhythms in human tissues. CIRCUST methodology is publicly available at https://github.com/yolandalago/CIRCUST/.